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P53 and bladder cancer outcome: A combined analysis from the Keck School of Medicine
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NOTE TO USERS
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P53 AND BLADDER CANCER OUTCOME: A COMBINED ANALYSIS
FROM THE KECK SCHOOL OF MEDICINE
Copyright 2004
by
Gregorio Cua Valin, Jr.
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(APPLIED BIOSTATISTICS/EPIDEMIOLOGY)
August 2004
Gregorio Cua Valin, Jr.
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UMI Number: 1422405
Copyright 2004 by
Valin, Gregorio Cua, Jr.
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Dedication
There were many times that I doubted I would actually make it this far in life
considering all of the stupid choices I’ve made. I truly thank God for his
unconditional love and for staying up with me during those long nights that I worked
on this project. Forever will I be indebted to him for his brilliance and utmost
kindness. He knew well enough to surround a foolish and weak person (namely, me)
with the most amazing people who will ever walk this good earth...
To my wonderful family and friends for all of the love, wisdom, and
encouragement that they have given me over the years. I know that I wouldn’t have
accomplished all of this without everyone’s support. I am truly blessed to have all of
you in my life. Thank you all so very much.
I love all of you.
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Acknowledgements
A very warm thank you to my committee members for their guidance, expert
knowledge, and constructive comments: Susan Groshen, PhD (thanks for the job and
data!), Richard Cote, MD, and W. James Gauderman, PhD. I hope this project was
able to meet your expectations. Thanks for expecting so much out of m e.. .1
wouldn’t have learned so much otherwise.
I also want to express my sincere gratitude to the USC Keck School of
Medicine, Department of Preventive Medicine (especially, the wonderful staff) for
this precious opportunity. I can only hope that I met the standards of a truly
outstanding department. I know the department took a chance when they admitted
me into the program. Thank you for taking that chance!
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iv
Table of Contents
Dedication ii
Acknowledgments iii
List of Tables v
List of Figures vi
Abstract vii
Introduction 1
Bladder Cancer 1
The Importance o f Classification 1
The Usefulness o f a Prognostic Marker 2
P53 as an Important Tumor Suppressor Gene 3
P53 Protein as a Controversial Marker 7
Meta-analysis 9
Defining Study Objectives, Research Outcomes, and Studies to Include 9
The Literature Search 11
Combining the Studies 13
A Combined Analysis o f p53 and Bladder Cancer Outcome 16
Methods 18
Publications, IPD, and Patients 18
Immunohistochemistry/Mutational Analysis 18
Statistical Considerations: Endpoints and the Hazards Ratio 21
Statistical Analysis 23
Results 27
Publication Data 27
Individual Patient Data 33
Comparison o f the Published Data and IPD Results 39
Discussion 44
p53 Findings 44
Combined Analysis 47
Conclusions 50
Bibliography 52
Appendix 1 61
Appendix 2 85
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V
List of Tables
Page
Table 1. Summary of 38 original publications 19
Table 2. Definitions of various study outcomes 21
Table 3. Results of studies examining survival/disease-specific survival 28
Table 4. Results of studies examining time-to-recurrence 30
Table 5. Results of studies examining time-to-progression 30
Table 6. Summary of IPD provided: by histology and p53 status 34
Table 7. Summary of IPD results with time-to-progression as endpoint 35
Table 8. Summary of IPD results with survival as endpoint 38
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vi
List of Figures
Page
Fig. 1 Estimated HR (In scale) plots estimated from publication data
with survival as the endpoint. 29
Fig. 2 Estimated HR (In scale) plots estimated from publication data
with recurrence as the endpoint. 31
Fig. 3 Estimated HR (In scale) plots estimated from publication data
with progression as the endpoint. 32
Fig. 4 Estimated HR (In scale) plot estimated from IPD with progression
as the endpoint. 37
Fig. 5 Estimated HR (In scale) plots estimated from IPD with survival
as the endpoint. 40
Fig. 6 Comparison of Time-to-Progression HR Estimates 41
Fig. 7 Comparison of Survival HR Estimates 42
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vii
Abstract
Despite its importance in cell cycle regulation and apoptosis, the role of p53
as a prognostic marker in bladder cancer patients remains controversial. Studies over
the past several decades examining the potential association between p53 and patient
prognosis have shown inconsistent results. Therefore, combined analyses using
publication data and individual patient data (IPD) were conducted to further
investigate the possible association.
In this analysis, pooled hazards ratio (HR) estimates from publication data
and IPD suggested that p5 3-positive patients experienced greater risk of recurrence,
progression, and death. Stratified log-rank tests showed statistically significant
associations between p53 status and prognosis. HR estimated from publication data
and IPD were compared. Although the Parmar method produced reasonable
estimates, problems with precision as well as discrepancies with IPD estimates
indicate the need to fine-tune the Parmar method. Moreover, differences in study
designs and patient characteristics necessitate further well-designed, prospective
studies with adequate sample size.
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1
Introduction
Bladder Cancer
The American Cancer Society estimated that 53,500 individuals were
diagnosed with bladder cancer and 14,000 patients died of the disease in 2003 (ACS
2002). It is the most frequently occurring malignancy of the urinary system and
appears to occur more often in males than females. Both genders have experienced
increased incidence rates for the past several decades, although mortality rates have
shown a decreasing trend. Much of the reason for the decreasing trend may be
attributed to greater understanding and more effective management of the disease.
The Importance o f Classification
A large part of bladder cancer management and treatment is based on the
physician’s ability to predict how the tumor is going to behave at certain stages of
the illness. Tumors are classified according to the degree of infiltration into the
bladder and any metastases to lymph nodes and/or other organs. Clinical staging is
assessed after endoscopic surgery and documented using the TNM system discussed
in the 2002 American Joint Committee on Cancer (AJCC 2002). Approximately
70% of bladder cancer cases are non-muscle invasive (Ta, Tl), 25% are classified as
muscle-invasive (T2-T4), and the remaining 5% as carcinoma in situ (cis) (Qureshi
et al. 1999). Research has consistently shown tumor stage and grade to be
significantly associated with patient prognosis. (Holmang et al. 1995, Qureshi et al.
1999). Similar to other types of malignancies, bladder cancers with higher stage and
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2
grade corresponded with worse prognosis. Patients with muscle-invasive tumors
accounted for a significant proportion of bladder cancer deaths, whereas the non
muscle invasive patients have shown better prognosis (Qureshi et al. 1999).
Knowing the extent of the disease allows the physician to recommend the
appropriate surgical and/or chemotherapeutic regimens that would improve a
patient’s chance of survival.
The Usefulness o f a Prognostic Marker
The improvements in patient prognosis may be attributed to advances in
surgical procedures and chemotherapeutic regimens. For example, intravesicle
bacillus-Calmette Guerin (BCG) therapy used to treat non-muscle invasive disease
has lowered cumulative disease progression rates to as low as 17% (Herr et al. 1990),
while initial cystectomy has shown a 5-year survival rate of 90% (Stockle et al.
1987).
However, the successes brought about by the use of such aggressive
treatments are not without their drawbacks. Many patients who have undergone
cystectomy experienced decreases in quality of life due to the negative effects on
their sexual functioning and physical perceptions (Cookson et al. 2003). Recent
advances in surgery have brought about sophisticated techniques, such as orthotopic
reconstruction, which have helped to improve quality of life for patients.
Unfortunately, many patients eventually progress or die despite aggressive
treatment—some sooner than others. Identification of higher-risk patients would be
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3
necessary if improvements in bladder cancer management are to be continued. This
has led some investigators to try to identify molecular features of tumors that would
help to predict the behavior of tumors. A feature already implicated with other types
of cancers is the frequent mutation of the tumor suppressor gene, p53 (Nigro et al.
1989, Hollstein et al. 1991). Researchers are looking to establish associations among
p53 gene mutations and nuclear accumulation of its subsequent mutated protein
product with patient prognosis in hopes of further improving bladder cancer
management.
p53 as an Important Tumor Suppressor Gene
In the late 1970s, Linzer and Levine observed a 54K Dalton protein that
specifically immunoprecipitated with both the SV40 (simian virus) large and small T
antigens in SV40-induced tumors from mice and hamster sera (Linzer and Levine
1979). The protein appeared to form a complex with SV40 T antigen allowing for
the possibility of immunogenic properties. They also found that the same 54 K
Dalton protein immunoprecipitated from sera of uninfected murine embryonal
carcinoma cell lines, as well as an Ad2+ ND4-transformed hamster cell line.
However, the protein demonstrated species specificity as the partial peptide maps of
the mouse and hamster proteins differed. Proteins of similar molecular weights,
ranging from 44K to 60K, were found in human and monkey SV40-infected or
SV40-transformed cell lines. Linzer and Levine concluded that the synthesis or
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4
stability of the protein was enhanced by SV40 infection or transformation, although
its role in transformation had yet to be determined.
DeLeo and colleagues also discovered a protein that appeared to be
implicated in the transformation of mouse cells. They detected expression of a 53K
Dalton protein in transformed adult mouse cells, but were unable to do so in normal
mouse cells (DeLeo et al. 1979). The protein was appropriately named p53.
Furthermore, they reasoned that “resident cellular genes” coded for p53 because it
was present in tumors that had not been infected by viruses. With the encouraging
findings in the mouse model, researchers began the search for a similar protein in
human cancer cells.
Normally found in low concentrations in non-transformed human cells, the
levels of p53 were frequently elevated in transformed cells and tumor cell lines
(Crawford et al. 1981, Dippold et al. 1981). Levels of p53 protein in SV40 or
adenovirus type 5 transformed cells were shown to be approximately 100-fold higher
than that of the non-transformed cells, with subsequent extensions in half-life when
found in complexes with SV40 large T antigen and adenovirus type 5 ElB-55Kd
protein (Oren et al. 1981). This led some to believe that elevated levels of p53
protein were associated with cellular transformation. However, other studies refuted
the idea that the p53 gene could be involved with transformation since the wild-type
version of the gene did not code for a transforming protein (Finlay et al. 1988).
Approximately one year later, Finlay and colleagues demonstrated that wild-
type p53 nearly eliminated the transforming ability of p53-mutant clones plus ras in
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5
REF cells through a tram-dominant fashion (Finlay et al. 1989). This meant that
rather than transforming normal cells into tumor cells, p53 had the ability to act as a
suppressor of transformation. Baker and colleagues further demonstrated its
suppressive ability in human colorectal carcinoma cells. Their group transfected
colorectal carcinoma cells with either the wild-type or mutant version of the gene.
Cells containing the wild-type p53 inhibited colony formation by five- to tenfold
when compared with the mutant version (Baker et al. 1990). Shortly thereafter, the
p53 protein was accepted as the product of a tumor suppressor gene.
The p53 gene, also referred to as TP53, is located on the 17pl3.1 locus and
produces the 53 K Dalton protein. The 393 amino acid protein has been divided into
4 distinct domains. Amino acids 1-43 form the N-terminus, which is the
transcriptional activation domain involved in regulating gene expression. The
second domain, or sequence-specific DNA-binding domain, is an antiparallel ( 3
(beta) sheet that the protein uses as a scaffold for the two a (alpha) helices
responsible for binding to DNA (Cho et al. 1994). The third and fourth domains of
the p53 protein comprise the tetramerization and C-terminal domains, respectively.
The tetramerization domain is responsible for the oligomerization of the protein,
which if disrupted, could lead to improper protein function. Finally, the C-terminal
domain appears to play a role in DNA mismatch-repair processes, as well as having
catalytic properties to bind DNA and RNA (Levine 1997). All four domains are
essential for proper protein function and ultimately, proper cell cycle regulation.
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It can be expected that as the number of domains increase, the chances of
acquiring defects that could lead to a loss of protein function increase as well. The
p53 protein is certainly no exception to this rule. Mutations occur at a high
frequency within the sequence-specific binding domain. Over 90% of p53’s
missense mutations occur in this domain resulting in a loss of its abilities to bind
DNA effectively and act as a transcription factor. Missense mutations in the first
domain most often result in a defective protein. Other mutations, though rare, occur
in the tetramerization domain; thus, altering protein conformation and DNA binding
(Levine 1997). Mutations in one or more of the protein’s domains, or even in the
gene itself, may result in serious consequences with the worst case being complete
loss of proper protein function.
Partial or complete loss of p53 activity could alter the fate of a normal cell as
p53 has various, important functions within the cell. In addition to regulating a cell’s
cycle, it is also involved with DNA repair and apoptosis. Repair and replication of
damaged DNA occurs during cell cycle arrest and is mediated by p53 pathways. p53
has been implicated with G1 arrest and more recent evidence links it to the G2/M
(Cross et al. 1995) and G0-G1-S phase transitions, as well (Del Sal et al. 1995).
Cells exposed to nocodazole and express the wild-type p53 are blocked in G2, yet
will proceed with DNA replication and experience increases in ploidy when native
p53 is not present (Cross et al. 1995). p53 also participates in DNA repair by
targeting the CIP1 gene downstream, which in conjunction with WAF1 produces the
p21 protein, an inhibitor of proliferating cell nuclear antigen (PCNA) during DNA
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replication but not in DNA repair (Levine 1997). Events that stimulate p53 function
also include, but are not limited to, DNA strand breaks caused by y-irradiation,
hypoxia, and depletion of ribonucleoside triphosphate (Graeber et al. 1996, Linke et
al. 1996, Levine 1997). However, more traumatizing events may cause irreparable
damage to DNA.
In such an event where the cell cannot repair its damaged DNA, p53 appears
to play a role in the regulation of apoptosis, or programmed cell death. p53 knockout
mice thymocytes have been shown to avoid apoptosis after experiencing DNA
damage from radiation; whereas, thymocytes from normal mice undergo apoptosis
(Lowe et al. 1993). Similar results are also observed in stem cells of intestines taken
again from knockout and normal mice (Lowe et al. 1993). Further research has
suggested associations between p53 and cell senescence (Tyner et al. 2002), as well
as between p53 and angiogenesis in experimental constructs (Dameron et al. 1994,
Fukasawa et al. 1996). As a result of its essential roles in cell cycle regulation, DNA
repair, and apoptosis, p53 has been recognized as the “guardian of the genome”
(Strachan and Read 1999).
p53 Protein as a Controversial Marker
It would be difficult to overemphasize the vital role that this guardian gene
and its protein product play in human cancer. Approximately 50% of malignancies
occurring within humans bear p53 mutations making it the most common mutation
in cancer (Hollstein et al. 1994). This is true for urological cancers, particularly
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8
those of the bladder (Sidransky et al. 1991, Fujimoto et al. 1992). The abnormal
product of the mutant gene is a more stable protein with a longer half-life than its
wild-type counterpart and is detectable using immunohistochemical staining. On the
other hand, the wild-type protein is usually undetectable due to its shorter half-life
(Finlay et al. 1988). Immunohistochemical analysis has revealed p53 protein
accumulation in tumor cells, including bladder transitional cell carcinomas (Sarkis et
al. 1993). With such evidence, coming to the conclusion that the p53 protein may be
used as a prognostic marker in bladder cancer management would be logical.
However, extensive research over the past several decades has not fully
proven p53 to be a factor in bladder cancer management, as its prognostic value
remains controversial. A search through the literature reveals conflicting results from
studies that have reported positive associations and those that have found the
opposite. Differences in study design among the numerous studies may account for
quite a bit of the heterogeneity in results, not to mention the lack of complete
understanding between the mutated p53 gene and the accumulation and inactivation
of its product (Schmitz-Drager et al. 2000). In an attempt to detect associations that
may have possibly been veiled by the inconsistent reports, Schmitz-Drager and
colleagues have initiated a combined analysis (Schmitz-Drager et al. 2000). As the
statistical principles of a combined analysis are similar to those of a meta-analysis, it
would be worthwhile to understand the basic steps of conducting a meta-analysis.
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Meta-analysis
A meta-analysis is generally thought of as a systematic synthesis and
statistical analysis of results extracted from a group of studies. The studies are
conducted independently of one another and may differ slightly in their methods.
However, all of the studies seek to prove, or disprove in some cases, a particular
hypothesis. Meta-analysis provides the researcher with a statistical tool to make
conclusions across a group of studies with conflicting results. Nevertheless, it is a
method that is not without its benefits and limitations. Researchers looking to reap
the full benefits of the technique while minimizing its potential problems must
approach and conduct it in a careful, systematic manner.
Defining Study Objectives, Research Outcomes, and Studies to Include
Normand has examined various components that must be dealt with in order
to complete a successful meta-analysis (Normand 1999). The first phase of a meta
analysis is similar to that of a single clinical trial or observational study; that is, a
well-defined hypothesis should be stated. In addition to explicitly stating study
objectives, the study designs to be included in the meta-analysis should be carefully
considered.
As features of one clinical trial distinguish it from another clinical trial, the
meta-analyst must consider the different types of studies that should be included in
the analysis. For example, Peto suggests including only well-designed randomized
trials that include features such as blinding and intent-to-treat analysis when
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conducting a meta-analysis of clinical trials (Peto 1987). This idea also applies to
observational studies. Each of the various observational studies has, by nature,
tendencies to be affected by certain types of biases and confounding; thus, a
synthesis of cross-sectional, cohort, and case-control studies may be fraught with
various problems. Establishing standards and inclusion criteria for the individual
studies prior to the literature search is necessary.
Operational definitions of research outcomes or endpoints, treatment
regimens, and the study populations should also be established. For example,
outcomes researchers may be interested in include both overall and disease-free 5-
year survivals (Nakanishi et al. 1996). Treatment regimens in some studies may be
limited to examining patients who were treated with a single agent such as
intravesicle bacillus-Calmette Guerin (BCG) therapy, while others examine patients
who have received a combination of mitomycin and BCG (Thomas et al. 1993,
Zlotta et al. 1999). Finally, a clear definition of study populations is essential, as this
problem appears to be problematic in studies analyzing superficial bladder cancer
and p53 status (Smith et al. 2003). Smith notes that most studies include both stages
of Ta and T1 cancers, and some include Tis lesions as well. However, including
both types of patients could be problematic as individuals with stage T1 tumors have
a 3-fold risk of death compared to individuals with stage Ta tumors (Holmang et al.
1995). Ultimately, such differences may cause difficulties in interpreting the data
and could possibly draw harsh criticism from other experts in the field. Indeed, the
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11
initial phase of any meta-analysis should be carefully outlined and carried out as if
one were conducting an independent clinical trial or observational study.
The Literature Search
Following the initial phase of the meta-analysis, a comprehensive literature
search is carried out. For reasons to be discussed, it is essential that the literature
review include all published studies, as well those not published, incomplete and in
progress. Citation indexes, abstract databases, and more comprehensive databases,
such as MEDLINE are useful sources for published literature. There are also
databases, which make unpublished documents such as doctoral dissertations
available. Works-in-progress and results discussed at scientific conventions may be
obtained by accessing conference indexes. Once a group of articles are retrieved and
reviewed, researchers return to the databases and refer to work cited in the literature
already retrieved to find more studies.
Failure to retrieve as many relevant studies as possible—whether published,
unpublished, or in-progress—may result in publication bias. It is a type of bias that
arises from the inclination of groups to submit or scientific journals to publish
research that yields statistically significant results. As with any independent study,
bias may distort the results of a study thereby impacting its validity. Thompson
points out that the results of a meta-analysis are valuable only if the component
studies themselves lack or have a small amount of bias (Thompson and Pocock
1991). A diagnostic tool known as a funnel plot can be used to detect publication
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12
bias (Normand 1999). Also, in an attempt to address this problem, the case for
developing international trial registries has been made (Simes 1986). However,
finding every study that should be included in the meta-analysis is not very likely.
Since it is highly unlikely to obtain all relevant work, some researchers may
wish to determine the amount of success the search yielded. Quantifying the success
of the retrieval process is accomplished by calculating the recall and precision of the
search (Normand 1999). Recall may be obtained by dividing the number of retrieved
documents by the total number that should have been retrieved. Precision, on the
other hand, is the number of documents that are retrieved and relevant for the meta
analysis divided by the number retrieved. Both quantities are multiplied by 100%
and higher percentages indicate higher recall and precision of the search. It is worth
mentioning that the denominator for the recall may be unknown as it would be
incorrect to assume that one has retrieved every document. Normand suggests the
use of capture-recapture models and other methods of estimating population size.
Once a sufficient number of documents have been retrieved, an evaluation of the
articles must be conducted.
The process of evaluating the studies is necessary and vital due to the
heterogeneity that exists among the studies. Differences in the sample populations,
study designs, and quality, are just several reasons for the heterogeneity. Each of the
studies may also introduce some degree of bias into the analysis, and as mentioned
above, may ultimately affect the validity of the results. Although no formal quality
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13
control regulations have been established, quality control criteria have been
suggested (Chalmers et al. 1981).
Chalmers and colleagues have suggested a framework, which may be used to
assess quality, particularly for randomized controlled trials (RCT). They suggest
focusing on four aspects: basic material that describes the study, the study protocol,
the statistical methods used to analyze the data, and presentation of results in a
manner that would allow ease of combining results from several RCTs. These four
components are necessary for quality assessment and if used universally, would
improve the quality of randomized studies (Chalmers et al. 1981). Other criteria
have been suggested, but such rules remain unclear and do not appear to be adopted
universally. Also unclear are the rules for “down-weighting” of lower quality studies
that end up being included in the analysis (Thompson and Pocock 1991). As the
inclusion/exclusion criteria remain unclear, the process of evaluating studies remains
both an art form and an exact science.
Combining the Studies
After evaluation and narrowing the field down to only those relevant for the
meta-analysis, results from the studies are coded and entered into a database.
Depending on the absence or presence of differences in treatment effects among the
individual studies, several different modeling procedures can be used. Upon
completion of the analysis, diagnostic procedures must be used to assess sensitivity
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14
and bias. However, before proceeding with the analysis, one or more statistical
measures universal to all of the individual studies must be identified.
Constructing one or more summary statistics for the meta-analysis from the
statistical measures found in the original publications may prove difficult. This may
especially be true when definitions of study endpoints differ. For example, results
from the original analyses may be presented in the form of odds ratios and relative
risks, while other studies show means and effect sizes. Of course, the types of data
collected will have dictated the measure used. Since a variety of measures exist,
combining them may not be possible in some cases.
Once the summary measures have been extracted, they can be combined.
Statistical modeling of the data will depend on the absence or presence of
homogeneity in treatment effects or other summary statistics among the primary
studies. In situations where mean outcomes and study characteristics do not differ
among the studies, statistical inferences using a fixed-effects model would be
suitable. Conversely, if treatment effects and characteristics varied among the
studies, then a random-effects model may be a more ideal approach.
A statistical test of homogeneity is a way to test for differences in treatment
effects among studies. DerSimonian and Laird present a rather detailed discussion of
this test (DerSimonian and Laird 1986). Using treatment group means as an
example, failure to reject the null hypothesis Ho, would suggest that the differences
between the means did not vary significantly. On the other hand, rejection of Ho
would show that at least two of the studies differ significantly from one another; that
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15
is, some degree of heterogeneity exists and use of a random-effects model may be
warranted. Unfortunately, the test for homogeneity lacks statistical power so using a
higher significance level, such as a=0.10, has been suggested (Fleiss 1993).
Furthermore, successfully rejecting the null hypothesis may not necessarily warrant
the use of a random-effects model.
The use of a random-effects model to account for the heterogeneity among
the primary studies has been scrutinized. Thus, it would be ideal to conduct a
sensitivity analysis, which would determine if the assumptions made during the
initial analysis were correct (Normand 1999). The basic idea behind a sensitivity
analysis is to estimate both types of models and compare the results. Normand also
suggests further assessing the sensitivity of distribution assumptions made or of a
combined estimate to one or several of the studies within a model.
Finally, after careful assessment of the combined estimates, the results must
be interpreted. One cannot stress enough the caution that should be exercised when
interpreting the final results. Since meta-analysis is viewed to be as much an art
form as a science, many researchers question its ability to answer complex scientific
questions with simple summary statistics. Further skepticism arises when the results
of a combined analysis conflict with those obtained from large, randomized trials
(DerSimonian and Levine 1999). However, this is not to dismiss the potential utility
of the statistical tool. With careful thought and interpretation of the quantitative
results, qualitative inferences drawn from meta-analyses may be used to help
develop broad treatment policies (Thompson and Pocock 1991).
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16
A Combined Analysis o f p53 and Bladder Cancer Outcome
The possibility that a meta-analysis could provide valuable qualitative
conclusions regarding health policies make it an attractive tool to address some of
the concerns regarding the association of p53 and patient prognosis in bladder
cancer. Through the last decade or so, numerous studies investigating the
association between p53 alteration and outcome have shown conflicting results
making it one of the most controversial topics in bladder cancer management. In
hopes of shedding some light on the issue, Schmitz-Drager and associates have
examined the feasibility of a combined analysis.
To show the viability of a combined analysis, Schmitz-Drager and associates
began by identifying studies through a 1997 MEDLINE search that focused on p53
immunohistochemistry in cancers of the bladder and upper urinary tract. The search
yielded forty-three studies from European, North American, and Asian institutions
that included a total of 3,764 patients. Using data from the publications, their group
attempted to not only summarize relevant observations, but to understand reasons for
the incompatible results and suggest improvements for further research on p53
(Schmitz-Drager et al. 1997). They were able to conclude that results from the trials
differed as expected since the studies themselves varied with regards to study
designs, definitions of endpoints, sample populations, and laboratory techniques
used. Unfortunately, they were not able to account for the heterogeneity of the
studies, which is the reason that a formal meta-analysis was not conducted.
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17
In order to be able to account for the heterogeneity, Schmitz-Drager later
invited the authors of the primary publications to submit their original data. Twenty-
five institutions from Europe, North America, Asia, and Australia complied, which
yielded a total of 3,421 bladder cancer patients. When compared to a normal bladder
cancer population, the sample population was comparable in terms of disease
staging, gender, and age distribution. Additionally, rates of participation from the
different global regions were found to be similar and the data collected were
representative of the institutions that were originally invited to participate. Studies
reporting negative results, however, may have been slightly overrepresented in their
sample. Nonetheless, the authors were able to show the feasibility of conducting a
combined analysis.
Building upon the idea of a combined analysis from Schmitz-Drager, the
objectives of this study are threefold. First, conduct a combined analysis using data
from the thirty-six of the primary publications first identified via the 1997
MEDLINE search and assess the prognostic significance of p53. Next, perform a
combined analysis using the individual patient data (IPD) provided by Schmitz-
Drager and again, examine the usefulness of p53 in predicting patient outcome.
Finally, compare results estimated from the publication data to those obtained from
the IPD. Again, it is important to reiterate that a combined analysis, rather than a full
meta-analysis, will be conducted. An exhaustive literature search was not performed
as the publication data and IPD were provided.
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18
Methods
Publications, IPD, and Patients
Schmitz-Drager and associates began the combined analysis in November
1997. Thirty-eight published studies were originally identified for the analysis
(Table 1). Of the thirty-eight published studies, twenty-four originated from Europe,
seven were from Asia, five were North American-based, and the remaining one from
Australia. Collectively, the publications provided a total sample size of 3,641
patients. Sample sizes from the individual studies ranged from 23 to 265 patients
(median 85).
Individual patient data (IPD) from twenty-five groups have also been made
available. Of these twenty-five groups submitting electronic data, seventeen are
European, three Asian, four North American, and one Australian. The twenty-five
studies varied in sample size with a range of 23 to 502 patients (median 109) for a
combined total of 3,370 patients.
Immunohistochemistry/Mutational Analysis
Thirty-six of the original thirty-eight published works examined the
association between p53 over-accumulation and patient prognosis, while the
remaining two studies examined p53 mutation. Archival tumor specimen from
biopsies or surgical procedures were obtained for each patient and immuno-
histochemistry (or polymerase chain reaction (PCR) based methods for p53
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Table 1. Summary of the 38 Original Publications Identified by Schmitz-Drager and Colleagues
No. of Patients
First Author (Year) Country Total Non-Invasive (%) Invasive (%)
p j j C U ld l l
<%) m A1 )
Abdel-Fattah (1998) United Kingdom 54 19 (35) 35 (65) 50 D 07
Barbareschi (1995) Italy 25 10 (40) 15 (60) 20 D 07
Bassi (1998) Italy 107 107 (100) 0
(0) n/r PB53-12-1
Burkhard (1997) Switzerland 46 46 (100) 0
(0)
20 D 07
Casetta (1997) Italy 59 59 (100) 0 (0)
0 D 07
Furihata (1993) Japan 90 49 (54) 41 (46) n/r D 07
Gao (2000) Japan 87 38 (44) 49 (56) 20 D 07
Gardiner (1994) Australia 28 28 (100) 0 (0) 10, 25 1801, D 07, CM1
Gasser(1995) Switzerland 138 n/r n/r n/r CM1
Grossman (1998) United States 45 45 (100) 0 (0)
10 DOl
Hudson (1995) United States 24 24 (100) 0 (0) 20 1801
Jahnson (1995) Sweden 154 41 (27) 113 (73) 30 1801
Kakehi (1998) Japan 60 0 (0) 60 (100) 10 1801
Karaggerud (1997) Norway 23 7 (30) 16 (70) 5 CM1
Leissner(1996) Germany 114 0 (0) 114 (100) 20 DOl
Leissner (2001) Germany 70 0 (0) 70 (100) 20 D07
Lipponen(1993) Finland 212 96 (45) 116 (55) 20 CM1
Liukkonen (1997) Finland 185 185 (100) 0 (0) 20 CM1
Liukkonen (1999) Finland 207 207 (100) 0 (0) 20 CM1
Moch (1993) Switzerland 178 78 (44) 100 (56) Fractions CM1
Nakanishi (1996)5 Japan 149 58 (39) 91 (61) 10 RSP53
Nakopoulou (1995) Greece 87 45 (52) 42 (48) 10 1801
Nakopoulou (1998) Greece 106 63 (59) 43 (41) 10 1801
Popov(1997) France 114 63 (55) 51 (45) 22 1801
Qureshi (1999) United Kingdom 83 0
(0) 83 (100) 20 1801
10 D 07
Schmitz-Drager (1997) Germany 61 61 (100) 0 (0) 5 DOl
Shiina (1996 Cancer) Japan 77 34 (44) 43 (56) n/r D 07
Shiina (1996) Japan 72 30 (42) 42 (58) 40 (PR) D 07
70 (PI)
Tetu (1996) Canada 265 265 (100) 0 (0) 0 Anti-Serum
Thomas (1993) United Kingdom 25 25 (100) 0 (0) 10 CM1
(Table 1 continued on next page)
___________ Associations___________ j^yj curve
Time-to-event Measure4 Univariate Multivariate2 provided
Survival 0.0325 0.132 yes
n/a n/a n/a -
Survival 0.0108 - yes
n/a n/a n/a -
Time to Recurrence 0.092 0.009 yes
Survival <0.05 <0.05 yes
Survival 0.114 0.126 yes
n/a n/a n/a -
n/a n/a n/a -
Time to Progression 0.076 - yes
n/a n/a n/a -
Cancer-Specific Survival n/s n/s yes
Cancer-Specific Survival 0.0086 - yes
n/a n/a n/a -
n/a n/a n/a no
Time to Progression n/s - yes
Survival 0.015 n/s no
n/a n/a n/a -
Cancer-Specific Survival 0.256 n/s no
Time to Progression 0.002 n/s
Time to Recurrence 0.028 n/s
n/a n/a n/a no
Overall Survival 0.0013 0.042 yes
Time to Recurrence 0.0039 0.11
Time to Recurrence 0.29 - no
Overall Survival 0.007 0.298
Overall Survival 0.02 0.55 yes
Cancer-Specific Survival <0.0001 - yes
Cancer-Specific Survival 0.15 (1801) n/s yes
0.14(DO7) n/s yes
Time to Progression 0.0022 0.0135 yes
Cancer-Specific Survival 0.0072 (quantity) n/s no
0.0053 (intensity)
Cancer-Specific Survival <0.01 (PR)3 0.2315 (PR)3 no
<0.01 (PI)3 0.2457 (PI)3
Time to Recurrence 0.0258 n/s yes
Survival 0.1516 - yes
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(Table 1 continued)
No. of Patients
First Author (Year) Country__________ Total Non-Invasive (%) Invasive (%)
Uchida(1995) Japan 43 13 (30) 30 (70)
Underwood (1996) United Kingdom 106 84 (79) 22 (26)
Vet (1994)’ Netherlands 45 21 (47) 24 (53)
Vet (1995) Netherlands 39 19 (49) 20
(51)
Volmer (1998) United States 229 n/r n/r
Wright (1995) United Kingdom 98 62 (63) 36 (37)
Wu (1996) United States 109 0
(0)
109 (100)
Zlotta (1999) Belgium 47 47 (100) 0
(0)
Abbreviations: n/a, not applicable; n/r, not reported; n/s, not significant
p-values listed when available
’Mutational analysis was performed instead o f IHC.
2Studies not examining p53 in a multivariate model are denoted by:
3 p53 immunostaining: Positive Rate (PR)/Positive Intensity (PI)
4Studies not examining survival data are denoted by: n/a.
5 Upper urinary tract cancers: excluded from analysis
p53 Cutoff Associations___________ KM curve
(% )____________ mAb_______ Time-to-event Measure4_______Univariate______ Multivariate2 provided
+/- Mutatic
Index > 65 Anti-Ser
+/- Mutatk
10 D07
20 1801
0 240
20 D07
10 D07
Survival
Overall Survival
Survival
Survival
n/a
n/a
Overall Survival
Time to Progression
Time to Recurrence
0.01
n/s
<0.001 (all patients)
n/s (invasive)
<0.01 (all patients)
n/s (non-invasive)
n/s (invasive)
n/a
n/a
0.14 (all patients)
0.006 (T3b)
n/s
n/s
yes
n/s yes
yes
yes
n/a
n/a
n/s yes
0.009 (T3b)
n/s no
n/s
21
Table 2. Definitions of Various Study Outcomes
Outcome Endpoint
Survival/Overall Survival Death due to any cause
Cancer-Specific Survival Death due to bladder cancer
Time to Recurrence Return or reappearance o f bladder cancer (any stage and any amount)
after complete surgical removal
Time to Progression
(1) Patients with non-invasive disease: Recurrence o f tumor with
increase in stage or grade
(2) Patients with invasive disease: Any recurrence at all (in this case,
recurrence implying either lymph node or distant metastases as the
bladder was removed)____________________________________________
mutations) were used to classify tumors as p5 3-positive (mutated) or -negative (wild-
type). Different types of monoclonal antibodies were used to detect p53 expression
levels, although it appeared that D07 was used most frequently (Table 1). The cut
off value for declaring altered expression of p53 varied among the studies, as well. It
appears that efforts were made in most studies to blind individuals reviewing the
tumor specimen of clinical outcome. According to the publications, there were no
significant differences in the tumor scoring between observers; therefore, the final
classifications for p53-positivity or negativity were consistent.
Statistical Considerations: Endpoints and the Hazards Ratio
In the original thirty-eight publications, the investigators examined the
relationship between p53 and one or more different types of outcomes (Table 1).
The different types of outcomes have been summarized above in Table 2. As the
outcome was not always clearly defined in the methods section of every publication,
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22
it was assumed to be the time from the patient’s diagnosis until the observation of the
endpoint. The diagnosis used for non-invasive bladder cancer patients was either the
diagnosis of the primary disease or the last diagnosis (i.e., the most recent) of
muscle-invasive recurrence. The first and only diagnosis was used for patients with
muscle-invasive disease. In some cases the date of definitive treatment for the
diagnosis of bladder cancer was used. Generally, the time interval between
diagnosis and treatment is short. Patients were censored if they had not experienced
the endpoint of interest at the time of last follow-up.
Although the endpoints remained the same for the individual patient data, the
primary outcome examined was time to progression, while survival was secondary.
The decision for this was based on the idea that time-to-progression is a more
effective indicator of the aggressiveness of the tumor. It was reasoned that (1) many
patients are treated aggressively following progression; therefore, the decision on
how to treat would impact overall survival in a way that might not reflect the
intrinsic tumor behavior and (2) as many of the patients are of older age, it is
possible that deaths due to other circumstances may attenuate or mask an association
with p53 status.
The association of patient outcome and p53 status was measured by the
hazards ratio (HR). As the name implies, the HR is a ratio of two hazard rates. The
hazard rate represents the force of mortality or the failure rate in a very small interval
of time conditional on surviving until that time without the event (Breslow and Day
1980). For this study, the HR quantifies the relative risk of experiencing an outcome
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23
for patients with p5 3-positive expression/mutation compared to those with negative
expression/mutation. A HR less than 1 indicates a beneficial effect of having p53-
positive status; thus, p53 accumulation/overexpression provides a protective effect
and may reduce the chance of experiencing the outcome. A HR greater than 1
suggests that altered p53 levels provide a negative effect and p5 3-negative patients
have a better chance of survival. In addition, 95% confidence intervals (Cl) have
been calculated for each HR to denote its statistical significance. A confidence
interval including unity indicates a non-significant HR; that is, not significantly
different from 1 or no statistically significant association between p53 status and
outcome at the a=0.05 level.
Statistical Analysis
Only time-to-event data from the publications and IPD will be considered for
this project. Parmar details the method used to extract summary statistics from the
published studies (Parmar et al. 1998). For each study i, the time axes of Kaplan-
Meier (KM) curves were divided into intervals (t = 1,...,T) in which the number of
patients at risk, the number of failures, and number of censored patients are
estimated. From these estimates, the natural log hazards ratio (HR) for the rth
interval is estimated with
ln(HRj(t)) = In
r Dri{t)IRri(t) N
\D ci{t)! Rci(t) j
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24
where D r j and D Cj are the number of deaths occurring in the p5 3-positive and p53-
negative groups, respectively. R r j and R c j are the number of patients at risk in the
p53-positive and p53-negative groups, respectively. The estimate of the variance for
the rth interval is given by
var[ln(HR;(/))] = — — + ■ 1 1
Dri(t) Rri(t) D J l) Rci(t)
The interval ln(HR) can then be combined to estimate the log hazards ratio and
variance for the /th study using an inverse-variance weighted method:
f HHRXO)
ln(HRl)=i ^ £ M M
tfv a r [ln (/ffl,(0 )]
and
r r i v
var[ln(HR,)] = Y- --------- .
L t? v a r [ln (^ (0 )]_
Obviously, as the ln(HR) has been calculated, taking the anti-log will yield the
estimate of the HR. Finally, the ln(HR) and variance for each study (/ = 1,...,K) are
pooled together to form an overall HR estimate and variance by
y H H R.)
ln(HR) = var[ln(//y?'). l and
X -----
t f v a r [ l n ( ^ ) ]
var[ln(HR,)]
tfvar[ln(//S,X
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25
which are essentially analogues of the preceding equations that estimated the HR and
variances for the individual studies. In addition, 95% confidence intervals for the
overall ln(HR) are estimated by
9 ± 1.96^ 1 / J ^
where 6 is the estimate of the overall ln(HR) and m > , is the inverse of the variance of
the ln(HR) (Whitehead and Whitehead 1991). A similar method was used to
calculate the 95% Cl for each individual study. Finally, testing for homogeneity of
the individual study estimates may be based on the Q statistic
where < 9 , is the ln(HR) for the ith study, 6 is the overall ln(HR) and again, w, is the
inverse of the variance of the ln(HR). This large sample test approximately follows a
chi-square distribution with (A >1) degrees of freedom (DerSimonian and Laird 1986).
A non-statistically significant test for homogeneity indicates relatively small
differences among the individual estimates and a pooled estimate would sufficiently
quantify the association between p53 and prognosis. If on the other hand the test
was significant, then the individual estimates more accurately reflect the true
association between p53 and outcome.
Only the first 60 months (5-year survival) of each study were considered in
this analysis as the majority of events occur within this time period. The time
intervals of the KM curves for the Parmar method were divided as appropriately for
each study up to 60 months (see Appendix 1 for the individual study calculations).
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26
Studies with more events tended to be divided into finer intervals, while those with
fewer events had wider intervals. The censoring method used assumed a constant
censoring rate during each time interval and can be found in the appendix of the
Parmar paper (Parmar et al. 1998). As survival curves are necessary to extract the
essential information to calculate summary statistics of interest, only 20 of the 38
publications providing plots were eligible for inclusion in this combined analysis.
However, all 25 groups contributing IPD provided time-to-event data and are
therefore eligible for inclusion in the combined analysis. The IPD, the log HR,
variances, and confidence intervals for each study may be estimated using Cox
Regression modeling. Overall estimates and Cl may be calculated using methods
similar to those described above, as are the tests of homogeneity. Stratified log-rank
tests (stratifying by institution) were also used to test for the association between p53
and outcome.
The results of the combined analysis are graphically presented with HR plots
and K-M curves (Appendix 2) to show the survival experiences for each group. A
significance level of 5% (a < 0.05) was used and reported p-values reported are 2-
sided. Calculations will be performed using Microsoft Excel 2002 (Microsoft Corp.,
Seattle, WA) and SAS, Version 8 (SAS Institute, North Carolina).
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27
Results
Publication Data
Each region of the world was represented reasonably well as seen by the
diversity of the participating institutions. European institutions provided thirteen
(62%) of the publications, three (14%) were North American, and five (24%) were
Asian. However, one study that examined upper urinary tract cancers was ultimately
excluded (Nakanishi et al. 1996). A total of 1,685 patients were used in the analysis.
597 (35%) of these patients had altered levels of p53 and/or p53 mutations.
Although time-to-progression was the primary endpoint, many of the original
publications examined survival and presented those results. Fifteen of the
publications with 1,185 patients examined the possible association between p53
status and overall survival/cancer-specific survival. 468 (39%) of the 1,185 patients
were considered p53-positive. There was no statistically significant presence of
heterogeneity among the studies, which deemed the overall HR to be a representative
pooled estimate of the individual studies (Q=9.90, d.f.=14, p=0.942). The overall
HR of 1.50 (95% Cl 1.20 to 2.15) implies that p53-positive patients are 50% more
likely to die at any given time during the first five years (Table 3 and Figure 1).
Slightly different results are seen when studies examining non-muscle
invasive or invasive patients only are separately pooled. Two studies contributed to
the overall HR estimate for non-invasive patients: Vet (1995) and Thomas (1993).
Five studies contributed to the overall HR estimate for invasive patients: Jahnson
(1995), Kakehi (1998), Vet (1994), Vet (1995), and Wu (1996). Testing for
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28
homogeneity among studies examining each type of patient showed no evidence of
statistical significance ( Q n o n - i n v a s i v c < 0 . 0 0 1 , d .f = 1 , p = 0 . 9 9 3 and Q i n v a s i v e = 0 . 9 4 7 , d.f.=5,
p=0.967), which again showed that pooled estimates are reasonable. The overall HR
for studies, which included only non-invasive bladder cancer patients, showed that
Table 3. Results of Studies Examining Survival/Disease-Specific Survival
No. of Patients
Author (year) p53+
(%)
p53-
(%)
HR 95% Cl
Abdel-Fattah (1998) 29 (56) 23 (44) 1.52 ( 0.50 - 4.60 )
Furihata (1993) 26 (42) 36 (58) 1.52 ( 0.45 - 5.16 )
Gao (2000) 50 (57) 37 (43) 1.25 ( 0.42 - 3.68 )
Jahnson (1995)4 65 (42) 89 (58) 1.12 ( 0.75 - 1.68 )
Kakehi (1998)1 ,4 14 (44) 18 (56) 2.08 ( 0.36 - 12.12 )
Kakehi (1998)2 ’ 4 14 (50) 14 (50) 1.40 ( 0.60 - 3.27 )
Lipponen (1993) 39 (18) 173 (82) 1.78 ( 0.92 - 3.44 )
Nakopoulou (1998) 53 (50) 53 (50) 1.63 ( 0.74 - 3.58 )
Popov (1997) 58 (51) 56 (49) 2.61 ( 0.65 - 10.43 )
Qureshi (1999) 21 (28) 55 (72) 0.77 ( 0.36 - 1.67 )
Thomas (1993)3 9 (50) 9 (50) 1.52 ( 0.43 - 5.41 )
Uchida (1995) 20 (47) 23 (53) 1.96 ( 0.53 - 7.24 )
Underwood (1996) 33 (31) 73 (69) 2.36 ( 0.95 - 5.87 )
Vet (1994)4 8 (18) 37 (82) 2.99 ( 1.05 - 8.51 )
Vet (1995)3 ’ 4 10 (50) 10 (50) 2.87 ( 0.76 - 10.91 )
Wu (1996)4 19 (63) 1 1 (37) 2.31 ( 0.23 - 22.93 )
Overall (non-inv)5 17 (47) 19 (53) 1.52 ( 0.43 - 5.41 )
Overall (inv)6 130 (42) 179 (58) 1.21 ( 0.88 - 1.67 )
Overall (all patients)7 468 (39) 717 (61) 1.50 ( 1.20 - 2.15 )
'Group 1: L ocally advanced patients (no m etastasis)
2Group 2: L ocally advanced patients (w ith m etastasis)
3Study contributes to overall H R estim ate for non-invasive patients
4Study contributes to overall H R estim ate for invasive patients
5O verall H R estim ate from studies w ith non-inv patients on ly (T hom as 1993, V et 1995). T est o f hom ogeneity:
Q < 0.001, d .f.= l,p = 0 .9 9 3 .
6Overall H R estim ate from studies w ith in vasive patients on ly (Jahnson 1995, K akehi 1998, V et 1994, V et 1995,
W u 1996). T est o f hom ogeneity: Q = 0 .9 4 7 , d .f.= 5, p = 0.967.
’ inclu d es all studies (n on -in vasive and invasive patients included). T est for hom ogeneity: Q = .9 .9 0 , d .f.= 14,
p= 0.942.
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29
A bdel-F attah (1 9 9 8 )
Furihata (1 9 9 3 ) i
G ao (2 0 0 0 ) i —
Jahnson (1 9 9 5 ) , ___
K akehi (1 9 9 8 ) i ---------
K akehi (1 9 9 8 ) i -------------------
L ipponen (1 9 9 3 ) i
N ak op ou lou (1 9 9 8 ) i —
Popov (1 9 9 7 ) h ____
Q ureshi (1 9 9 9 ) i — •
T hom as (1 9 9 3 ) i --------
U ch id a (1 9 9 5 ) ..
U nderw ood (1 9 9 6 )
V et (1 9 9 4 )
V et (1 9 9 5 )
W u (1 9 9 6 ) ( _______________
O verall (in v a siv e) h
O verall (n on -in vasive) | __________
O verall (all patients)
-4 .0 0 -3 .0 0 - 2.00 - 1.00 0.00
InHR
1.00 2.00 3 .0 0 4.0 0
Fig. 1. Estim ated H R (In scale) plot o f studies investigating the association o f p53 accum ulation/m utation
and overall/can cer-sp ecific survival. (O verall (invasive): Invasive patients only; O verall (non-invasive):
N on -in v a siv e patients only; O verall (all patients): all patient included.
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30
Table 4. Results of Studies Examining Time-to-Recurrence
No. of Patients
Author (year) p53+ (%) p53-
(%)
HR 95% Cl
Casetta (1997) 20 (34) 39 (66) 2.18
(
1.02 - 4.66 )
Tetu (1996) 39 (15) 226 (85) 2.05
(
1.38 - 3.05 )
Overall 59 (18) 265 (82) 2.08
(
1.47 - 2.95 )
p53-positive patients were 52% more likely to experience death, although it was not
statistically significant (HR 1.52, 95% Cl 0.43 to 5.41). p53-positivity showed a
more modest effect across the five studies that considered only invasive patients
albeit a non-significant one (HR 1.21, 95% Cl 0.88 to 1.67).
Out of all of the studies examining survival, only one had a HR less than 1
and was not significant (HR 0.77, 95% Cl 0.36 to 1.77). This was consistent with
the findings in the original publication (Qureshi et al. 1999), which showed that p53-
positive patients fared better survival although it was not statistically significant.
Table 5. Results of Studies Examining Time-to-Progression
No. of Patients
Author (year) p53+ (%) p53-
(%)
HR 95% Cl
Grossman (1998)1 26 (58) 19 (42) 3.18
(
0.75 - 13.52 )
Leissner (2001)3 21 (30) 49 (70) 1.13
(
0.43 - 2.97 )
Schmitz-Drager (1997)1 23 (38) 38 (62) 2.72
(
1.18 - 6.24 )
Overall2 70 (40) 106 (60) 2.04
(
1.14 - 3.63 )
Overall 49 (46) 57 (54) 2.82
(
1.37 - 5.81 )
'Study contributes to overall H R estim ate for non-invasive patients.
2Include all studies above (in vasive and non-invasive patients included). T est for H om ogeneity: Q =T .32, d.f.=2,
p = 0.517).
O nly 1 study (L eissner 2 0 0 1 ) included invasive patients only; therefore, the H R est. for this study is the overall
H R est. for in vasive patients.
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31
There were only two studies examining the association of p53 status and
time-to-recurrence/disease-free survival and both included only non-muscle invasive
bladder cancer patients. Table 4 and Figure 2 summarize the results of these studies.
The majority of patients in this study were considered p53-negative. The test for
C asetta (1 9 9 7 )
Tetu (1 9 9 6 )
O verall
-2 0
In llR
Fig. 2. Estim ated H R (In scale) plot o f studies in vestigating the association o f p53 accum ulation
and tim e-to-recurrence. N ote: Both studies included non-invasive patients only.
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32
heterogeneity did not show statistical significance (Q=0.020, d .f=1, p=0.888).
Again, the pooled estimate of HR showed that p53-positive patients showed a
statistically significant increase of experiencing recurrence within the first five years
after diagnosis (HR 2.08, 95% Cl 1.47 to 2.95).
HR estimates from three articles examining altered p53 levels and time-to-
progression were pooled as there was no statistically significant amount of
Grossman (1998) , ._____________________i
Leissner (2001) i ---------------------- 1
Schmitz-Drager (1997) i , ___________ .___________ ,
Overall (all patients) | ,________.________,
Overall (non-invasive)1 , __________.__________,
- 2 - 1 0 1 2 3
InHR
Fig. 3. Estim ated H R (In scale) plots estim ated from publication data w ith progression as the
endpoint.
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33
heterogeneity among the studies (Q=L32, d.f.=2, p=0.517; Table 5 and Figure 3).
When all patients (both non-invasive and invasive) were grouped together, positive
p53 status again appeared to confer a statistically significantly worse prognostic
outcome for those patients (HR 2.04, 95% Cl 1.14 to 3.63). Non-muscle invasive
bladder cancer patients with altered levels of p53 expression were also more likely to
experience progression (HR 2.82, 95% Cl 1.37 to 5.81).
Individual Patient Data
Twenty-five groups submitting IPD datasets combined to give a total of
3,370 patients of which 2,276 (68%) were classified with non-invasive tumors and
1094 (32%) with muscle-invasive tumors (Table 6). Furthermore, of the 3,370
patients, 1,414 (42%) were graded as p53-positive, 1,857 (55%) were p53-negative,
and p53 status was missing for 99 (3%) of the patients.
Only twenty-three datasets were included in the final analysis examining the
association between p53 and time to progression, as one institution did not provide
data (Leissner) and there were no patients who experienced progression in another
(Vet). Of the 3,162 patients eligible for inclusion, 637 (21%) progressed while 2046
(65%) did not (Table 7). When both non-invasive and muscle-invasive patients were
included in the analysis, the stratified log-rank test (stratified by study center)
indicated that there was a statistically significant association between p53 and time
to progression (log-rank x 1 =37.99, d.f.=l, p<0.001). When examining datasets that
included only non-invasive patients, there was still a significant association (log-rank
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34
X 1 =20.74, d .f=1, p<0.001). However, p53 showed no prognostic significance in
the one dataset (Wu) that included muscle-invasive bladder cancer patients only (log-
rank x 1 =l-34, d.f.=l, p=0.25). To further investigate the association of p53 and
time to progression, Cox Regression models were used.
Cox regression modeling was used to estimate the HR for each individual
dataset. Eighteen of the twenty-three studies show that p5 3-positive patients had a
Table 6. Summary of IPD Provided: By Histology and p53 status
Total No. Histology (%)_________________ p53 Status (%)
Source Patients Non-invasive Invasive p53+ p53- Missing
Barbareschi 102 88 (86) 14 (14) 36 (35) 66 (65) 0
(0)
Bassi 153 107 (70) 46 (30) 80 (52) 73 (48) 0
(0)
Burkhard 34 1
(3) 33 (97) 28 (82) 4 (12) 2
(6)
Cassetta 164 154 (94) 10
(6)
56 (34) 107 (65) 1
(1)
Furihata 129 65 (50) 64 (50) 51 (40) 78 (60) 0
(0)
Gardiner 88 87 (99) 1
(1)
54 (61) 32 (36) 2
(3)
Gasser 502 322 (64) 180 (36) 247 (49) 227 (45) 28
(6)
Grossman 45 45 (100) 0
(0)
26 (58) 19 (42) 0
(0)
Jahnson 154 41 (27) 113 (73) 65 (42) 89 (58) 0
(0)
Kakehi 80 62 (78) 18 (22) 35 (44) 42 (52) 3
(4)
Popov 112 68 (61) 44 (39) 52 (46) 60 (54) 0
(0)
Leissner 166 3
(2) 163 (98) 45 (27) 69 (42) 52
(31)
Lipponen 211 96 (46) 115 (55) 40 (19) 171 (81) 0
(0)
Liukkonnen 207 207 (100) 0
(0)
72 (35) 133 (64) 2
(1)
Nakopoulou 99 57 (58) 42 (42) 50 (51) 49 (49) 0
(0)
Qureshi 143 98 (69) 45 (31) 75 (52) 68 (48) 0 (0)
Schmitz-Drager 61 61 (100) 0
(0)
23 (38) 38 (62) 0
(0)
Tetu 369 303 (82) 66 (18) 158 (43) 211 (57) 0
(0)
Thomas 23 23 (100) 0
(0)
10 (43) 13 (57) 0
(0)
Uchida 57 46 (81) 11 (19) 31 (54) 26 (46) 0
(0)
Underwood 85 65 (76) 20 (24) 23 (27) 58 (68) 4
(5)
Vet 4 2 4 2 (100) 0
(0)
16 (38) 2 3 ( 5 5 ) 3
(7)
Vollmer 188 188 (100) 0
(0)
59
(31)
127 (68) 2
(1)
Wu 109 0
(0)
109 (100) 61 (56) 48 (44) 0
(0)
Zlotta 47 47 (100) 0
(0)
21 (45) 26 (55) 0
(0)
Total 3370 2276 (68) 1094 (32) 1414 (42) 1857 (55) 99
(3)
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35
Table 7. Summary of IPD Results with Time-to-Progression as Endpoint
Patient Status (%)
Source Progression No Progression Missing HR 95% Cl
Barbareschi 19 (19) 83 81) 0 (0)
6.31 ( 2.27 - 17.58 )
Bassi1 28 (18) 30 20) 95 (62) 1.14 ( 0.54 - 2.40 )
Burkhard 22 (65) 8 24) 4
(11)
0.43 ( 0.14 - 1.31 )
Cassetta 45 (27) 116 71) 3
(2)
1.54 ( 0.85 - 2.80 )
Furihata 24 (19) 90 70) 15
(11)
0.96 ( 0.42 - 2.20 )
Gardiner 28 (32) 58 66) 2
(2)
0.63 ( 0.30 - 1.34 )
Gasser1 31 (6) 266 53) 205 (41) 2.02 ( 0.99 - 4.13 )
Grossman2 11 (24) 34 76) 0
(0)
3.54 ( 0.76 - 16.41 )
Jahnson 75 (49) 79 51) 0
(0)
0.90 ( 0.57 - 1.43 )
Kakehi 16 (20) 60 75) 4
(5)
2.23 ( 0.81 - 6.14 )
Lipponen 84 (46) 127 54) 0
(0)
1.66 ( 1.02 - 2.70 )
Liukkonnen2 27 (13) 176 85) 4
(2)
3.50 ( 1.60 - 7.65 )
Nakopoulou 2 (2) 95 96) 2
(2)
Inf ( n/e - n/e )
Popov 50 (45) 62 55) 0
(0)
4.12 ( 2.21 - 7.66 )
Qureshi1 12 (8) 85 59) 46 (32) 2.63 ( 0.79 - 8.73 )
Schmitz-Drager2 23 (44) 38 56) 0
(0)
3.22 ( 1.39 - 7.46 )
Tetu 23 (6) 335 91) 11
(3)
1.13 ( 0.49 - 2.57 )
Thomas2 13 (59) 10 43) 0
(0)
1.80 ( 0.59 - 5.51 )
Uchida 7 (12) 50 88) 0
(0)
2.13 ( 0.41 - 11.00 )
Underwood 26 (31) 55 65) 4
(4)
2.12 ( 0.96 - 4.69 )
Vollmer 21 (11) 152 81) 15
(8)
1.56 ( 0.66 - 3.71 )
Wu1 42 (39) 1
(0)
66 (61) 1.22 ( 0.65 - 2.27 )
Zlotta 8 (17) 36 77) 3
(6)
0.67 ( 0.16 - 2.81 )
Overall3 637 (20) 2046 65) 479
(15)
1.59 ( 1.35 - 1.88 )
Overall4 524 (23) 1664 74) 67
(3)
1.62 ( 1.35 - 1.94 )
Overall5 103 (18) 446 78) 22 (4) 2.31 ( 1.54 - 3.47 )
Inf: num erical approx. o f infinity. T he estim ated value w as 3.61E 07.
n/e: not estim able due to extrem ely large variance. T he on ly tw o patients w ith progression w ere p53+.
’Dataset w ith e x c e ssiv e am ount o f m issin g data.
D ataset contributes to overall H R estim ate for non-invasive patients.
3 A ll patients w ere included. T est for hom ogeneity: Q = 47.74, d .f.= 22, p = 0.001.
4A11 patients included, but 4 datasets w ith ex cessiv e am ounts o f m issin g data w ere excluded. T est for
hom ogeneity: Q = 4 5 .1 2 , d .f.= 18, p < 0.001.
5S ix datasets w ith n on -in vasive patients only: G rossm an, L iukkonen, Schm itz-D rager, T hom as, V ollm er, Zlotta.
Test for hom ogeneity: Q = 5.83, d.f.= 5, p=0.32.
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36
higher chance of progressing within the first five years following diagnosis of
bladder cancer, although not all of them were significant (Table 7 and Figure 4).
Five of the datasets showed quite the opposite effect, where having altered p53
expression actually benefited the patients even though none of them achieved
statistical significance at the a=0.05 level.
Tests for homogeneity were again used to examine the possibility of pooling
the individual HR estimates. For the overall estimate that includes all patients (both
non-invasive and invasive), there was a significant lack of homogeneity among the
individual HR estimates (Q=47.74, d.f.=22, p=0.001). Therefore, the individual HRs
better reflect the true association of p53 and time-to-progression. As four of the IPD
datasets (Bassi, Gasser, Qureshi, and Wu) had large amounts of missing data, a
separate overall HR was computed although it was not truly representative as the test
for homogeneity was significant (Q=45.12, d.f.=18, p<0.001). On the other hand,
the individual HRs of the six studies including only non-invasive patients were
appropriately combined (Q=5.83, d.f.=5, p=0.32) and showed a statistically
significant increased risk of progression in p53-positive patients (HR 2.31, 95% Cl
1.54 to 3.47).
All 25 groups examined the secondary endpoint of survival and provided
data. Information was available for 3,370 patients. 974 (29%) of the patients died
(Table 8). As with the time-to-progression data, a stratified log-rank test (stratifying
by institution) was performed and showed a statistically significant correlation
between p53 and survival (log-rank j 2 =43.70, d .f=1, p<0.001). Yet, there was no
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37
B assi |_
Burkhard (-
C assetta i-
Furihata |__________
Gardiner |_________ ,
Barbareschi
I —
H
G asser
G rossm an |—
Jahnson ( _____ ,
K akehi |__
L ipponen
Liukkonnen
Qureshi i —
S chm itz-D rager
Tetu |_________
T hom as |----------
U chida |----------------
U nderw ood
V ollm er |____
Z lotta i-
P opov |-
_l O verall (n on -in vasive)
♦O verall (all patients)
♦♦O verall (all patients)
r—i
-4
InHR
Fig. 4. Estim ated H R (In scale) plot o f tim e-to-progression IPD. (O verall (non-invasive): O verall InHR
for n on -in vasive patients; ♦O verall (all patients): all patients exclu d in g 5 studies w ith ex cessiv e am ounts
o f m issin g data; ♦♦O verall: all patients/all studies.)
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38
Table 8. Summary of IPD Results with Survival as Endpoint
__________Patient Status (%)__________
Source Dead Alive Missing HR 95% Cl
Barbareschi 2 (2) 100 (98) 0
(0)
2.16 ( 0.13 - 34.80 )
Bassi 31 (20) 122 (80) 0
(0)
2.09 ( 0.98 - 4.44 )
Burkhard 23 (68) 9 (2 6 ) 2
(6)
0.59 ( 0.20 - 1.74 )
Cassetta 19 (12) 144 (88) 1
(0)
2.99 ( 1.20 - 7.44 )
Furihata 39 (30) 90 (70) 0
(0)
1.20 ( 0.64 - 2.26 )
Gardiner1 23 (26) 11 (13) 54 (61) 0.71 ( 0.31 - 1.63 )
Gasser 175 (35) 296 (59) 31
(6)
1.60 ( 1.18 - 2.17 )
Grossman2 17 (38) 28 (62) 0
(0)
1.00 ( 0.38 - 2.63 )
Jahnson 109 (71) 45 (29) 0
(9)
1.16 ( 0.79 - 1.69 )
Kakehi 13 (16) 63 (78) 4
(5)
2.63 ( 0.81 - 8.56 )
Leissner1 67 (40) 47 (28) 52
(31)
1.31 ( 0.81 - 2.13 )
Lipponen 90 (43) 121 (57) 0
(0)
1.52 ( 0.94 - 2.46 )
Liukkonnen 32 (15) 173 (84) 2
(1)
1.33 ( 0.66 - 2.70 )
Nakopoulou 47 (47) 52 (53) 0
(0)
1.94 ( 1.08 - 3.50 )
Popov 42 (38) 69 (62) 1
(1)
3.38 ( 1.77 - 6.43 )
Qureshi 37 (26) 106 (74) 0
(0)
1.85 ( 0.94 - 3.64 )
2
Schmitz-Drager 7 (11) 54 (89) 0
(0)
0.26 ( 0.03 - 2.12 )
Tetu 74 (20) 294 (80) 1
(0)
1.91 ( 1.20 - 3.02 )
Thomas2 16 (70) 7 (30) 0
(0)
1.21 ( 0.45 - 3.22 )
Uchida 8 (14) 49 (86) 0
(0)
1.46 ( 0.35 - 6.13 )
Underwood1 24 (28) 9 (1 1 ) 52 (61) 1.84 ( 0.80 - 4.19 )
1 7 * 1,2
Vet
3 (7) 8 (1 9 ) 31 (74) 0.57 ( 0.05 - 6.32 )
Vollmer2 19 (10) 167 (89) 2
(1)
1.74 ( 0.70 - 4.31 )
Wu 56 (51) 53 (49) 0
(0)
1.59 ( 0.92 - 2.73 )
Zlotta1 - 2 1 (2) 8 (17) 38 (81) 2.12E-08 ( n/e - n/e )
Overall3 974 (29) 2125 (63) 271
(8)
1.53 ( 1.35 - 1.75 )
Overall4 856 (29) 2042 (69) 44
(2)
1.58 ( 1.38 - 1.82 )
Overall5 95 (15) 445 (73) 73 (12) 1.22 ( 0.80 - 1.85 )
Overall6 91 (17) 429 (82) 4
(1)
1.23 ( 0.80 - 1.88 )
n/e: N o t estim able due to very large variance.
’Dataset w ith e x c e ssiv e am ounts o f m issin g data.
2Dataset contributes to overall H R estim ate for non-invasive patients.
3A1I patients w ere included. T est for hom ogeneity: Q = 25.43, d .f.= 24, p=0.38.
4A11 patients included, but fiv e datasets w ith ex cessiv e am ounts o f m issin g data w ere excluded. T est for
hom ogeneity: Q = 2 0 .7 1 , d .f.= 1 9 , p = 0.35.
5O verall H R estim ate for n on -in vasive patients. S even datasets w ith non-invasive patients only: G rossm an,
Liukkonen, Schm itz-D rager, T hom as, V et, V ollm er, Zlotta. T est for hom ogeneity: Q = 2.94, d .f.= 6, p=0.82.
6O verall H R estim ate for n on -in vasive patients exclu d in g five studies w ith large am ounts o f m issin g data. Test
for hom ogeneity: Q = 2 .8 9 , d .f.= 4, p = 0.58.
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39
significant association when patients were subdivided by histological classification
(non-invasive: log-rank %2 =1.43, d.f.=l, p=0.23; invasive (Wu): log-rank x 2 =2.88,
d.f=1, p=0.09).
As none of the tests for homogeneity were significant at the a=0.05 level
(Table 8), four different pooled HR estimates were estimated. Two pooled estimates
were formed from datasets that included both non-invasive and invasive patients,
although the second overall estimate excludes the estimates from five datasets
(Gardiner, Leissner, Underwood, Vet, and Zlotta) with large amounts of missing
data. The third and fourth overall HRs shown in Table 8 are for those studies that
used non-muscle invasive patients only, with the fourth overall HR again excluding
the Vet and Zlotta studies. Once again, p53-positive patients were shown to pose a
significantly greater risk of death by 53% compared to p53-negative patients (HR
1.53, 95% Cl 1.35 to 1.75). Increased risk of death due to p53-positivity was also
seen in non-invasive patients; however, the result was not significant (HR 1.22, 95%
Cl 0.80 to 1.85; Table 8 and Figure 5).
Comparison o f the Published Data and IPD Results
Three of the original 38 published works examined the association of p53 and
time-to-progression, and provided Kaplan-Meier plots in the final publications;
however, only two groups (Grossman and Schmitz-Drager) provided IPD.
Comparisons of the estimated HRs are presented graphically in Figure 6. Upon
examination, it is clear that the HRs calculated for both studies using the Parmar
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40
V et h
-4 -3
Bassi
Burkhardi-
Cassetta
Furihata i ------
Gardiner |________ ._ _
Grossm an t-
Jahnson t-
Kakehi i-
Leissner i-
Lipponen t
Liukkonnen i ------
N akopoulou
Qureshi \ .
Thom as h
U chidai— .
U nderw ood
V ollm eri-
Wu
O verall 1 i-
O verall 2 i-
h Gasser
—i
H PopOV
1
_i Schm itz-D rager
, -------1 Tetu
1
H
H
Overall 3
O verall 4
-2 0
InHR
Fig. 5. Estim ated H R (In scale) plot o f survival IPD. (O verall 1: O verall InHR for n on -in vasive patients;
O verall 2: n on -in vasive patients; O verall 3: all patients exclu d in g 5 studies w ith e x cessiv e am ounts o f
m issin g data; O verall 4: all patients/all studies.)
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41
method of reconstructing the data from the Kaplan-Meier curves, are slightly less
than those obtained from the IPD. Nevertheless, p53 confers a greater increased in
risk of progression, although the Grossman estimates did not achieve statistical
significance. These estimates are consistent with the results presented in the original
publications, in terms of the effect of p53 and statistical significance.
However, such consistency is not seen quite as well when survival/cancer-
specific death was of interest. Sixteen of the original 38 studies examined the
IPD HR
Estimates
l
0-----------------i---------------- 1------------------- ■ i — — i
1.5 2 2.5 3 3.5 4
Publication Data HR Estimates
Author_______________ HR*__________ 95% Cl______________ HR**____________ 95% Cl________
Grossman 3.18 ( 0.75 - 13.52 ) 3.54 ( 0.76 - 16.41 )
Schmitz-Drager 2.72 ( 1.18 - 6.24 ) 3.22 ( 1.39 - 7.46 )
Fig. 6. C om parison o f T im e-to-Progression H R Estim ates. (*H azards R atio estim ated from Published Data,
**H azards R atio estim ated from IPD )
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42
association between p53 and some form of survival (Table 1) and provided Kaplan-
Meier curves. In most cases, the Parmar method produced HR estimates that were
larger than the estimates based on the IPD (Figure 7). In two studies (Qureshi and
IPD HR
Estim ates
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.0 0.5 1.0 1.5 2.0 2.5
Publication Data H R Estimates
3.0 3.5
Author HR* 95% Cl HR** 95% Cl
Furihata 1 .5 2 ( 0 .4 5 - 5 .1 6 ) 1 .2 0 ( 0 .6 4 - 2 .2 6 )
Jahnson 1 .1 2 ( 0 .7 5 - 1 .6 8 ) 1 .1 6 ( 0 .7 9 - 1 .6 9 )
Lipponen 1 .7 8 ( 0 .9 2 - 3 .4 4 ) 1 .5 2 ( 0 .9 4 - 2 .4 6 )
Nakopoulou 1 .6 3 ( 0 .7 4 - 3 .5 8 ) 1 .9 4 ( 1 .0 8 - 3 .5 0 )
Popov 2 .6 1 ( 0 .6 5 - 1 0 .4 3 ) 3 .3 8 ( 1 .7 7 - 6 .4 3 )
Qureshi 0 .7 7 ( 0 .3 6 - 1 .6 7 ) 1 .8 5 ( 0 .9 4 - 3 .6 4 )
Thomas 1 .5 2 ( 0 .4 3 - 5 .4 1 ) 1.21 ( 0 .4 5 - 3 .2 2 )
Uchida 1 .9 6 ( 0 .5 3 - 7 .2 4 ) 1 .4 6 ( 0 .3 5 - 6 .1 3 )
Underwood 2 .3 6 ( 0 .9 5 - 5 .8 7 ) 1 .8 4 ( 0 .8 0 - 4 .1 9 )
Vet 2 .9 9 ( 1 .0 5 - 8 .5 1 ) 0 .5 7 ( 0 .0 5 - 6 .3 2 )
Wu 2 .3 1 ( 0 .2 3 - 2 2 .9 3 ) 1 .5 9 ( 0 .9 2 - 2 .7 3 )
Fig. 7. Comparison o f Survival HR Estimates. (*Hazards Ratio estimated from Published Data,
**Hazards Ratio estimated from IPD)
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43
Vet), the effect of p53 differs. For the Qureshi study, the HR estimated from the
publication data showed that p53 provided a protective effect (HR 0.77), while the
IPD HR obtained from the Cox model showed the opposite—an 85% increase (HR
1.85) in death for p53-positive individuals. Referring back to the results of the
original publication, it was shown that p53 had a protective effect, even though it
was not statistically significant (Table 1). For the Vet study, the publication data HR
estimate showed a statistically significant detrimental effect of p53 (HR 2.99, Figure
7), but the IPD HR suggested a protective effect (HR 0.57). Looking back to the
results of the original publication, P5 3-positive patients had a greater chance of
dying. The direction of the HR estimates based on the IPD for the Qureshi and Vet
studies were inconsistent with the published results. On the other hand, the HRs
estimated from the publication data were consistent with the results presented in the
original publications in terms of showing whether or not p53 contributed to greater
risk of death. However, the statistical significance of some of the publication data
estimates was different from what had originally been reported, which indicated a
potential problem with precision.
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44
Discussion
The purpose of this study was to examine the possible prognostic role of p53
in bladder cancer patients. Analyzed univariately, that is, not adjusting for other
factors such as stage and grade of the tumor, p53 was statistically significantly
associated with prognosis. For the most part, pooled estimates of the HR (from both
the publication data and IPD) showed significant increases in the risk of recurrence,
progression, and death whether examining non-invasive and invasive patients
collectively, or by subgroups. The method proposed by Parmar, which attempts to
simulate the original follow-up patient data from Kaplan-Meier survival curves, was
used to extract summary statistics from the publications. The Parmar estimates were
compared to estimates computed from IPD provided by the respective institutions.
Parmar’s method appeared to correctly produce HR estimates that reflected the effect
of p53 in patients, but appeared to lack precision when those results were compared
with the IPD estimates.
p53 Findings
With regards to the association of p53 and prognosis in bladder cancer
patients, this study’s findings are quite encouraging as the statistically significant
results of the stratified log-rank tests and estimates of the pooled HR are consistent
with the positive results reported in some of the earliest investigations and most
recent studies (Sarkis et al. 1993, Esrig et al. 1994, Smith et al. 2003, Chatterjee et al.
2004).
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45
Conflicting results of prior studies may be the product of many factors, but
only a few of those that would perhaps have had the greatest impact on the results
will be discussed here. First, it appears that some of the individual studies may have
lacked the statistical power to detect differences between p53-positive and -negative
patients due to inadequate sample size.
Of course, the problem of small sample sizes cannot solely account for the
inconsistencies, as there was quite a wide range in the sample sizes of the various
studies (Table 1). Lab techniques differed somewhat among the institutions and the
cut-points used to determine p53 status varied as well. But perhaps of greater
importance is that the original investigators utilized two different methods to detect
p53 mutations—IHC and PCR-SSCP. Different methods used to detect p53
mutations certainly have the potential of encountering problems with false-
positives/negatives. Previous studies have shown that when IHC and genetic
analyses were performed for each tumor specimen, inconsistent results were seen:
IHC might have shown positive staining but sequence analysis of the gene would
have shown no mutation (Sjogren et al. 1996, Shiao et al. 2000). False-
positives/negatives may help to explain why a smaller study consisting of 45 cases
using mutation PCR-SSCP (Vet et al. 1994) showed a significant association, while
the results of a larger study with 83 cases using IHC (Qureshi et al. 1999) were non
significant. The use of two different methods is a contributing factor to some of the
inconsistencies between studies.
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46
Another contributing factor, particularly among studies using IHC to detect
p53 mutations, was the use of different antibodies. Antibodies recognize mutations
within different locations of the protein and may have more success binding to a
protein so the results of two studies each using different antibodies may differ. For
example, Zhang compared four antibodies (CM1, pAbl801, D07, and DOl) and
found that each one detected different amounts p53 staining (Zhang 1999).
Ultimately, Zhang found that p53 accumulation was an independent predictor of
patient prognosis when using CM1 or DOl, while staining with D07 or pAbl801
were not. Unfortunately, no single antibody has been chosen to be the “gold
standard" and until some standard is established, it will continue to contribute to the
discrepancies among studies.
Finally, the variety of surgeries performed and treatment regimens given (or
not given) to patients may have accounted for some of the inconsistent associations
reported. The surgical procedure and the choice of therapeutic treatment may have
changed the patients’ probabilities of progressing or dying. There is the possibility
that a study in which patients received aggressive surgery and treatment regimens
shows a modest or no association, whereas another study that included patients who
received surgery with less aggressive treatment shows a stronger association.
It would certainly not be surprising if at this point the decision to pool the
studies would be questioned, as there appears to be some heterogeneity among them.
Again, it is important to point out that the results of this analysis are consistent with
previous reports, particularly those focusing on non-muscle invasive patients (Sarkis
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47
et al. 1993, Holmang et al. 1995, Smith et al. 2003). It is also important to note that
despite all of the “noise” created by the heterogeneity, patterns were detected that
suggest an association between p53 and prognosis with larger sample sizes.
Heterogeneity should not invalidate the findings of this study, but instead should
encourage further research using large, prospective trials with standardized methods.
Combined Analysis
The Parmar method demonstrated in this study that it was able to extract
summary statistics from the literature and correctly reflected the effects of p53
(based on the publications). However, the precision with which this method
estimates the natural log of the HR and its variance is questionable. Although the
method correctly estimated a HR that shows a detrimental effect of p53 (as compared
with the reported results), the significance of the estimated HR was incorrect in some
cases. For example, while Abdel-Fattah reported a significant p-value of 0.0325
(univariate association, Table 1), the HR estimated by the Parmar method was not
statistically significant as the confidence interval included the value of 1. Part of the
reason for this may have been the choice of intervals used to partition the time axis
of the original KM curves during the data extraction phase of this study.
It appears that the method is quite sensitive to the size of the time intervals
chosen to partition the time axis of the KM curve, especially when few failures or
events occur in the study. One very good example is the Qureshi study (see
Appendix 1 for specific sizes of the intervals used for each study). For the Qureshi
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48
study, when finer intervals were used and the ln(HR) from each of the intervals were
combined, the overall study estimate of the ln(HR) was positive—which translated to
an estimated HR of greater than 1 (detrimental effect of p53) and did not agree with
the published results. However, when wider intervals were used, the overall
estimated ln(HR) became negative, which of course, showed a protective effect
(estimated HR less than 1) of p53 that is consistent with the published results.
This of course, does not suggest that using wider intervals was the solution.
The use of wider intervals was explored in several studies, one being the Furihata
study (Furihata et al. 1993). When wider intervals were used, a ln(HR) of 0.707 (HR
2.01—see Appendix 1 calculations) was estimated. This is larger than the originally
estimated HR of 1.52 (Table 3) using the finer intervals and the even larger than the
estimate of 1.20 based on the IPD (Table 8). The choices of interval sizes chosen for
this study were based on the suggestion of Parmar to prevent event rates in a
particular interval to exceed 20% at the beginning of the interval. Just based on this
example, it is clear that the widths of the intervals chosen impact the estimate,
although it is not possible to make generalizations regarding the direction or
magnitude of the impact.
Also contributing to the method’s precision problem is the fact that the
method assumes constant censoring across the time intervals. Of course, this may
not be the case for every study and certainly did not appear to be true for all of the
individual studies used in this analysis. Such an assumption would have an effect on
the variance estimate, which in turn, affects the ln(HR) estimate. Further research
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49
will be needed to determine the effect that this assumption has on the estimates.
What would also be of use is to compare the results of this method to the more
traditional method of directly estimating the log HR and its variance by calculating
the observed and expected number of events for each group.
With regards to the IPD analysis, some of the HR estimates were different
from the HR estimated by the Parmar method, as well as to the results reported in the
original publications. It was mentioned earlier in the results section that several of
the IPD estimates were quite different from the published results, particularly the Vet
and Qureshi studies (Figure 7). One possible explanation for some of the variations
is that different sets of patients were used or excluded in the original analyses for
reasons that were often unclear in the publications. For example, the published Vet
study included both non-invasive and invasive patients (Vet et al. 1995), while the
IPD submitted by the group included only 42 non-invasive patients (Table 6). A
similar situation occurred with the Qureshi study (Qureshi et al. 1999), in which the
publication included only 83 muscle-invasive patients (Table 1), while the IPD
submitted included both non-invasive and invasive patients (Table 6). As the dataset
of IPD used in this study was limited and did not include all pertinent information
necessary for including or excluding patients, such sub-grouping could not be
achieved in this analysis. This was also the case for several of the other studies
included in this analysis and may have contributed to some of the inconsistencies
between estimates obtained from the publication data and IPD.
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50
Another possible explanation for the differences in publication data and IPD
estimates may lie in the fact that all patients were censored after 60 months in the
IPD analysis. Follow-up data for many of these studies exceeded this limit and
complete follow-up data were used in the original analyses. It is unknown as to how
the results would change if complete follow-up data were used since this analysis
focused on the first 5-years following diagnosis of bladder cancer. Again, that is left
to further investigation. It would have also been helpful, if more of the original
publications provided KM plots from which ln(HR) could be estimated and then
compared with the IPD. Indeed, differences in the standards of reporting results
presented challenges to this analysis.
Conclusions
During the last several decades, the prognostic relevance of p53 in bladder
cancer has been controversial. A combined analysis using data from studies that
examined the association between p53 and bladder cancer outcomes was undertaken
to determine if any consistent patterns emerged from conflicting results reported in
the original publications. With larger sample sizes, patterns have emerged that
suggest an association does indeed exist.
A method developed by Parmar was used to estimate HR from the
publications that were subsequently compared to HR estimated using the IPD.
However, the estimates obtained via this method were inconsistent with some of the
IPD estimates. Surprisingly, the results of the IPD analysis were inconsistent with
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51
results from the original publications, which may have resulted from changes in the
data submitted.
Again, this combined analysis suggests an association between p53 and
prognosis in patients with transitional cell carcinomas of the urinary bladder.
Nevertheless, large, well-designed, prospective studies examining the association are
needed to confirm these results. Much of the motivation behind this project was to
further encourage the idea that an association exists and to suggest directions for
future research in bladder cancer, as well as in the methodologies of meta-analyses.
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52
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Appendix 1
HR Calculations from Publication Data
Microsoft Excel 2002 (Microsoft Corp., Seattle, WA) was used to calculate
HR estimates from the publication data. The tables are listed in alphabetical order by
the first author’s last name. In some cases, multiple ln(HR) estimates were
calculated for each study because: patients were subdivided by stage and/or grade of
tumor (or extent of disease) and analyzed separately, or different endpoints were
examined.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
Abdel Fattah 1998 Overall Surviviai
p53-
Fmin -
Fmax =
1
84
month
month
p 5 3 -: n -
p53+: n *
23
29
p53+ Calculating the overall ln(HR(t)) and its variance
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t) ln(Hri(t)) var[ln(HR(t)) Overall ln(Hr(t))
Reciprocal
o f variance
o f overall
ln(HR(t))
0-3 0 3 100 96 23 0.27711 22.7229 0.92 100 87 29 0.3494 28.6506 3.77 1.178655 1.27329675 0.925671882 0.78536288
3-6 3 6 96 92 21.8029 0.40376 21.3991 0.90845 87 82 24.8806 0.46075 24.4199 1.42992 0.32158362 1.71243025 0.187793707 0.58396539
6-9 6 9 92 92 20.4907 0.39405 20.0966 IE-06 82 72 22.9899 0.44211 22.5478 2.80365 34.7313466 1000000.26 1.47313E-05 IE-06
9-12 9 12 92 87 20.0966 0.40193 19.6947 1.09221 72 61 19.7442 0.39488 19.3493 3.01647 1.03357982 1.14463323 0.902979045 0.8736423
12-15 12 15 87 87 18.6025 0.38755 18.2149 IE-06 61 54 16.3328 0.34027 15.9925 1.87426 14.5738421 1000000.42 1.45738E-05 IE-06
15-18 15 18 87 87 18.2149 0.39598 17.819 IE-06 54 47 14.1183 0.30692 13.8114 1.83015 14.6746785 1000000.42 1.46747E-05 IE-06
18-21 18 21 87 87 17.819 0.40498 17.414 IE-06 47 43 11.9812 0.2723 11.7089 1.01968 14.2319202 1000000.84 1.42319E-05 IE-06
21-24 21 24 87 69 17.414 0.41462 16.9994 3.60289 43 39 10.6892 0.25451 10.4347 0.99435 -0.79936939 1.12857929 -0.708297063 0.88606978
24-30 24 30 69 64 13.3965 0.66982 12.7266 0.97076 39 39 9.44039 0.47202 8.96837 IE-06 -13 4358391 1000000.84 -I.34358E-05 IE-06
30-36 30 36 64 64 11.7559 0.6531 11.1028 IE-06 39 39 8.96837 0.49824 8.47013 IE-06 0.27065037 1999999.79 1.35325E-07 5E-07
36-42 36 42 64 64 11.1028 0.69392 10.4089 IE-06 39 31 8.47012 0.52938 7.94074 1.73746 14.638586 1000000.35 1.46386E-05 IE-06
42-48 42 48 64 64 10.4089 0.74349 9.66537 IE-06 31 31 6.20328 0.44309 5.76019 IE-06 0.51757876 1999999.72 2.58789E-07 5E-07
48-54 48 54 64 59 9.66537 0.80545 8.85992 0.75511 31 31 5.76019 0.48002 5.28017 IE-06 -13.0170355 1000001.02 -1.3017E-05 IE-06
54-60 54 60 59 48 8.10481 0.81048 7.29433 1.51107 31 31 5.28017 0.52802 4.75215 IE-06 -13.7998269 1000000.31 -1.37998E-05 IE-06
Censorine
If t_s < Fmin and t_e < Fmin then number censored = 0
Will need to aDnlv the orecedine rule startine at interval:
Will not occur in this study
1.308180562
Overall ln(HR(i))
Variance(i):
3.12904935
0.41807604
0.31958588
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
Will not occur in this study
Will not occur in this study
Will not occur in this study
Using wider intervals
Abdel Fattah, 1998 Overall Survival Fmin =
Fmax =
1 month
84 month
p 5 3 -: n =
p53+: n =
23
29
P 5 3 - Calculating the overall ln(HR(t)) and its variance
Time Interval s e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t) ln(Hri(t)) var[ln(HR(t)) Overall ln(Hr(t))
Reciprocal
o f variance
o f overall
ln(HR(t))
0-6 0 6 100 92 23 0.69277 22.3072 1.84 100 82 29 0.87349 28.1265 5.22 0.81093022 0.65466697 1.238691197 1.52749419
6-12 6 12 92 87 20.4672 0.7872 19.68 1.11235 82 61 22.9065 0.88102 22.0255 5.8663 1.55015386 0.97324841 1.592762792 1.02748691
12-18 12 IS 87 87 18.5677 0.77365 17.794 IE-06 61 47 16.1592 0.6733 15.4859 3.70867 15.2651164 1000000.15 1.52651E-05 IE-06
18-24 18 24 87 69 17.794 0.80882 16.9852 3.68152 47 39 11.7772 0.53533 11.2419 2.00463 -0.1951697 0.62264334 -0.313453442 1.60605587
24-36 24 36 69 64 13.3037 1.33037 11.9733 0.96403 39 39 9.23726 0.92373 8.31353 IE-06 -13.4140872 1000000.83 -1.34141E-05 IE-06
36-60 36 60 64 48 11.0093 2.75232 8.25696 2.75232 39 31 8.31353 2.07838 6.23515 1.70534 -0.19782574 0.66823216 -0.296043436 1.4964859
Censorine
If t s < Fmin and t e < Fmin then number censored = 0
Will need to aoDlv the nrecedine rule startine at interval:
Will not occur in this study
2.221958962
Overall ln(HR(i)):
Variancefi):
5.65752488
0.392744
0.17675574
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s - Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
Will not occur in this study
Will not occur in this study
Will not occur in this study
O n
to
Casetta, 1997 Tim e t o recurrence, Super only Fmin = 3 month p 5 3 -: n * 39
Fmax = 7 2 month p53+: n = 20
p 5 3 - p 5 3 + C alculating the o verall ln(H R (t)) and its v a ria n c e
R e c ip ro c a l
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
Furihata, 1993 Overall survival, Super/Inv Fmin =
Fmax =
1 month
12 0 month
p 5 3 -: n =
p53+: n =
36
26
p 5 3 + Calculating the overall ln(HR(t)) and its variance
Reciprocal
o f variance
o f overall
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t) ln(Hn(t)) var[ln(HR(t))' Overall ln(Hr(t)) ln(HR(t))
0-3 0 3 100 96 36 0.30252 35.6975 1.4279 100 96 26 0.21849 25.7815 1.03126 0 1.60321599 0 0.62374627
3-6 3 6 96 94 34.2696 0.43935 33.8302 0.7048 96 89 24.7503 0.31731 24.4329 1.78157 1.252762968 1.9096649 0.656011936 0.52365208
6-9 6 9 94 94 33.1254 0.43586 32.6896 IE-06 89 89 22.6514 0.29804 22.3533 IE-06 0.380080813 1999999.92 1.9004E-07 5E-07
9-12 9 12 94 92 32.6896 0.44175 32.2478 0.68612 89 89 22.3533 0.30207 22.0513 IE-06 -13.0587325 1000001.38 -1.30587E-05 IE-06
12-15 12 15 92 92 31.5617 0.43836 31.1233 IE-06 89 77 22.0513 0.30627 21.745 2.93191 15.24973874 1000000.26 1.52497E-05 IE-06
15-18 15 18 92 90 31.1233 0.44462 30.6787 0.66693 77 73 18.8131 0.26876 18.5443 0.96334 0.871130336 2.45094378 0.355426486 0.40800609
18-21 18 21 90 84 30.0118 0.44135 29.5704 1.97136 73 69 17.581 0.25854 17.3224 0.94917 -0.19611488 1.46926424 -0.133478291 0.68061277
21-24 21 24 84 82 27.5991 0.41817 27.1809 0.64716 69 66 16.3733 0.24808 16.1252 0.70109 0.602175402 2.87273752 0.209617272 0.34810002
24-30 24 30 82 82 26.5337 0.82918 25.7046 IE-06 66 66 15.4241 0.482 14.9421 IE-06 0.542486933 1999999.89 2.71243E-07 5E-07
30-36 30 36 82 82 25.7046 0.85682 24.8477 IE-06 66 66 14.9421 0.49807 14.444 IE-06 0.542486961 1999999.89 2.71243E-07 5E-07
36-42 36 42 82 82 24.8477 0.88742 23.9603 IE-06 66 61 14.444 0.51586 13.9282 1.05516 14.411693 1000000.83 1.44117E-05 IE-06
42-48 42 48 82 82 23.9603 0.92155 23.0388 IE-06 61 57 12.873 0.49512 12.3779 0.81166 14.22810957 1000001.11 1.42281E-05 IE-06
48-54 48 54 82 82 23.0388 0.95995 22.0788 IE-06 57 57 11.5662 0.48193 11.0843 IE-06 0.689090379 1999999.86 3.44545E-07 5E-07
54-60 54 60 82 82 22.0788 1.00358 21.0752 IE-06 57 51 11.0843 0.50383 10.5805 1.11373 14.61231756 1000000.76 1.46123E-05 IE-06
Censoring
If t_s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
Will need to apply the preceding rule starting at interval:
Will not occur in this study
Occurs in 1st interval
Will not occur in this study
Will not occur in this study
1.087623924 2.58412424
Overall ln(HR(i»: 0.42088685
VarianceQ): 0.3869783
using wider intervals
Furihata, 1993 Overall survival, Super/Inv Fmin ~
Fmax =
1 month
1 2 0 month
p 5 3 -: n =
p53+: n =
36
26
P53- Calculating the overall ln(HR(t)) and its v
Time Interval t s t e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t) ln(Hri(t)) var[ln(HR(t)) Overall ln(Hr(t))
Reciprocal
o f variance
o f overall
ln(HR(t))
0-6 0 6 100 94 36 0.7563 35.2437 2.11462 100 89 26 0.54622 25.4538 2.79992 0.606135804 0.76239061 0.795046265 1.31166359
6-12 6 12 94 92 33.1291 0.87182 32.2573 0.68632 89 89 22.6539 0.59615 22.0577 IE-06 -13.0590252 1000001.38 -1 3059E-05 IE-06
12-18 12 18 92 90 31.5709 0.87697 30.694 0.66726 89 73 22.0577 0.61271 21.445 3.85528 2.112593749 1.67883995 1.25836519 0.5956494
18-36 18 36 90 82 30.0267 2.64941 27.3773 2.43354 73 66 17.5897 1.55203 16.0377 1.53786 0.075818837 0.96229906 0.078789266 1.03917798
36-60 36 60 82 82 24.9438 3.56339 21.3804 IE-06 66 51 14.4998 2.0714 12.4284 2.82464 15.39637867 1000000.23 1.53964E-05 IE-06
Censoring
If t s < Fmin and t e < Fmin then number censored * 0
Will need to annlv the Dreceding rule starting at interval:
Will not occur in this study
2,132203058 2.94649297
Overall ln(HR(i)): 0.72364098
Variance(i): 0.33938652
If t_s < Fmin and Fmin < - t_e <= Fmax then set t_s - Fmin
If t_s < Fmin and t_e > Fmax, then set t_s - Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
Occurs in 1 st interval
Will not occur in this study
Will not occur in this study
O N
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
Gao, 2000 Overall Survival, Super/Inv Fmin = 1 month p 5 3 -: n = 37
Fmax = 150 month p53+: n = 50
__________________________ p53-_________________________ __________________________ p53+
Time Interval t_s t e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t)
0-3 0 3 100 100 37 0.24832 36.7517 IE-06 100 100 50 0.33557 49.6644 IE-06
3-6 3 6 100 100 36.7517 0.37502 36.3767 IE-06 100 94 49.6644 0.50678 49.1576 2.94946
6-9 6 9 100 100 36.3767 0.37892 35.9977 IE-06 94 86 46.2082 0.48134 45.7269 3.89165
9-12 9 12 100 97 35.9977 0.38295 35.6148 1.06844 86 80 41.8352 0.44506 41.3902 2.88769
12-15 12 15 97 94 34.5463 0.3755 34.1708 1.05683 80 78 38.5025 0.41851 38.084 0.9521
15-18 15 18 94 94 33.114 0.36793 32.7461 IE-06 78 77 37.1319 0.41258 36.7193 0.47076
18-21 18 21 94 94 32.7461 0.37211 32.374 IE-06 77 75 36.2485 0.41192 35.8366 0.93082
21-24 21 24 94 90 32.374 0.37644 31.9975 1.3616 75 74 34.9058 0.40588 34.4999 0.46
24-30 24 30 90 86 30.6359 0.72943 29.9065 1.32918 74 68 34.0399 0.81047 33.2294 2.69428
30-36 30 36 86 86 28.5773 0.71443 27.8629 IE-06 68 65 30.5352 0.76338 29.7718 1.31346
36-42 36 42 86 82 27.8629 0.73323 27.1296 1.26184 65 62 28.4583 0.7489 27.7094 1.2789
42-48 42 48 82 82 25.8678 0.71855 25.1493 IE-06 62 62 26.4305 0.73418 25.6963 IE-06
48-54 48 54 82 71 25.1492 0.73968 24,4096 3.27445 62 62 25.6963 0.75577 24.9406 IE-06
54-60 54 60 71 71 21.1351 0.66047 20.4746 IE-06 62 62 24.9406 0.77939 24.1612 IE-06
Censoring
IF t_s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin < - t_e <= Fmax then set t j = Fmin
Ift_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
Will need to apply the preceding rule startin g a t interval:
Will not occur in this study
Occurs in first interval
Will not occur in this study
Occurs in last interval
Calculating the overall ln(HR(t)) and its variance
Reciprocal
o f variance
o f overall
ln(Hri(t)) var[ln(HR(t)) Overall ln(Hr(t)) ln(HR(t))
-0.30110509 1999999,95 -1 50553E-07 5E-07
14.5960272 1000000.29 1.4596E-05 IE-06
14.9351133 1000000.21 1.493 51 E-05 IE-06
0.84397007 1.23000062 0.686154185 0.81300772
-0.21278076 1.94101449 -0.109623481 0 51519451
12.9475847 1000002.07 1.29476E-05 IE-06
13.6422065 1000001.02 1.36422E-05 IE-06
-1.16048769 2.84811288 -0.407458462 0.35110968
0.60120969 1.0599706 0.567194682 0.9434224
14.0219104 1000000.69 1.40219E-05 IE-06
-0.00772205 1.50146655 -0.005143002 0.6660155
-0.02152039 1999999.92 -1.07602E-08 5E-07
-15.0231821 1000000.22 -1.50232E-05 IE-06
-0.16555972
1999999 91
-8.27799E-08 5E-07
0.731178798 3.28875731
Overall ln(H R(i)); 0.22232677
V ariance(i): 0.30406622
C \
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
G rossm an, 1998 Time to progression, Super only
P53-
Fm in =
F m ax =
6 m onth
144 month
p 5 3 -: n =
p53+: n =
19
26
p53+ Calculating the overall ln(HR(t)) and its variance
Reciprocal
o f variance
o f overall
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t) ln(Hri(t)) var[ln(HR(t))' Overall ln(Hr(t)) ln(HR(t))
0-3 0 3 100 100 19 0 19 IE-06 100 100 26 0 26 IE-06 -0.31365756 1999999.91 -1.56829E-07 5E-07
3-6 3 6 100 100 19 0 19 IE-06 100 85 26 0 26 3.9 14.8628295 1000000.17 1.48628E-05 IE-06
6-9 6 9 100 100 19 0.20652 18.7935 IE-06 85 81 22.1 0 24022 21.8598 1,0287 13.6926635 1000000.87 1.36927E-05 IE-06
9-12 9 12 100 89 18.7935 0.20882 18.5847 2.04431 81 81 20.8311 0.23146 20.5996 IE-06 -14.6335087 1000000.39 -1.46335E-05 IE-06
12-15 12 15 89 89 16.5403 0.18796 16.3524 IE-06 81 81 20.5996 0.23409 20.3655 IE-06 -0.21947042 1999999.89 -1.09735E-07 5E-07
15-18 15 18 89 89 16.3524 0.19014 16.1622 IE-06 81 81 20.3655 0.23681 20 1287 IE-06 -0.21947043 1999999.89 -1.09735E-07 5E-07
18-21 18 21 89 89 16.1622 0.19241 15.9698 IE-06 81 69 20.1287 0.23963 19.8891 2.94653 14.6766696 1000000.23 1.46767E-05 IE-06
21-24 21 24 89 89 15.9698 0.19475 15.7751 IE-06 69 69 16.9426 0.20662 16.736 IE-06 -0.05912785 1999999.88 -2.95639E-08 5E-07
24-30 24 30 89 89 15.7751 0.39438 15.3807 IE-06 69 65 16.736 0.4184 16.3176 0.94595 13.700812 1000000.93 1 37008E-05 IE-06
30-36 30 36 89 89 15.3807 0.40476 14.9759 IE-06 65 65 15.3716 0.40452 14.9671 IE-06 0.00059131 1999999.87 2.95657E-10 5E-07
36-42 36 42 89 89 14.9759 0.416 14.5599 IE-06 65 65 14.9671 0.41575 14.5513 IE-06 0.00059131 1999999.86 2.95657E-10 5E-07
42-48 42 48 89 89 14.5599 0.42823 14.1317 IE-06 65 65 14.5513 0.42798 14.1234 IE-06 0.00059131 1999999.86 2.95657E-10 5E-07
48-54 48 54 89 89 14.1317 0.44162 13.6901 IE-06 65 65 14.1234 0.44135 13.682 IE-06 0.00059131 1999999.85 2.95657E-10 5E-07
54-60 54 60 89 89 13.6901 0.45634 13.2338 IE-06 65 65 13.682 0.45607 13.2259 IE-06 0.00059131 1999999.85 2.95657E-10
4.18951E-05
5E-07
9.5E-06
Censoring
If t_s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
Will need to apply the preceding rule starting at interval:
Occurs in first interval
Occurs in second interval
Will not occur in this study
Will not occur in this study
Overall Ju(HR(i»: 4.41000698
Variance(i): 105263.183
Using wider time intervals
Grossman, 1998 Time to progression, Super only
______________ E 5 3 i_
Fmin =
Fmax =
6 month
144 month
p 5 3 -: n *
p53+: n =
19
26
p53+ Calculating the overall ln(HR(t)) and its variance
Reciprocal
o f variance
o f overall
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cn(t) Rn(t) Dri(t) ln(Hri(t)) var[In(HR(t)) Overall ln(Hr(t)) ln(HR(t))
0-30 0 30 100 89 19 1.65217 17.3478 1.90826 100 65 26 2.26087 23.7391 8.3087 1.15745279 0.54462455 2.I2523066I 1.8361273
30-60 30 60 89 89 15.4396 2.03152 13.408 IE-06 65 65 15.4304 2.03032 13.4001 IE-06 0.00059154 1999999.85 2.95771E-10 5E-07
Censoring
If t_s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
Will need to apply the preceding rule starting at interval:
Occurs in first interval
Occurs in second interval
Will not occur in this study
Will not occur in this study
Overall ln(HR(i»: 1.15745247
Variance(i):_______ 0.5446244
Os
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Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
Kakehi, 1998 Overall Survival, LocAdv Fm in =
Fm ax -
7 month
122 month
p 5 3 -: n =
p53+: n =
P 5 3 -
18
14
p53+
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rn(t) Dri(t)
0-3 0 3 100 100 18 0 18 IE-06 100 100 14 0 14 IE-06
3-6 3 6 100 100 18 0 18 IE-06 100 100 14 0 14 IE-06
6-9 6 9 100 100 18 0.15652 17.8435 IE-06 100 100 14 0.12174 13.8783 IE-06
9-12 9 12 100 100 17.8435 0.23686 17.6066 IE-06 100 85 13.8783 0.18422 13.694 2.0541
12-15 12 15 100 100 17.6066 0.24009 17.3665 IE-06 85 85 11.6399 0.15873 11.4812 IE-06
15-18 15 18 100 100 17.3665 0.24346 17.1231 IE-06 85 85 11.4812 0.16095 11.3202 IE-06
18-21 18 21 100 100 17.1231 0.24697 16.8761 IE-06 85 77 11.3202 0.16327 11.157 1.05007
21-24 21 24 100 100 16.8761 0.25064 16.6255 IE-06 77 68 10.1069 0.1501 9.9568 1.16378
24-30 24 30 100 88 16.6255 0.50894 16.1165 1.93398 68 51 8.79302 0.26917 8.52385 2.13096
30-36 30 36 88 88 14.1825 0.46247 13.7201 IE-06 51 51 6.39289 0.20846 6.18442 IE-06
36-42 36 42 88 88 13.7201 0.47861 13.2415 IE-06 51 41 6.18442 0.21574 5.96869 1.17033
42-48 42 48 88 88 13.2415 0.49655 12.7449 IE-06 41 41 4.79836 0.17994 4.61842 IE-06
48-54 48 54 88 88 12.7449 0.51669 12.2282 IE-06 41 41 4.61842 0.18723 4.43118 IE-06
54-60 54 60 88 88 12.2282 0.53948 11.6887 IE-06 41 41 4.43118 0.19549 4.23569 IE-06
Censoring
If t_s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
W ill need to apply the preceding ru le startin g a t interval:
Occurs in first 2 intervals
Occurs in 6-9 interval
Will not occur in this study
Will not occur in this study
Calculating the overall ln(HR(t)) and its variance
Reciprocal
o f variance
o f overall
ln(Hri(t)) var[ln(HR(t)) Overall ln(Hr(t)) ln(HR(t))
0 25131443 1999999.87 1.25657E-07 5E-07
0.25131444 1999999.87 1.25657E-07 5E-07
0.25131446 1999999.87 1.25657E-07 5E-07
14.7866653 1000000.36 1.47867E-05 IE-06
0.41383335 1999999.86 2.06917E-07 5E-07
0.41383338 1999999.85 2.06917E-07 5E-07
14.2781992 1000000.8 1.42782E-05 IE-06
14.4798651 1000000.7 1.44799E-05 IE-06
0.73396918 0.80697339 0.909533301 1.23919823
0.79682554 1999999.77 3.98413E-07 5E-07
14.7696224 1000000.61 1.47696E-05 IE-06
1.01507912 1999999.71 5.0754E-07 5E-07
1.01507926 1999999.69 5.0754E-07 5E-07
1.0150794 j 9 9 9 9 9 9 68 5.0754E-07 SE-07
0.909594327 1.23920673
Overall ln(HR(i)>: 0.73401339
V ariance(i): 0.80696786
Using wider intervals
Kakehi, 1998 Overall Survival, LocAdv Fm in *
Fm ax *
7 month
122 month
p 5 3 -: n *
p53+: n =
p53-
18
14
p53+ Calculating the overall ln(H R(t» and its variance
Reciprocal
o f variance
o f overall
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t) In(Hri(t)) var[ln(HR(t)). Overall ln(Hr(t)) ln(HR(t)>
0-12 0 12 100 100 18 0.3913 17.6087 IE-06 100 85 14 0.30435 13.6957 2.05435 14.7867834 1000000.36 1.47868E-05 IE-06
12-24 12 24 100 100 17.6087 1.30151 16.3072 IE-06 85 68 11.6413 0.86044 10.7809 2.15617 14.9976783 1000000.31 1.49977E-05 IE-06
24-36 24 36 100 88 16.3072 2.05612 14.2511 1.71013 68 51 8.62469 1.08746 7.53723 1.88431 0.73396918 0.912606 0.804256354 1.09576312
36-60 36 60 88 88 12.5409 1,7499 10.791 IE-06 51 41 5.65292 0.78878 4.86414 0.95375 14.5649856 1000000.75 1.4565E-05 IE-06
0.804300703 1.09576612
Censoring
If t_s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
W ill need to apply the preceding rule startin g a t interval:
Occurs in first 2 intervals
Occurs in 6-9 interval
Will not occur in this study
Will not occur in this study
Overall ln(H R (i»: 0.73400764
V ariance(i):_______ 0.9126035
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Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
Leissner, 2001 Time to progression, Grd2 pTa only Fmin = 14 month
Fmax = 109 month
______________ £ 5 3 :______________
p 5 3 -: n =
p53+: n =
49
21
p53+ Calculating the overall ln(H R(t» and its variance
Reciprocal
o f variance
o f overall
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t) ln(Hri(t)) var[ln(HR(t)) Overall ln(Hr(t)) ln(HR(t))
0-3 0 3 100 96 49 0 49 1.96 100 95 21 0 21 1.05 0.22314355 1 39455782 0.160010254 0.71707317
3-6 3 6 96 96 47.04 0 47.04 IE-06 95 89 19.95 0 19.95 1.26 14.9043914 1000000.72 1 49044E-05 IE-06
6-9 6 9 96 96 47.04 0 47.04 IE-06 89 89 18.69 0 18.69 IE-06 0.92300966 1999999.93 4.61505E-07 5E-07
9-12 9 12 96 96 47.04 0 47.04 IE-06 89 89 18.69 0 18.69 IE-06 0.92300969 1999999.93 4.61505E-07 5E-07
12-15 12 15 96 89 47.04 0.24758 46.7924 3.41195 89 84 18.69 0.09837 18.5916 1.04447 -0.26076041 1 17534925 -0.221857813 0.85081094
15-18 15 18 89 87 43,3805 0.69224 42.6882 0.95929 84 84 17.5472 0.28001 17.2671 IE-06 -12.8688271 1000000.96 -1.28688E-05 IE-06
18-21 18 21 87 87 41.7289 0.68784 41.0411 IE-06 84 84 17.2671 0.28462 16.9825 IE-06 0.88238928 1999999.92 4.41195E-07 5E-07
21-24 21 24 87 87 41.0411 0.69956 40.3415 IE-06 84 84 16.9825 0.28947 16.693 IE-06 0.88238932 1999999.92 4.41195E-07 5E-07
24-30 24 30 87 87 40.3415 1.42382 38.9177 IE-06 84 71 16.693 0.58917 16.1039 2.49227 15.6110927 1000000.31 1.56111E-05 IE-06
30-36 30 36 87 87 38.9177 1.47789 37.4398 IE-06 71 71 13.6116 0.5169 13.0947 IE-06 1.05052625 1999999.9 5.25263E-07 5E-07
36-42 36 42 87 79 37.4398 1.53862 35.9012 3.30126 71 71 13.0947 0.53814 12.5566 IE-06 -13.9592886 1000000.2 -1.39593E-05 IE-06
42-48 42 48 79 79 32.5999 1.4597 31.1402 IE-06 71 57 12.5566 0.56223 11.9943 2.36508 15.6303891 1000000.31 1.56304E-05 IE-06
48-54 48 54 79 68 31.1402 1.53149 29.6088 4.12274 57 57 9.62926 0.47357 9.15569 IE-06 -14.0583335 1000000.1 -1.40583E-05 IE-06
54-60 54 ' 60 68 68 25.486 1.39015 24.0959 IE-06 57 57 9.15569 0.4994 8.65629 IE-06 1.02375465 1999999.84 5.11877E-07 5E-07
-0.061839457 1.56789311
Censoring
I f t_s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin <=* t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s - Fm in and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
Will need to apply the preceding rule starting at interval:
Occurs in first 4 intervals
Occurs in 5th interval
Will not occur in this study
Will not occur in this study
Overall ln(HR(i»: -0.0394411
Variance(i): 0.63779858
with w ider intervals
Leissner, 2001 Time to progression, Grd2 pTa only Fmin — 14 month
Fmax = 109 month
______________ £ 5 3 :______________
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t)
0-6 0 6 100 96 49 0 49 1.96
6-12 6 12 96 96 47.04 0 47.04 IE-06
12-18 12 18 96 87 47.04 0.99032 46.0497 4.31716
18-36 18 36 87 87 41.7325 4.12739 37.6051 IE-06
36-60 36 60 87 68 37.6051 6.18167 31.4235 6.8626
p53- : n =
p53+: n =
49
21
p53+
Censoring
If t_s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
Sri(ts)
100
84
71
Sn(te)
89
89
84
71
57
Rri(ts)
21
18.69
18.69
17.2686
13.1525
Cri(t)
0
0
0.39347
1.70789
2.16206
Rri(t)
21
18.69
18.2965
15.5607
10.9905
Will need to apply the preceding rule starting at interval:
Will not occur in this study
Will not occur in this study
Will not occur in this study
Will not occur in this study
Dri(t)
2.31
IE-06
1.02789
2.40821
2.16714
Calculating the overall ln(HR(t)) and its
Reciprocal
o f variance
o f overall
ln(Hn(t)) var[ln(HR(t)) Overall ln(Hr(t)) ln(HR(t))
1.01160091 0.8750773 1.156013197 1.14275618
0.92300968 1999999.93 4.61505E-07 5E-07
-0.51207484 1.12812533 -0.453916626 0.88642633
15.5767837 1000000.32 1.55768E-05 IE-06
-0.10215341 0.4843448 -0.210910508 2.06464486
0.491202102 4.09382887
Overall ln(HR(i)): 0.11998599
Varianceli): 0.2442701
O
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Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
Nakanishi, 1996 Time to recurrence/mets, Superflnv Fmin =
Fmax ■
1 month
2S8 month
p53-: n -
p53+: n =
106
36
p53+ Calculating the overall ln(HR(t)) and its variance
Time Interval t_s t e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t) ln(Hri(t)) var(ln(HR(t))j Overall ln(Hr(t))
Reciprocal of
variance of
overall
ln(HR(t))
0-3 0 3 100 100 106 0.412451 105.5875 0.000001 100 100 36 0.140078 35.85992 0.000001 1.079920156 1999999.963 5.3996E-07 5E-07
3-6 3 6 100 90 105.5875 0.621103 104.9664 10.49664 100 89 35.85992 0.210941 35.64898 3.921388 0.09531018 0.312702149 0.30479541 3.19793133
6-9 6 9 90 80 94.4698 0.56232 93.90748 10.43416 89 78 31.72759 0.188855 31.53874 3.898046 0.10648348 0.310021965 0.343470762 3.225577905
9-12 9 12 80 77 83.47332 0.502851 82.97046 3.111392 78 61 27.64069 0.16651 27.47418 5.987963 1.759918863 0.439950932 4.000261698 2.27298075
12-15 12 15 77 76 79.85907 0.486946 79.37213 1.030807 61 50 21.48622 0.131014 21.35521 3.850939 2.63082683 1.170364942 2.247868795 0.854434343
15-18 15 18 76 74 78.34132 0.483588 77.85773 2.048888 50 49 17.50427 0.108051 17.39622 0.347924 -0.274436846 3.291930339 -0.083366541 0.303773135
18-21 18 21 74 74 75.80884 0.473805 75.33504 0.000001 49 44 17.04829 0.106552 16.94174 1.728749 15.85507351 1000000.506 1.58551E-05 9.99999E-07
21-24 21 24 74 74 75.33504 0.476804 74.85823 0.000001 44 44 15.21299 0.096285 15.11671 0.000001 1.59979562 1999999.92 7.99898E-07 5E-07
24-30 24 30 74 73 74.85823 0.959721 73.89851 0.998629 44 44 15.1167 0.193804 14.9229 0.000001 -12.21434247 1000000.921 -1.22143E-05 9.99999E-07
30-36 30 36 73 70 72.89988 0.959209 71.94067 2.956466 44 44 14.9229 0.196354 14.72655 0.000001 -13.31331512 1000000.256 -1.33133E-05 1E-06
36-42 36 42 70 70 68.98421 0.932219 68.05199 0.000001 44 31 14.72654 0.199007 14.52754 4.292227 16.81654223 1000000.149 1.68165E-05 1E-06
42-48 42 48 70 70 68.05199 0.945166 67.10682 0.000001 31 31 10.23531 0.142157 10.09315 0.000001 1.894428371 1999999.886 9.47214E-07 5E-07
48-54 48 54 70 70 67.10682 0.958669 66.14815 0.000001 31 31 10.09315 0.144188 9.948965 0.000001 1.894428456 1999999.884 9.47214E-07 5E-07
54-60 54 60 70 69 66.14815 0.972767 65.17538 0.931077 31 31 9.948964 0.146308 9.802655 0.000001 -11.84966861 1000000.957 -1.18497E-05 9.99999E-07
Censoring
If t_s < Fmin and
If t_s < Fmin and
If t_s < Fmin and
If t_s > Fmin and
Nakanishi, 1996
t_e < Fmin then number censored - 0
Fmin <= t_e <= Fmax then sett_s = Fmin
t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
t_e > Fmax, then set t_e = Fmax in (26)
Overall Survival, Super/lnv Fmin = 1
Will need to aoolv the orecedino rule starting at interval:
Will not occur in this study
Occurs in 1st interval
Will not occur in this study
Will not occur in this study
month p53-: n = 109
6.813028652
Overall ln(HR(t)):
Variance:
9.854704463
0.691347841
0.101474377
p53-
p53+: n = 40
p53+ Calculating the overall ln(HR(t)) and its variance
Time Interval t s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t)
0-3 0 3 100 100 109 0.424125 108.5759 0.000001 100 100 40 0.155642 39.84436 0.000001
3-6 3 6 100 100 108.5759 0.638682 107.9372 0.000001 100 97 39.84436 0.234379 39.60998 1.188299
6-9 6 9 100 100 107.9372 0.642483 107.2947 0.000001 97 95 38.42168 0.2287 38.19298 0.787484
9-12 9 12 100 98 107.2947 0.646354 106.6484 2.132967 95 93 37.40549 0.225334 37.18016 0.78274
12-15 12 15 98 95 104.5154 0.637289 103.8781 3.179942 93 90 36.39742 0.221935 36.17548 1.166951
15-18 15 18 95 91 100.6982 0.621594 100.0766 4.21375 90 86 35.00853 0216102 34.79243 1.54633
18-21 18 21 91 90 95.86281 0.599143 95.26367 1.046854 86 77 33.2461 0.207788 33.03831 3.457498
21-24 21 24 90 87 94.21682 0.596309 93.62051 3.120684 77 70 29.58082 0.18722 29.39359 2.672145
24-30 24 30 87 84 90.49982 1.160254 89.33957 3.080675 70 63 26.72145 0.342583 26.37887 2.637887
30-36 30 36 84 81 86.25889 1.134985 85.12391 3.04014 63 63 23.74098 0.312381 23.4286 0.000001
36-42 36 42 81 81 82.08377 1.10924 80.97453 0.000001 63 55 23.4286 0.316603 23.112 2.934857
42-48 42 48 81 80 80.97453 1.124646 79.84988 0.985801 55 51 20.17714 0.280238 19.8969 1.447047
48-54 48 54 80 79 78.86408 1.12663 77.73745 0.971718 51 51 18.44985 0.263569 18.18628 0.000001
54-60 54 60 79 79 76.76573 1.128908 75.63683 0.000001 51 51 18.18628 0.267445 17.91884 0.000001
Censoring
If t_s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s * Fmin and t_e = Fmax in (26)
If t_s > Fmin and > Fmax, then set l_e = Fmax in (26)
Wilt need to aoolv the preceding role starting at interval:
Will not occur in this study
Occurs in 1st interval
Will not occur in this study
Wil) not occur in this study
Reciprocal of
variance of
overafl
ln(Hri(t)) varpn(HR(t))] Overall ln(Hr(t)) ln(HR(t))
1.002468428 1999999.966 5.01234E-07 5E-07
14.99050217 1000000.807 1.49905E-05 9.99999E-07
14.60952609 1000001.234 1.46095E-05 9.99999E-07
0.051293294 1.710120896 0.029993958 0.58475398
0.052367986 1.134135396 0.046174368 0.881728939
0.054067221 0.845276444 0.063963951 1.183044916
2.253736788 1.203704912 1.872333298 0.830768397
1.003302109 0.649971367 1.543609703 1.538529311
1.064710737 0.654593161 1.626522856 1.527666435
■13.6372635 1000000.275 -1.36373E-05 1E-06
16.14595203 1000000.285 1.61459E-05 1E-06
1.773410331 1.642683314 1.079581387 0.608760064
-12.33415161 1000000.961 -1.23341 E-05 9.99999E-07
1.44009073 1999999.931 7.20045E-07 5E-07
6.262200517 7.155258043
Overall ln(HR{t)): 0.875188635
Variance: 0.139757364
Nakopoulou, 1998 O verall Survival, Super/inv F m in = 1 m onth p53-: n = 53
F m ax = 7 0 m onth p53+: n = 53
p53- p53+ C alculating th e overall in(H R ft)) a n d it s variance
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
Cancer-specific survival, Super/lnv
___________________________ p53-
Fmin =
Fmax =
1 month
121 month
p53-: n =
p53+: n =
55
21
p53+ Calculating the overall ln(HR(t)) and Its variance
Reciprocal of
variance of
overall
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) C riC D Rri(t) Dri(t) ln(Hri(t)) vartln(HR(t))] Overall ln(Hr(t)) tn(HR(t))
0-3 0 3 100 100 55 0.458333 54.54167 0.000001 100 100 21 0.175 20.825 0.000001 0.962810748 1999999.934 4.81405E-07 5E-07
3-6 3 6 100 98 54.54167 0.693326 53.84834 1.076967 100 100 20.825 0.264725 20.56027 0.000001 -12.92684834 1000000.861 -1.29268E-05 9.99999E-07
6-9 6 9 98 92 52.77137 0.688322 52.08305 3.188758 100 96 20.56027 0.268177 20.2921 0.811684 -0.425667815 1.477128118 -0.288172576 0.676989347
9-12 9 12 92 73 48.89429 0.654834 48.23946 9.962497 96 91 19.48041 0.260898 19.21951 1.001016 -1.377560681 1.026600765 -1.341866019 0.974088501
12-15 12 15 73 65 38.27696 0.526747 37.75021 4.13701 91 88 18.2185 0.250713 17.96778 0.592345 -1.201229318 1.84778209 -0.650092522 0.541189356
15-18 15 18 65 63 33.6132 0.475659 33.13755 1.019617 88 76 17.37544 0.245879 17.12956 2.335849 1.488809925 1.320314591 1.127617565 0.75739525
18-21 18 21 63 58 32.11793 0.467737 31.65019 2.51192 76 65 14.79371 0.215442 14.57827 2.110013 0.600858746 0.771842026 0.778473737 . 1.295601906
21-24 21 24 58 50 29.13827 0.437074 28.7012 3.958786 65 65 12.46826 0.187024 12.28123 0.000001 -14.34258139 1000000.136 -1.43426E-05 1E-06
24-30 24 30 50 48 24.74241 0.765229 23.97718 0.959087 65 58 12.28123 0.379832 11.9014 1.281689 0.990398704 1.697148241 0.583566409 0.58922372
30-36 30 36 48 47 23.0181 0.758838 22.25926 0.463735 58 58 10.61971 0.3501 10.26961 0.000001 -12.27349862 1000002.014 -1.22735E-05 9.99998E-07
36-42 36 42 47 46 21.79552 0.769254 21.02627 0.447367 58 58 10.26961 0.362457 9.907152 0.000001 -12.25861992 1000002.087 -1.22586E-05 9.99998E-07
42-48 42 48 46 46 20.5789 0.781477 19.79742 0.000001 58 58 9.907151 0.376221 9.53093 0.000001 0.731009492 1999999.845 3.65505E-07 5E-07
48-54 48 54 46 46 19.79742 0.813593 18.98383 0.000001 58 58 9.530929 0.391682 9.139247 0.000001 0.731009546 1999999.838 3.65505E-07 5E-07
54-60 54 60 46 32 18.98383 0.850022 18.13381 5.518985 58 58 9.139246 0.40922 8.730026 0.000001 -14.79269489 1000000.011 -1.47927E-05 1E-06
Censoring
If t_s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e * Fmax in (26)
Will need to apply the preceding rule starting at interval:
Will not occur in this study
Occurs in 1st interval
Will not occur in this study
Will not occur in this study
0.209461213 4.83449458
Overall ln(HR(t)): 0.043326393
Variance:________ 0.206646855
Cancer-specific survival, Super/lnv Fmin =
Fmax =
1 month
121 month
p53-: n =
p53+: n =
55
21
Calculating the overall ln(HR(t)) and its variance
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t) ln(Hri(t)) var(in(HR(t))] Overall ln(Hr(t))
Reciprocal of
variance of
overall
ln(HR(t))
0-6 0 6 100 98 55 1.145833 53.85417 1.077083 100 100 21 0.4375 20.5625 0.000001 -12.92695658 1000000.861 -1.29269E-05 9.99999E-07
6-12 6 12 98 73 52.77708 1.376793 51.40029 13.11232 100 91 20.5625 0.536413 20.02609 1.802348 -1.041853955 0.561706037 -1.854802844 1.78029064
12-18 12 18 73 63 38.28797 1.053797 37.23417 5.100572 91 76 18.22374 0.501571 17.72217 2.921236 0.185065043 0.455093705 0.40665261 2.197349667
18-24 18 24 63 50 32.1336 0.93593 31.19767 6.437615 76 65 14.80093 0.431095 14.36984 2.079845 •0.354652699 0.534498278 -0.663524492 1.870913417
24-36 24 36 50 47 24.76006 1.53155 23.22851 1.39371 65 58 12.28999 0.760206 11.52979 1.241669 0.584933596 1.393094201 0.419880863 0.717826547
36-60 36 60 47 32 21.8348 3.08256 18.75224 5.984757 58 58 10.28812 1.45244 8.835676 0.000001 -14.85221083 1000000.001 -1.48522E-05 1E-06
Censoring
If t s < Fmin and t e < Fmin then number censored = 0
Will need to apply the orecedinc
Will not occur in this study
rule starttn g at interval:
-1.691821642
Overall ln(HR(t)):
Variance:
6.566382271
•0.257648972
0.15229086
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e * Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e * Fmax in (26)
Occurs in 1st interval
Will not occur in this study
Will not occur in this study
-0
L /i
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
Schmitz-Drager, 1997 Time to progression (superficial only)
__________________________ p53-
Fmin =
Fmax =
2 month
85 month
p53-: n =
P53+: n =
38
23
psz* Calculating the overall ln(HR(t)) and its variance
Reciprocal of
variance of
overall
Time Interval t S t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t) ln(Hri(t)) var(ln(HR(t))] Overall in(Hr(t)) ln(HR(t)>
0-3 0 3 100 100 38 0.228916 37.77108 0.000001 86 86 23 0.140244 22.85976 0.000001 0.502165856 1999999.93 2.51083E-07 5E-07
3-6 3 6 100 93 37.77108 0.699465 37.07162 2.595013 86 74 22.85976 0.423329 22.43643 3.130664 0.68981939 0.633230328 1.089365686 1.579204211
6-9 6 9 93 90 34.47661 0.663012 33.81359 1.090761 74 69 19.30576 0.371265 18.9345 1.279358 0.739360024 1.616045564 0.457511867 0.618794434
9-12 9 12 90 88 32.72283 0.654457 32.06838 0.712631 69 65 17.65514 0.353103 17.30204 1.003017 0.958850346 2.311264012 0.414859722 0.432663683
12-15 12 15 88 88 31.35575 0.653245 30.7025 0.000001 65 65 16.29902 0.339563 15.95946 0.000001 0.654292528 1999999.905 3.27146E-07 5E-07
15-18 15 18 88 86 30.7025 0.667446 30.03505 0.682615 65 59 15.95946 0.346945 15.61251 1.441155 1.401561833 2.061497215 0 679875686 0.485084332
18-21 18 21 86 86 29.35244 0.667101 28.68534 0.000001 59 59 14.17136 0.322076 13.84928 0.000001 0.728152866 1999999.893 3.64076E-07 5E-07
21-24 21 24 86 85 28.68534 0.682984 28.00235 0.325609 59 55 13.84928 0.329745 13.51953 0.916579 1.763104213 4.052506021 0.435065168 0.246760892
24-30 24 30 85 80 27.67674 1.383837 26.29291 1.546642 55 47 12.60296 0.630148 11.97281 1.741499 0.905321701 1.099224373 0.823600461 0.909732375
30-36 30 36 80 80 24.74627 1.374793 23.37147 0.000001 47 47 10.23131 0.568406 9.662903 0.000001 0.883222084 1999999.854 4.41611E-07 6E-07
36-42 36 42 80 78 23.37147 1.460717 21.91076 0.547769 47 40 9.662902 0.603931 9.05897 1.349208 1.784642001 2.410735333 0.740289478 0.414811193
42-48 42 48 78 75 21.36299 1.525928 19.83706 0.762964 40 38 7.709762 0.550697 7.159065 0.357953 0.262364264 3.914245437 0.067028057 0.255477081
48-54 48 54 75 71 19.07409 1.589508 17.48459 0.932511 38 30 6.801112 0.566759 6.234352 1.312495 1.373049134 1.616685788 0.849298698 0.618549385
54-60 54 60 71 71 16.55208 1.655208 14.89687 0.000001 30 30 4.921857 0.492186 4.429671 0.000001 1.212825607 1999999.707 6.06413E-07 5E-07
Censoring
If t_s < Fmin and t_e < Fmin then number censored * 0
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax. then set t_e = Fmax in (26)
Will need to aoolv the preceding rule starting at interval:
Will not occur in this study
Will not occur in this study
Will not occur in this study
Will not occur in this study
5.556896814 5.561080087
Overall ln(HR(t)): 0.999247759
Variance:________ 0.179821183
Schmitz-Drager, 1997 Time to progression (superficial only)
__________________________ p53-
Fmin =
Fmax =
2 month
85 month
Time interval t_s t_e Sci(ts) Sci(te) Rci(ts)
0-12 0 12 100 88 38
12-24 12 24 88 85 31.42554
24-36 24 36 85 80 27.8247
36-46 36 48 80 75 23.56916
48-60 48 60 75 70 19.33407
Censoring
If t s < Fmin and t e < Fmin then number censored = 0
If t_s < Fmin and Fmin <« t_e<= Fmax then set t._s = Fmin
Cci(t) Rci(t) Dci(t)
2.289157 35.71084 4.285301
25.04223 1.473072
20.62301 1.288938
p53-: n =
p53+: n =
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then sett_e = Fmax in (26)
38
23
pS3+
Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Drift)
86 65 23 1.385542 21.61446 5.277949
65 55 16.33651 2.165079 14.17143 2.18022
55 47 11.99121 2.456031 9.535179 1.386935
47 38 8.148244 2.257947 5.890297 1.127929
38 30 4.762367 1.66396 3.098408 0.652296
Will need to aoolv the preceding rule starting at interval:
Will not occur in this study
Will not occur in this study
Will not occur in this study
Will not occur in this study
Calculating the overall ln(HR(t)) and its variance_______
Reciprocal of
variance of
overall
Overall ln(Hr(t)) ln(HR(t))
2.038237854 2.868984922
1.506922349 1.371670693 1.098603591 0.729037957
0.905321701 1.255060245 0.721337246 0.796774501
1.119665698 1.444152624 0.775309811 0.692447587
1.149905583 2.079231318 0.553043605 0.480946969
5.186532106 5.568191936
ln(Hri(t)) var(ln(HR(t))]
0.710438678 0.348555335
Overall ln(HR(t)): 0.931457135
Variance:________ 0.17959151
Os
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
Tetu,1996 Time to recurrence, Super only Fmin = 2 month p 5 3 -:n = 226
Fmax - 40 month p53+: n = 39
___________________________p53-__________________________ p53+
Time Interval t_S t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t)
0-3 0 3 100 98 228 2.973684 223.0263 4.460526 100 93 39 0.513158 38.48684 2.694079
3-6 3 6 98 77 218.5658 8.860775 209.705 44.93679 93 70 35.79276 1.451058 34.34171 8.49311
6-9 6 9 77 66 164.7682 7.269186 157.499 22.49986 70 45 25.8486 1.140379 24.70822 8.824363
9-12 9 12 66 59 134.9992 6.532218 128.467 13.62528 45 45 15.88385 0.768574 15.11528 0.000001
12-15 12 15 59 53 114.8417 6.152233 108.6894 11.05316 45 42 15.11528 0.809747 14.30553 0.953702
15-18 15 18 53 48 97.63628 5.858177 91.7781 8.658311 42 42 13.35183 0.80111 12.55072 0.000001
18-21 18 21 48 48 83.11979 5.667258 77.45253 0.000001 42 38 12.55072 0.855731 11.69499 1.113808
21-24 21 24 48 45 77.45253 6.114673 71.33786 4.458616 38 29 10.58118 0.835356 9.745823 2.308221
24-30 24 30 45 43 66.87924 12.53986 54.33938 2.415084 29 16 7.437602 1.39455 6.043052 2.708954
Censoring Will need to aoolv the preceding rule starting a t interval:
If t_s < Fmin and t_e < Fmin then number censored = 0 Wilt not occur in this study
If t_s < Fmin and Fmin <= t_e <= Fmax then sett_s = Fmin Occurs in 1st interval
If t_s < Fmin and t_e > Fmax, then set !_s = Fmin and t_e = Fmax in (26) Will not occur in this study
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26) Will not occur in this study
Calculating the overall ln(HR(t)) and its variance
Reciprocal of
variance of
overall
ln(Hri(t)) varlln(HR(t»] Overall ln(Hr(t)> !n(HR(t))
1.252762968 0.56490648 2.21764666 1.770204513
0.143339764 0.106108266 1.350882158 9.424336435
0.916290732 0.110945732 8.258909257 9.013415688
-14.2874721 999999.9995 -1.42875E-05 1E-06
-0.422272226 1.059913726 -0.398402451 0.943473016
-13.98443457 1000000.025 -1.39844E-05 1E-06
15.81380056 1000000.799 1.58138E-05 9.99999E-07
1.33222714 0.540893004 2.463014182 1.84879448
2.311168837 0.599328305 3.856265119 1.668534578
17.74830247 24.66876171
Overall ln(HR(t)): 0.719464669
Variance: 0.040537098
-j
-j
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
Overall Survival (Superficial only) Fmin = 6 month p53-: n = 9
Fmax = 120 month p53+: n ■ 9
p53-_____________________________________________ p53+
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) Cri(t) Rri(t) Dri(t)
0-3 0 3 100 100 9 0 9 0.000001 100 100 9 0 9 0.000001
3-6 3 6 100 100 8.999999 0 8.999999 0.000001 100 100 8.999999 0 8.999999 0.000001
6-9 6 9 100 100 8.999998 0.118421 8.881577 0.000001 100 89 8.999998 0.118421 8.881577 0.976973
9-12 9 12 100 100 8.881576 0.120021 8.761555 0.000001 89 89 7.904604 0.106819 7.797785 0.000001
12-15 12 15 100 89 8.761554 0.121688 8.639865 0.950385 89 78 7.797784 0.108303 7.689481 0.950385
15-18 15 18 89 89 7.68948 0.10985 7.579631 0.000001 78 67 6.739096 0.096273 6.642823 0.936808
18-21 18 21 89 89 7.57963 0.111465 7.468164 0.000001 67 67 5.706015 0.083912 5.622103 0.000001
21-24 21 24 89 89 7.468163 0.113154 7.355009 0.000001 67 67 5.622102 0.085183 5.536918 0.000001
24-30 24 30 89 78 7.355008 0.229844 7.125164 0.880638 67 56 5.536917 0.173029 5.363889 0.880638
30-36 30 36 78 78 6.244526 0.208151 6.036375 0.000001 56 56 4.48325 0.149442 4.333808 0.000001
36-42 36 42 78 78 6.036374 0.215585 5.820789 0.000001 56 45 4.333807 0.154779 4.179029 0.820881
42-48 42 48 78 56 5.820788 0.223876 5.596912 1.578616 45 22 3.358148 0.12916 3.228988 1.650372
48-54 48 54 56 56 4.018296 0.167429 3.850867 0.000001 22 22 1.578617 0.065776 1.512841 0.000001
54-60 54 60 56 56 3.850866 0.175039 3.675826 0.000001 22 22 1.51284 0.068765 1.444074 0.000001
Censoring Will need to apply the preceding rule starting at interval:
If t_s < Fmin and t_e < Fmin then number censored = 0 Occurs in the first interval
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin Occurs in the 2nd interval
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26) Will not occur in this study
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26) Will not occur in this study
Calculating the overall ln(HR(t)) and its variance
Reciprocal of
variance of
overall
ln(Hri(t» var[ln(HR(t))] Overall ln(Hr(t)) ln(HR(t))
0 1999999.778 0 5E-07
0 1999999.778 0 5E-07
13.79221477 1000000.798 1.37922E-05 9.99999E-07
0.116533704 1999999.758 5.82669E-08 5E-07
0.116533816 1.858619445 0.062699127 0.538033756
13.88216146 1000000.785 1.38822E-05 9.99999E-07
0.28394352 1999999.688 1.41972E-07 5E-07
0.283943564 1999999.683 1.41972E-07 5E-07
0.28394375 1.94430027 0.146039043 0.51432385
0.331356994 1999999.604 1.65679E-07 5E-07
13.94949003 1000000.807 1.39495E-05 9.99999E-07
0.594498099 0.751025779 0.791581483 1.331512218
0.934308989 1999999.079 4.67155E-07 5E-07
0.93430939 1999999.035 4.67155E-07 5E-07
1.000362718 2.383876823
Overall ln(HR(t)): 0.419636916
Variance: 0.419484761
OO
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission.
Vet, 1994 Overall survival, Super/lnv
p53 mutations, NOT IHC
Fmin =
Fmax =
2 month
66 month
p53-: n -
p53+: n =
p53-
37
8
p53+
Time Interval t_s t_e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) cm Rri(t) Dri(t)
0-3 0 3 100 100 37 0.289063 36.71094 0.000001 100 75 8 0.0625 7.9375 1.984375
3-6 3 6 100 89 36.71094 0.87407 35.83687 3.942055 75 50 5.953125 0.141741 5.811384 1.937128
6-9 6 9 89 82 31.89481 0.79737 31.09744 2.445866 50 38 3.874256 0.096856 3.7774 0.906576
9-12 9 12 82 73 28.65157 0.753989 27.89759 3.06193 38 26 2.870824 0.075548 2.795276 0.882719
12-15 12 15 73 73 24.83566 0.689879 24.14578 0.000001 26 26 1.912557 0.053127 1.85943 0.000001
15-18 15 18 73 73 24.14578 0.71017 23.43561 0.000001 26 26 1.859429 0.054689 1.80474 0.000001
18-21 18 21 73 71 23.4356 0.732363 22.70324 0.622007 26 26 1.804739 0.056398 1.748341 0.000001
21-24 21 24 71 68 22.08124 0.736041 21.34519 0.90191 26 26 1.74834 0.058278 1.690062 0.000001
24-30 24 30 68 68 20.44328 1.460235 18.98305 0.000001 26 14 1.690061 0.120719 1.569343 0.724312
30-36 30 36 68 61 18.98305 1.581921 17.40113 1.791293 14 14 0.845031 0.070419 0.774611 0.000001
Censoring
If t_s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t_s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e * Fmax in (26)
if t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
Will need to aoolv the preceding rule starting at interval:
Will not occur in this study
Occurs in 1st interval
Will not occur in this study
Will not occur in this study
Vet, 1994 Overall Survival, Inv only
p53 mutations, NOT IHC
Fmin =
Fmax =
2 month
66 month
p 5 3 -:n «
p53+: n =
p53-
16
8
p53+
Time Interval t_s t e Sci(ts) Sci(te) Rci(ts) Cci(t) Rci(t) Dci(t) Sri(ts) Sri(te) Rri(ts) c m Rri(t) Dri(t)
0-3 0 3 100 100 16 0.125 15.875 0.000001 100 75 8 0.0625 7.9375 1.984375
3-6 3 6 100 75 15.875 0.377976 15.49702 3.874256 75 50 5.953125 0.141741 5.811384 1.937128
6-9 6 9 75 56 11.62277 0.290569 11.3322 2.870823 50 38 3.874256 0.096856 3.7774 0.906576
9-12 9 12 56 38 8.461374 0.222668 8.238707 2.648156 38 25 2.870824 0.075548 2.795276 0.956279
12-15 12 15 38 38 5.590551 0.155293 5.435258 0.000001 25 25 1.838997 0.051083 1.787914 0.000001
15-18 15 18 38 38 5.435257 0.15986 5.275396 0.000001 25 25 1.787913 0.052586 1.735327 0.000001
18-21 18 21 38 25 5.275395 0.164856 5.110539 1.748342 25 25 1.735326 0.054229 1.681097 0.000001
21-24 21 24 25 25 3.362197 0.112073 3.250124 0.000001 25 25 1.681096 0.056037 1.62506 0.000001
24-30 24 30 25 25 3.250123 0.232152 3.017971 0.000001 25 12 1.625059 0.116076 1.508983 0.784671
30-36 30 36 25 18 3.01797 0.251498 2.766473 0.774612 12 12 0.724312 0.060359 0.663953 0.000001
Censoring
If t__s < Fmin and t_e < Fmin then number censored = 0
If t_s < Fmin and Fmin <= t_e <= Fmax then set t_s = Fmin
If t__s < Fmin and t_e > Fmax, then set t_s = Fmin and t_e = Fmax in (26)
If t_s > Fmin and t_e > Fmax, then set t_e = Fmax in (26)
Will need to aoolv the preceding rule starting at interval:
Wilt not occur in this study
Occurs in 1st interval
Will not occur in this study
W ill n o t o c c u r in th is s tu d y
Calculating the overall ln(HR(t)) and its variance
Reciprocal of
variance of
overall
ln(Hri(t)) vartln(HR(t))] Overall ln(Hr(t)) ln(HR(t»
16.03229093 1000000.351 1.60323E-05 1E-06
1.108662625 0.569922653 1.945286116 1.75462406
1.115609865 1.215015357 0.918185815 0.823034865
1.05681516 1.065863333 0.991510944 0.938206587
2.563839247 1999999.421 1.28192E-06 5E-07
2.563839743 1999999.403 1.28192E-06 5E-07
-10.77686578 1000000.992 -1.07769E-05 9.99999E-07
-11.17620833 1000000.47 -1.11762E-05 1E-06
15.98586714 1000000.691 1.59859E-05 9.99999E-07
-11.28651921 999999.2096 -1.12865E-05 1E-06
3.854984217 3.515871512
Overall ln(HR(t)): 1.096451962
Variance: 0.284424501
Calculating the overall ln(HR(t)> and its variance
Reciprocal of
variance of
overall
ln(Hri(t» var(ln(HR(t))] Overall !n(Hr(t)) ln(HR(t))
15.19396174 1000000.315 1.5194E-05 1E-06
0.287682072 0.537737673 0.534985899 1.859642815
-0.054067221 1.098407201 •0.049223295 0.910409181
0.062343131 0.944217001 0.066026274 1.059078579
1.111857452 1999999.257 5.55929E-07 5E-07
1.111857828 1999999.234 5.55929E-07 5E-07
-13.26232048 999999.7814 -1.32623E-05 1E-06
0.693148474 1999999.077 3.46574E-07 5E-07
14.26616886 1000000.28 1.42662E-05 1E-06
-12.13300032 999999.4234 -1.2133E-05 1E-06
0.551794402 3.829136076
Overall ln(HR(t)): 0.144104151
Variance: 0.261155514
0 0
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Fmax® 1 4 4 month p53+:n® 19
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84
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85
Appendix 2
Kaplan-Meier Plots from the IPD
SAS, Version 8 (SAS Institute, North Carolina) was used to create the
Kaplan-Meier (KM) plots from the IPD. The plots are listed in alphabetical order by
the first author’s last name. Two KM plots have been included for each study: one
for time-to-progression and one for survival (with the exception of Leissner who did
not provide time-to-progression data).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (time to progression)
p i = B o s s i
t . 2 5 -
l b
J -
H '
1 0 . 5 1 ) -
C /J
0 . 2 5
0 10 20 JO t t
p r o g l i i e
S I R A I A : 1 H H 2 p 5 j = N o r i r i o I / l l 0 1 0 C e n s o i e d p 5 J = l o r i i l / I I H t p 5 J = p 5 J t
o ...
c ----- (~
50
0 C C C e n s o r e d p 5 J = p 5 J r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (survival)
f i = B o s s i
87
H i
H
H t 1 - -- - c -c c -
0 . 7 5 -
- c -c t c -
0 . 2 5
S iir v i v o I l i m e
S TRAf A: D i r t p 5 3 = N o r n a l / W f C C C C e n s m e d p 5 3 - N o r m o i / I I H t p 5 J = p S J C C C C C e r i s o r e d p 5 j = p 5 3 f
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
88
IPD analysis (time to progression)
« i = C « s s t l In
1 1 5
60 1 0
: t i i p 5 J = N o [ i « l / I I 0 C C C e n s o r e d p 5 J = N o f i n o l / K I H t p 5 3 = p 5 i l C C C C e u o i e d p S J = p 5 3 t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
^
89
IPD analysis (survival)
[ i = C « : s e l l o
-e — «-e— W C I t~
) f - f — •- H
rt“
-£-f—t ' ~~t t
-c -c -e — ti— c -f
C -C '- C - f -Cf c -
I
H C i
0 . 7 5 -
. ( . 5 0 -
( . 2 5
S i n i t i l t i n e
STRATA: H M T p 5 J = N o r m o l / H T C C C C e n s o r e d p S H o n o l / I I t t f p 5 3 = p 5 3 t C C C C e n s o r e d p 5 3 - p 5 J l
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
p i = £ i i t p i i ( P o p o v }
1. 51)
0 . 2 5
1 0
p i o p l i i e
STRATA: I M M T p 5 3 = N o r m a l / W [ C C 0 C e n s o r e d p 5 3 = R o ( i o I / I T H t p 5 J = p 5 J t C C C C e o s o f e d p 5 5 = p 5 3 t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
IPD analysis (survival)
V
-tt— e -
D . / 5 -
J . 5 0 -
rc-
h
h -
-ti-
f £ - ------ -
0 . 2 5
I d 20 i d TO SO
S i m i o l l i m e
STRATA: H i p S 3 = N o f m a 1/WT C C C C e n s o r e d p 5 J = H o r i a l / I T H O i T p 5 J = p 5 J t C C C C e n s o r e d p 5 J = p S J t
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92
IPD analysis (time to progression)
p i - f i d t l ( I c l i )
0. 5(1
0 ) 5
5 0 50 0 0 1 0
p r o j l i i e
S I RAT A: H I p 5 0 = N o r » i o I / I T 0 C C C e n s o r e d p 5 J = N o n o l / I I I I O i t p 5 J = p 5 0 t C 0 0 C e n s o r e d p 5 J = p 5 J t
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93
IPD analysis (survival)
p i = F r o d e ! ( I t l u )
H t
0 .1 5
( 0 50 ( 0 1 0
S i i i i n l l i n e
S I RAT A: D i r t C C C C e n s o r e d p 5 3 = N o r n i o l / WI H t | ) 5 J = p 5 J t C C 0 C e n s o i e d p 5 J = p 5 i t
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94
IPD analysis (time to progression)
p '
0 .0 1 )
? 0 30
f i o j l i i e
C C C C e n s o r e d p 5 3 = N o r « o I / I T H t p 5 3 = p S 3 f C C C C e n s o r ed p 5 3 = p 5 3 t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (survival
p i = F u [ i h l o
95
H -
I d 2 0 JO 1 0
S u m i o l I i m e
STRATA: D i r t p 5 J = H o f n l / H T C C C C e n s o r e d p 5 T = No ( r a a l / WT H t p 5 J = p 5 J l C 0 0 C e n s o i e d p 5 J - p 5 J t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (time to progression)
p i : C l [ J i « e i
0 . 7 5
8 - f
H C -
- t i
f 8 , 5 8
a
< /l
( 1 , r
18 18 58 5!
p r o j l i i e
S 1 RA1A: f M r t p 5 J = N o r m o l / U f C C C C e n s o r e d p 5 3 = N ( r « a l / W T 8 i t p 5 J = p 5 3 t
i f i - - f - i i
---e -----------------e —
i—
58
C 8 8 C e n s o r e d p 5 J = p 5 5 t
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IPD analysis (survival)
p i = C « i i ) i » e [
I-
S m i i o l l i n t
S I l M I J l : t H H > )>53=K o ; b o l / WI £ £ C t e i s o i e d p 5 3 = N o r « o l / W T H t p 5 3 = p 5 i t C C C C e n s o r e d p 5 i = p 5 3 t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (time to progression)
p i = C i i l N l l s ( Q i r e s l i )
£
l
H - C - f t -
0 . 7 5 -
. . 0 . 5 0 -
0 . 2 5 -
p i s j l i i e
STRATA: fTi T- fr p 5 3 = N o r i r i o I / I T C C C C e n s o f e d p 5 T = N o i i o l / W T H t p 5 3 = p 5 J t C C C C e m o i e i p 5 3 = p 5 J t
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IPD analysis (survival
p i = E [ i l l i l l s ( O r r t s l i )
99
t-1
i-e-i
- m -
0 . 7 5 -
H
» ------
tr - i - H - C - £ H i : t ,
f i H i 1
0 . 2 5 -
ID 2D 3D 10
S u r v i v a l l i n e
S f R A f A : M - f r p 5 3 = N o r « a I / D I C C C C e n s o r e d p 5 j = N o r m o l / ( f l H t p 5 3 = p 5 3 f
— E —
I ---------
£ —
i - - - - - - - - - - - - - - - - - - - - - - - C -
50 SO
C C C C e n s o r e d p 5 3 = p 5 3 t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (time to progression)
p i =Gr o s smo n
100
) . / 5
H ■ i
f ) . S d
0 . 2 5
S I R A I A : I H H t p 5 3 = N o r m a l / l i C C C C e n s o r e d p 5 3 = N o [ f i i a l / I T l i t p 5 3 = p 5 3 t C C C C e n s o r e d p 5 3 = p 5 5 +
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (survival
p i =G( os sbo ri
I) ?5
f 0. 51)
------
0 . 2 5
S i m i o l l i m e
STRATA: H i ) p S J = N o t i o l / I I C C C C e n s o r e d p 5 J = N o r n i a l / R T H D IT p 5 3 = p 5 J t C C C C e n s o r e d p S J = p 5 3 t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
102
IPD analysis (time to progression)
p j ^ H i i d s o n ( V o l l i e i )
DO
0 - t f - C - i t C i M J ~ t
0 . ? 5
10 10 JO 1 0 50 00
p r o g t i me
STRATA: D 1 H T p 5 J = l o r i i o l / l ! C C C C e n s o r e d p 5 3 = N o r no I/ WT H t p 5 J = p 5 J t C 0 C C e n s o r e d p 5 J = p 5 J (
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
103
IPD analysis (survival
p i = Hi i ( l s o i ( V u l l i t i )
f 11.50
50 1 0
S u r v i v o I I i «
STRATA: p 5 3 = No f i n o l / KT 0 C C C e n s o r ed p 5 3 = N o i i o l / l ( T H t p 5 i = p 5 J t C C C C e n s o f e d p 5 3 - p 5 J t
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IPD analysis (time to progression)
p i - J o h n s o n
104
M
0 . 5 0
50 1 0 30 1 0
pi og 1 1 me
S T R A T A : M H O p 5 3 = h o n i l / I T C C C C e n s o f t d p 5 J - N o f a o l / W T H t p 5 3 = p 5 3 f C C C C e n s o i t d p 5 J = p 5 J t
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105
IPD analysis (survival)
p i = J o b s o n
0 . 2 5
TO
S i m i o l l i n e
STRATA: D i r t p 5 3 = N » n o l / I T C C C C e n s o i e i l p 5 3 ~ No r mo I/ WT H t p 5 3 = p 5 3 P C C C C e n s o r e d p 5 3 = p 5 3 t
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IPD analysis (time to progression)
p i = K o k c h i
106
I
8 C _ 0 C i
-1 H-tt 1
0 . 7 5 - B t
8 - - C - C - t C“ - C“ - C - 1 f
0 . 5 0
0 1 5
----------------1 ----------------r--------------- 1 r
! 0 30 ( 0 5 0 ( 0
S H U I t : f r ' t t p 5 3 = B o [ u l / l l C C 0 C t i i s o i t O p 5 3 = i » i n l / i r H t p 5 3 = p 5 3 t 0 0 0 C e n s o r e d p 5 3 = p 5 3 l
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (survival)
p i i o i e l i
107
i- rt
k - i
e -t -c- ~ t
i rt
0 . 2 5 -
[- £ frt" ~ £ t |
0 -
0 . 2 5
p - r - | i i
10 20 JO JO 50
S y m ti! liie
STRATA: f l i r t p53' - No r n i o l / WT C C C C e n s o r e d p 5 3 = No r n t a l/S F H t p 5 J = p 5 J f C C £ C e n s o r ed p 5 J = p 5 J t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (time to progression)
p i H i p p o i w i
108
0 . 0 0
ID
p r o p l i i t
S TBAI A: D i r t p 5 3 - N o r m o l / K T E C C C e n s o r e d p 5 J = N o r r n o I / # T H 1 p 5 J = p 5 i t C C C C e n s o i e d p 5 J = p 5 3 l
R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (survival)
p i - l i p p m i e i
3 . 5 0
1 . 2 5
( 0 1 0 50
S m t i t o ! l i n t
STRATA: H ' t p 5 5 = l » [ i o l / l l l 0 C 0 C e n s o r e d p 5 J = N o r m o l / K T H l p 5 J = p 5 } ( C C C C e n s o r e d p 5 3 = p 5 3 f
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (time to progression)
p i =L i u Honn en
110
1 1 — II- - - - - - 1
n - r
- t t 0 0
- c -
£ i
J f
0./5-1 £ C f
“ « - |
» i « f |
B-c-t f -c - e t
! ! ! ! 1 1
10 00 JO JO 00 £0
pioj liie
STRATA: t + 1 p 5 3 = Uo r » i D l / WT C C C C e n s o r e d p S 3 = N o i « n I / K T H t p 5 J = p 5 J t 0 0 0 C e n s o r e d [ 5 J : p 5 J l
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (survival
p r - L i u l k M M !
I l l
-i-m .
e-c t c- H - t f
11
K f ( M f C - t
0 . / 5 -
- - - - - - - - - - - - - - - - - - - - - 1 i i- - - - - - - - - - - - - - - - - - - - - - - r .~ . . . ■” . . . . . . . . . . . r
I I n JO 4 1 51
S u r v i v a l l i n e
S I K H k : f r t i p S H o m l / I I t C C C t n s m t i l } 5 5 = S « ( « I / I ! H t p 5 5 = p 5 J t C C C C e n s o r e d p 5 5 = p 5 5 t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
112
p i i i c i o i ( B a r b a r e s c h i )
0 . 1 5
. 0 . 5 0 -
l
D - - i
0 - c- t c
I
H - t l i t C - - C -
(/I
0 . 2 5
10 20 30
pr n g ! i me
S I R A1 A: H “ t p 5 3 = N o r « o l / K T C 0 C C e n s o r e d p 5 3 = l o i i « l / l l H t p 5 3 = p 5 3 r
5 0 00
C 0 C C e n s o r e d p 5 3 = p 5 3 t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
113
IPD analysis (survival)
p i = l « t i o « i ( B o r t ) a t e s c h i )
C - t e - t t l i f t f - f
0 . 7 5
0 . 5 0
0 . 7 5
10 70 JO ( 0 50
S u n i v o I l i n t
S I R A I A : f r + i p 5 J = l o [ i « l / l f C 0 0 C t i s o i e d p 5 J = l l o i i i l / I I f H t p 5 J : p 5 J f 0 0 0 C e n s o r e d p 5 J = p 5 J t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
114
f « f - 1 1 - t
I ) is
0 1 5
p r o j l m e
S I R A I A : i + t p 5 3 = N o r n o l / WI C C C C e n s o r ed p 5 3 = N o r « o I/ WT H t p 5 3 = p 5 3 t C C C C e n s o r e d p 5 3 = p l ) J t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
D . / 5
J . S d
i). I S
p i = N n U p i ) i i I Du
H C - C - " H f -
S TRATA: m p S M e r i o i m
i i
n i d
Sii r v i vo 1 l i m e
t C C C e n s o r e d p 5 J = N o r r r i a l / H l H t p 5 3 = p S J t
h
C C C C e n s o r e d p 5 J = p 5 S t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (time to progression)
p i = P o l l « c t ( 1 1 1 )
116
0 7 5 -
f 0 . 5 0 -
0 . 1 5 -
h
o -
o -
h
o -------------
H i ) p S J - N o i f r i a l / y / f H O D p 5 J = p 5 5 t C C C C e n s o r e d p 5 3 = p 5 J t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
117
IPD analysis (survival)
j i
0 . / 5
0 . 2 5
0 . 0 0
I) 10 TO 30 10 SO SO
S i m v i l 1 i me
S TRATA: D i r t p 5 3 = H « r i i l / I t C C 0 C e n s o r e d p 5 3 = N o [ i * o l / K T D i r t p 5 J = p 5 J 0 0 C C C e n s o r e d p 5 J = p 5 S t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (time to progression)
p i = S « i i t e r ( G i s s e d
118
0 . 7 5 -
0 . 5 0 -
0 . 2 5 -
0 .0 0 - 1
D i
S 1 t-ci- c- - t i - n f in
-e £ - ,
£ - c-l - [-1 t C i
-Ci
STRATA: p 5 J = N o f i t o l / W T C C C C e n s o r e d p5 3=No i mi ) l / l AT B i t p 5 J - - p 5 . l t £ C C C e i u o i e i l p 5 J = p 5 3 t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (survival)
p i = S n « l e r ( G o s s e r )
0 . 7 5 -
0 -
o - ,
T -C -j
t “ C - H I j - t -
“ i f H
H t t -
11 H C -
f 0 . 5 0 -
0 . 2 5 "
S I R A I A : U r t p 5 J = N o r m ( i I / I T
S u r v i v a l l i n t
C C C C e n s o r e d p 5 J = H o ( i o l / I I H t p 5 3 = j ) 5 J t C C 0 C e n s o r e d p 5 J = p 5 J t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
120
IPD analysis (time to progression)
p i = S c b » I k e s ( V e t 1 9 9 4 )
1 .0 0 ---- — ......... = z = z =
0 . 2 5
0 . 2 5
! ! ! | !
10 20 J # t o 50
p r o g l inie
S I R A I A : D i r t p 5 j = H o n o l / l l l C C t C e n s m e d p 5 3 = N o r me I / I I H f p 5 J = p 5 J t C C C C e n s o r e d p 5 3 = p 5 3 t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
121
IPD analysis (survival)
p i = S c ) i a i t e t ( V t l l S I H )
- i ■
) . / 5 '
1 . 2 5 -
S T R A U :
1 1 -----
2 0 20
S u r v i v a l l i m e
C t C C e n s o r e d | 5 3 - N o r i o l / I l l C C C C e n s o r e d p 5 J = ( i 5 3 t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (time to progression)
p i = S c h i i l z - D r « ) e !
0 . 7 5 -
o.so
t-f
0 . 2 5
p r o g l n e
S I R A1 A: D i r t p 5 3 = N o r i n a l / W I C C C C e n s o r e d f 5 J - H o i n n l / I I I H f p 5 J = p S S t C C C C e n s o r e d p 5 3 - p 5 J t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0 . / 5 -
0 . S O
U S '
IPD analysis (survival)
pi =Sctt(ni I z - O r a g e r
-c
-ti C - f -
t - - c - f - t - e - c - - c i e-c--
f i -
S u f v i v a I l i i e
C C C C e n s o r e d p 5 J = l o n o l / l l I H t p S i p S J t C C C C e r i b o r e d p 5 3 = p 5 J t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
124
IPD analysis (time to progression)
( i = S l i i t [ ( B m H u n t )
0 . 7 5 -
D - -
f 0 . 5 0 -
0 . 2 5 -
0 . M l
d - f C - - - - - - - - - - - - - - -
p i o j l i i e
S I M : C C C C e n s o i e J p 5 3 = | i 5 M
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
125
IPD analysis (survival)
p S I i d e i ( B u d l i o r d )
u s -
3 . 5 0 -
0 . 2 5 '
i- - i
S I RATA: p 5 3 = N o i n i a l / WT
1 -----
30
S i t v i v o ! [ i i t
f i t p 5 3 = p 5 3 t t C C C e n s o t e d p 5 3 = p 5 3 t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (time to progression)
S m i A : m p 5 3 = l l o f i « ] / f [ C C C C e n s o r e d p 5 J = N o m o l / K T t t t p 5 J = p 5 3 t C C C C e n s o r e d p 5 i = p S J t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
127
IPD analysis (survival)
0 . 7 5 -
0 . 2 5 -
6 -
r
S I R A I A : 1 H H ) f i 5 J = N o r m o l / I F
1 1
n j o
S i i o i v o l l i n e
C C C C e n s o i e d p S H o n o l / I ! H t p 5 3 = p 5 J f C C C C e n s o r e d p 5 J - p 5 3 t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
H—
C H t r f [ C “ C C f C
STRATA: C t C C e n s o r e d p 5 3 = N o r m I / I T M l t p 5 i = p l ) J t C C C C e n s o r e d p 5 J = p ! ) J t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
129
IPD analysis (survival)
p M c l id o
l . / S
J . S O
. . . c_
M l - C M
- 1 t ------
h - - c - - c -
f -
in
! ! ! ! !
10 n j o t o s o
S«[
H i p 5 3 = N o f m o i / W f C C C C e o s o i e i p 5 j = N o f i o l / W t H t p 5 J = p 5 J t C 0 C C e m o i t d p 5 3 = p 5 J t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
130
IPD analysis (time to progression)
pi=D«Jer»ood
I H H 3 p 5 3 = N o f i i o l / l f l C C C C e n s o f e d p S j - N o r i r i c l / K T H t p S 3 = p 5 3 t C C C C e n s o i e d p S 3 = p 5 3 t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0 . 1 5 -
0 . 5 0 -
0 , 2 5 '
h
o - -
\r ->
IPD analysis (survival)
131
STRATA: 8 + 1 p 5 J = H o r i o l / I T
2 0
S n i i y o l f i n e
0 0 C C e n s o r e d p 5 3 = N o r « o ! / I T H t p 5 J = p 5 J t C C C C e n s o r e d p 5 3 - p 5 3 t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
132
IPD analysis (survival)
p i = t e l l e t ( L e i s s i e i )
c
c
3
u _
0
3
Q
o
l i ~
D . I V
SO
S u r v i v a l l i n e
STRATA: M H t p S J = N o r r i r a l / ^ T C C C C e n s o r e d p S J = N o r i a I / W T f l i t p 5 3 = p 5 3 t C C C C e n s o r e d p 5 3 = p S J t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IPD analysis (time to progression)
p i - I l i l l o
133
-h-
- £ - 1 - - t C C - - t
I . / 5 -
—t-
0 . 5 0 -
0 . 2 b -
STRATA: f r t f p 5 3 = N « [ i o l / I [ C C C C e n s o r e d p 5 j = N o n o l / W I H t p 5 3 = p S 3 ( C C C C e n s o r e d p 5 J = p 5 3 t
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
134
IPD analysis (survival)
p i - Z l o l I r i
9 . 7 5
( ' . 2 5
! ! ! ] !
10 20 3 0 10 50
S u r v i v a l I l i e
S I R A I A : H t t p S 3 = N o r m n l / K I C C C C e n s o r e d p 5 3 = N o r m a l / W [ H t p 5 J = p 5 3 t C C C C e n s o r e d p S3 =p S3 i -
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Asset Metadata
Creator
Valin, Gregorio Cua, Jr.
(author)
Core Title
P53 and bladder cancer outcome: A combined analysis from the Keck School of Medicine
Degree
Master of Science
Degree Program
Applied Biostatistics and Epidemiology
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
biology, biostatistics,health sciences, oncology,OAI-PMH Harvest
Language
English
Contributor
Digitized by ProQuest
(provenance)
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c16-321006
Unique identifier
UC11337336
Identifier
1422405.pdf (filename),usctheses-c16-321006 (legacy record id)
Legacy Identifier
1422405.pdf
Dmrecord
321006
Document Type
Thesis
Rights
Valin, Gregorio Cua, Jr.
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA
Tags
biology, biostatistics
health sciences, oncology