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The use of cubic splines for estimating the prognostic effect of age at diagnosis in childhood acute lymphoblastic leukemia

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The use of cubic splines for estimating the prognostic effect of age at diagnosis in childhood acute lymphoblastic leukemia

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Content THE USE OF CUBIC SPLINES FOR ESTIMATING THE PROGNOSTIC EFFECT OF AGE AT DIAGNOSIS IN CHILDHOOD ACUTE LYMPHOBLASTIC LEUKEMIA by Christopher James Ruel 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 (Biometry) August 1994 Copyright 1994 Christopher James Ruel JMI Number: EP54951 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Olsseftalion Rublishing UMI EP54951 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA 90007 5 This thesis, w ritte n by ............ under the direction of h ^c^ Thesis Committee, and approved by a ll its members, has been p re sented to and accepted by the Dean of The Graduate School, in p a rtia l fu lfillm e n t of the requirements fo r the degree of Dean HESy COMMITTEE Chgirman ... .. DEDICATION This thesis is dedicated to my wife Lita and our four children Marisa, Belen, Noah and Kaleb for their patients I and loving support. 11 ACKNOWLEDGMENTS I would like to express my gratitude to Dr. Harland Sather and Dr. Stanley Azen for their invaluable guidance j ! and support during my graduate studies. I also want to express my thanks to Dr. Mark Krailo and Dr. Jae Won Lee for . serving on my thesis committee. Ill TABLE OF CONTENTS | ^ PAGE ; I LIST OF TABLES ...... V j LIST OF FIGURES ........................................ vi \ ! CHAPTERS : ! I I. INTRODUCTION 1 , ' II. MATERIALS & METHODS I 2 .1 SPLINE THEORY .......................... 6 I ! 2.2 KNOT LOCATION & NUMBER......................... 13 2.3 PATIENTS ........................................ 15 2.4 STATISTICAL ANALYSIS .......................... 22 I III. RESULTS 25 , : IV. DISCUSSION...... 48 , REFERENCES ............................................... 54 IV LIST OF TABLES TABLE PAGE 1 Member Institutions of the Childrens Cancer Group ........................................... 16 2 Results of fitting Cox proportional hazards models using a spline function to estimate the prognostic effect of age at diagnosis ....... 27 3 Kaplan-Meier life table estimates (EFS) for infants ................................... 32 4 Relative risk comparison within age groups adjusted for significant clinical variables .... 33 5 Results of interaction effects for other covariates with age at diagnosis ................ 35 6 Kaplan-Meier life table estimates (EFS) for prognostic effect of CALLA stratified by age .... 38 7 Relative risk of CALLA within age groups ....... 41 8 Kaplan-Meier life table estimates (EFS) for prognostic effects of CALLA stratified by treatment group ...................... 42 9 Kaplan-Meier life table estimates for CALLA effect by age, in patient groups treated with intensive therapy, adjusted for study group .... 43 10 Significance of CALLA-AGE interaction after adjustment for clinical variables ............... 45 11 Kaplan-Meier life table estimates (EFS) for prognostic effects of CALLA stratified by age within cell lymphoblast lineage .................. 46 V LIST OF FIGURES I ' FIGURE PAGE 1 Proportional incidence of acute lymphoblastic i leukemia by age group.............................. 20 2 Spline estimated relative risk by age group, relative to children diagnosed at 5 yrs........... 29 3 Relative risk comparisons using linear, guadratic, cubic polynomial age covariates and the spline function estimate of the age effect.............. 30 4 Estimated relative risk, using spline technigues stratified by CALLA expression levels..............37 VI Chapter I INTRODUCTION Acute leukemia is the most frequently occurring malignancy in individuals aged 21 years or less. Nearly one third of childhood (defined as less than 16 years of age) cancers can be attributed to the most common leukemia subtype, acute lymphoblastic leukemia (ALL). Four per one hundred thousand children in the United States are diagnosed with ALL each year, which represents 75% of those children afflicted with leukemia^'^. Before the introduction of effective antileukemic therapy, the prognosis for children with ALL was extremely poor (usually fatal within two to three months after diagnosis). With the advent of single-agent chemotherapy combined with maintenance chemotherapy and central nervous system preventive chemotherapy, prognosis for children with acute lymphoblastic leukemia has dramatically improved. About 60% to 70% of ALL patients can expect to maintain disease-free survival for more than five years after the date of diagnosis with modern therapy^. Identifying the risks associated with clinical and immunologic features, and determining a course of treatment based on the patient’s risk level, has added greatly to the success of ALL outcome and quality of life for patients during treatment. Children presenting ALL clinical or laboratory features that are known to be associated with poor outcomes are treated with more aggressive (or intensive) therapies. For those whose presenting features indicate a better prognosis, less intensive treatments can often be used which will avoid unwarranted side effects sometimes associated with the toxicity of more intensive treatments. As medical science gains knowledge about the behavior of risk factors, identification of appropriate treatments for ALL patients consistently improves. It has been particularly useful to examine the behavior of a quantitative factor and characterize its association with disease outcome in a detailed manner. This allows for the visualization of risk trend effects graphically. For highly prognostic risk factors, one might be able to use this information to customize treatments to the predictive profile of the risk factor. One method frequently used to analyze data in this fashion is the Cox proportional hazards regression model^. To obtain more accurate estimates of relative risk by not imposing potentially inappropriate linearity assumptions, Durrleman and Simon^ suggest the application of polynomial spline functions to model the prognostic behavior of covariates in a Cox proportional hazards regression ■ model. Generally speaking, spline functions make less | restrictive assumptions concerning the underlying form of I j i ; ' the covariate, and their behavior in a small section do not ^ dictate behavior elsewhere. In other words, the spline ! ; I I function does not require a single form of the covariate , ________ 2 Î over the entire region of interest. Instead, the space of i interest is divided into appropriate sections, with the best ; fitting form of the covariate (i.e., linear, quadratic, I cubic polynomial) estimated in each section. These sections j j or splines are joined together at "knot" points to form a i I I smooth piecewise polynomial. When knots are fixed at pre- 1 ) specified points, the spline function can be considered to : be "linear" in its modified regression coefficients and I standard inference methods for covariate significance can ' easily be applied. There are a number of features associated with ALL that have been documented as risk factors for poor outcomes. Some , of these are: white blood cell count (WBC), age, mediastinal ' mass, hepatosplenomegaly, immunophenotype, sex, race, ' central nervous system involvement^'^"^^. Age at diagnosis has been well documented as a strong predictor for disease ; outcome for The highest incidence of ALL for I children, in the United States occurs at approximately four years of age at the time of diagnosis^^'^°. Other countries have reported a similar early peak, but sometimes at slightly different ages. In addition to age having an important relationship to the incidence of ALL and possibly the etiologies of the disease, it is also an important prognostic factor for disease outcome^^"^®. Sather et al.^° reported that reasonably distinct break points occur at one and ten years of age at diagnosis for five-year disease-free survival rates. They found infants (i.e., less than one year of age) and children over 10 years of age at diagnosis were at higher risk for disease recurrence and death than the intermediate age group. However, interesting variations in outcome according to ranges of age at diagnosis make the association between age and disease outcome more complicated than a simple categorical grouping. Even the use of linear or polynomial relationships may not be adequate to describe the effect. To gain better insight into the effects of age at diagnosis on disease outcome, the spline analysis technique was applied to 3801 children diagnosed with ALL between 1983 to 1989 and enrolled in clinical trails conducted by the Childrens Cancer Group (CCG). The analysis of age at diagnosis as a spline function covariate in a Cox proportional hazards model provided more detailed and accurate information since no arbitrary categorization, or polynomial assumptions over the entire range of age at diagnosis were imposed. Using truncated polynomials, or functions, as detailed in the methods section, a spline function for age I at diagnosis was created. The spline function was used to develop a hazard function estimate. Maximum likelihood ! methods were used to determine covariate (or spline ■ function) coefficients, based on the smoothly joined piecewise polynomial sections (i.e., spline) with | adjustments for other covariates. The hazard function, or instantaneous failure rate, was used because of its time- varying risk properties making it useful for describing survival analysis types of disease outcome data. Relative risk estimates were based on the results obtained from the Cox model. Tests for interaction of prognostically important clinical and laboratory patient variables with the age spline were preformed to determine their potential effect modification on age at diagnosis. Comparisons were made of these spline-model findings to standard univariate and multivariate analysis (i.e., without using a spline model for the effect of age). Chapter II MATERIALS AND METHODS 2.1 Spline Theory Conceptually a spline can be thought of as a flexible line between two fixed points (or knots). By varying the number and location of the fixed points, the shape of each flexible line changes as it adjusts to fit new conditions. These flexible lines can be modelled by some mathematical functions called splines. There are three prominent methods of fitting a smooth spline : 1) penalized least squares, 2) a penalized least squares method with loosened specifications on the interpolating constraints often referred to as one hundred percent confidence intervals, and (3) regression splines . Due to their relative simplicity and receptiveness to standard hypothesis testing techniques, and the fact that little if any accuracy is lost when using the technique compared to the other two procedures, the regression spline method was chosen for this study^. To obtain the type of continuity smoothing restrictions (i.e., location and number of knots) we may desire, and maintain the ability to perform standard hypothesis testing procedures, functions were used to develop the spline j models. The notation used is the same as that used by ■ Smith^^, I I u+=u if u>0 ! u^=0 if u<0. I A spline function of x with no continuity restrictions can be expressed as (using the above notation): s ^ - 1 ( X - i . Here there are k knots t.,< • • • <tj^, and k+1 polynomial segments each of degree n and regression coefficients . To obtain the smoothest possible spline (since most regression models are quite smooth, we should expect the spline model to also have this feature )^^ we can constrain S(x) and its first n-1 derivatives to be continuous at the knots (or joint points). This can be achieved by deleting terms with degree lower than n. It therefore follows that ■S(x)=Ej^BojX^+Ei.i®in(X-t>:. (1) The choice of n (degree of the spline function) depends on the number of derivatives available in the regression model. Since this information is rarely obtainable, an attractive choice is n=3 (or cubic spline) due to its visually smooth appearance, low degree, and adaptability for fitting data^'^^. Then, 5(%) +ELi 6,3 ( X-1, ) !. ( 2 ) 7 : I It has been suggested that the two end regions (or tails) should be linear since substantial deviance from a straight line is rarely observed in the tails^'^^. To satisfy the requirement that S(x) be linear for x<t implies JBo2= % = 0^ Furthermore, S(x) linearity in the region x>t|, demands that quadratic and cubic coefficients for x>t,^ must sum to zero. Thus, E i - 1 or, and (-3t,6,j)x2-o or, Ei.i^i3=0 and ELi^i3trO- Since J 3q3=0, then Ei-o ^13 = 0 (2) Imposing these restrictions on Eq(2) we have, S(X)-fioo+6oiX+EÏ- 1 ® i 3 < X - t i ) ! -6(io+BQiX+ (Ei-i ) ^+B|j3(x-t|,) + ). ( 4 ) Using, Ei4)6,3=0, or J î | ^ 3 = 6,3 in Eg (4), we have 8 ' -600+60,x+ ( 6,3 [ ( X-1, ) ^- ( X-1|, ) ^ ] + 6(k_i)3(X-t|,.i)^ - 6(k_D3(X-tk)!) . (5) Using Eg (3), El-1^i3ti = 0 ^ (k -1)3^ k -1= ( “ E i - 1 ^ i 3 ^ i ) ~^k3^k = ( " E i - 1 ^ i 3 ^ i ) + E L l ^ i3 ^ k “( ~Ei-1 ^i3^i ) +[ (Ei-1 ^is) +^(k-1)3]^k Finally, . (6) ^k-1“^k (Substituting Eg (6) into Eg (5) we have, 5 ( X ) .B00+601X+E':: 8,3 [ ( X-t, ) !- ( x-t, ) : + (t,-ti)(x-t,,^ ] ^k- 1 ^k I 9 _ _ _ _ _ t S(x)-Boo+6oi^+E?:?6,3[(x-t,)! - ^k"^k- 1 (^-tk)!(^^^i)] ^k- 1 ^k &k * ' k - i (x-tk)!(tk_,-t,) + _ -------- — J . {/) ^k“^k- 1 For completeness this study also investigated the significance of quadratic and cubic polynomial end pieces. A k knot spline with the first piece linear, center pieces cubic and last piece quadratic imposes the following restrictions : •^02 and since cubic terms for x>t,^ sum to zero we have, E5-1 6, 3X^=0 or ELi 6i3-0 and 6|<3- - Ei-i ^i3- 10 Substituting into Eq(4), S(x )-Boo+BoiX+E iZ ^ 6,3[ (x-t,)^-(x-t|,)^] and restricting the end section to be a quadratic polynomial gives E i - 1 ^ 0 3 “ ® and, S(x)-Boo+6oiX+Bo2X^+5^^-;j 8,3[ (x-t,)^-(x-tj^] . (8) Tests for a quadratic first section, cubic center sections and linear final section use Eq(8) rewritten in the form, such that " + " functions are run in reverse leaving the final section determined by J 3qq+J3q,,X+J3q2X^ , S(x)-Boo+6oiX+6o2x2+Ei:^ 6,3: (t,-x)^-(t,-x)^] . (9) Tests for cubic end pieces use Eq(4) in a similar manner to that shown for the quadratic model above. Pointwise approximate 100(l-a)% confidence bands for S(x) were developed using methods outlined by Durrleman and Simon^ with the band given by ÔX±Z(,.„)(XV3^)^ where : “ the upper percentile of the standard normal distribution, . I 11 I V = covariance matrix associated with J3, B = (Bq, • • ' r^k_2) parameter estimate vector associated with covariates, B is the maximum likelihood estimator of B, and 2L = (Xq, • • ',x^_2) the vector representing spline covariates. Here Xq = x, and Ck-tk_«i for i = 1,2,' • »,k-2. 12 2.2 Knot Location and Number General guidelines for knot selection using cubic j splines, as suggested by Wold^^ based on his practical | experience, are: ' 1. Have as few knots as possible, with at least four to five observations between knot points, to avoid over fitting. 2. Locate knot points at data points. 3. Allow no more than one extremum point and one inflection point per spline interval. A cubic polynomial is incapable of approximating additional extremum and inflection points. 4. Extrema points are placed in the middle ofintervals, while inflection points are positioned near the knot points. Since most disease outcome events examined in medical studies do not have effects which change quickly over the covariate space (i.e., no sudden jumps in the response variable for a given covariate level), some researchers believe that at most five knots and more likely only three I I I may be needed for most medical applications^'^^. Location of | , the knots can either occur at known structural change points ' ! (i.e., change of exposure, change in treatment, etc.), I I I 1 equally spaced intervals, or one can treat knot location as : ! an additional parameter of the model to be estimated^^'^^. The ; 13 ; latter method requires specialized procedures and software and does not allow for the use of standard methods of hypothesis testing available in popular statistical analysis packages (e.g., SAS, BMDP, EGRET, SPLUS, EPILOG). The first method requires knowledge of structural change points. Since there are no established biologic or therapeutic reasons for particular structural changes in outcome within the range of ages at diagnosis, a variation on the equally spaced knot selection method was implemented. Suggestions made by Durrleman and Simon for selection of knot location were used in this analysis. They reason that a cubic spline with three knots (and linear end segments) should adequately fit the data (especially when events occur smoothly over the covariate space, as does age at diagnosis), and the following approach may be used. One locates two knots at the tenth and ninetieth percentile points, and then uses a stepwise Cox regression procedure to select one additional knot from among the twentieth, thirtieth, • • • ,eightieth percentile points, while competing I with other clinical variables. The most significant knot . included in the regression model determines the location of i the third knot. I I 14 2.3 Patients Data used in these analysis were obtain from the Children Cancer Group, a large multi-institution research group specializing in pediatric cancer, accessing approximately one-third of newly diagnosed cases of ; childhood ALL in the United States. The 36 primary institutions of CCG from which these data were submitted are shown in Table 1. In addition, there are 76 affiliate institutions also providing patient entries to the study data base. This study concentrated on 3801 patients diagnosed during the period 1983 - 1989 and treated on the CCG-lOOs series of studies (CCG-104, -105, -106, -107, -123, -139). Patients in the CCG-lOOs series where treated with either standard, intensive, or "lymphoma—like" therapies. Most of these studies used statistical designs employing randomized assignment to the treatment groups. Included in this patient population is a subset of patients presenting with clinical characteristics suggestive of disease in extramedullary locations in addition to the bone marrow, who were referred to as a "lymphomatous" ALL subgroup. These patients were randomized to various treatments, two of which used chemotherapy/radiation therapy regimens that have been shown to be effective in the treatment of children with lymphoblastic non-Hodgkin's lymphoma. 15 ' Table 1. Member Institutions of the Group. Childrens Cancer Institution Location University of Michigan Med. Center Ann Arbor, Michigan University of Calif. Med. Center San Francisco, Calif. University of Wisconsin Hospital Madison, Wisconsin Children's Hospital & Med. Center Seattle, Washington Rainbow Babies & Children's Hospital C1eve1and, Ohio Children's Hospital National Medical Center Washington, D.C. Children's Memorial Hospital Chicago, Illinois Children's Hospital of Los Angeles Los Angeles, Calif. Children's Hospital of Columbus Columbus, Ohio Columbia Presbyterian College of Physicians & Surgeons New York, New York Children's Hospital of Pittsburgh Pittsburgh, Penn. Vanderbilt University School of Medicine Nashville, Tennessee Doernbecher Memorial Hospital for Children Portland, Oregon University of Minnesota Health Sciences Center Minneapolis, Minnesota University of Texas Health Sciences Center San Antonio, Texas 16 Table 1 (Continued) Institution Location Children's Hospital of Philadelphia Philadelphia, Penn. Memorial Sloan-Kettering Cancer Center New York, New York James Whotcomb Riley Hospital for Children Indianapo1i s, Indi ana Hospital for Sick Children Toronto, Ontario, Canada University of Utah Med. Center Salt Lake City, Utah Strong Memorial Hospital Rochester, New York University of British Columbia Vancouver, British Columbia, Canada Children's Hospital Med. Center Cincinnati, Ohio Harbor/UCLA and Miller Children’s Med. Center Torrance & Long Beach, Calif. University of Calif. Med. Center Los Angeles, Calif. University of Iowa Hospitals & Clinic Iowa City, Iowa Children's Hospital of Denver Denver, Colorado Mayo Clinic Rochester, Minnesota Izaak Walton Killam Hospital for Children Halifax, Nova Scotia, Canada University of North Carolina Chapel Hill, North Carolina University of Medicine & Dentistry of New Jersey Camden, New Jersey ...... ...................... ........... 17 1 Table 1 (Continued) Location Institution Children’s Mercy Hospital University of Nebraska Medical Center Kansas City, Missouri Omaha, Nebraska Cleveland Clinic Foundation Cleveland, Ohio Wyler Children's Hospital M.D. Anderson Cancer Center Chicago, Illinois Houston, Texas 18 Figure 1 demonstrates the proportional age distribution of ALL for our group of 3801 children. Age at diagnosis ranged from birth to 248 months, with a median age of 56 months. Patients older than 216 months (or 18 years) comprised less than one percent of the patient population. To achieve more reliable results, patients over 18 years were excluded or grouped with other older patients such as those 15 years or older. The proportional incidence was found to be slightly higher for males than females (males - 59%, females - 41%). Seventy-eight percent of the patients were classified as white, 11% Hispanic, 6% black, 2% Asian, and 3% other. For this study we categorized race into the two subgroups white and "all other" (due to the small number in non-white categories). White blood cell (WBC), hemoglobin, and platelet counts were categorized such that approximately equal patient counts were contained in each group. The categorization for these variables were: WBC - < 10 x 10^/L, 10-60 X lO^/L, > 60 X 10*/L; platelet - < 50 x lO^/L, 50 - 100 X 10^/L, > 100 X IoV l ; hemoglobin - < 8g/dL, 8 - llg/dL, > llg/dL (white blood cell, and platelet are denoted as count per liter). Spleen, liver, lymph nodes, and mediastinal mass were all categorized into normal or enlarged. Central nervous system (CNS) involvement at diagnosis was classified as either present or absent. 19 31 cq’ cz s “Ü o “ D O O q! (D 3 O (D o ( t > 3 T3 ZT O g ( / ) r“ '+ Ô ’ m" c (D 3 m' cr (O CD (Q o c "D PERCENT OF TOTAL GROUP o cn o o CO CO CO N ) I cn cn 4 : ^ w :_______ : : > CD m m i : 00 o ; CO cn z o O ) œ CO o o z H 00 % (/) ro r o s 8 CO 00 20 Categorization of age at diagnosis, used for stratification purposes, was divided into the following groups: < 1 year, 1-2 years, 2-3 years, 3-4 years, 4-6 years, 6-10 years, 10- I 14 years, and > 14 years. These age groups were chosen such ’ that each group had approximately an equal number of patients, with a separate group for infants (< 1 year of age at diagnosis) who possess unique characteristics at presentation in comparison to older age groups (i.e., WBC, immunophenotype, etc.). When age at diagnosis was used as a qualitative variable it was grouped into distinct prognostic categories: < 1 year, 1-10 years, > 10 years'*®. Classification of patients into B and T cell lymphoblast lineages utilized lineage specific antigens with possibly a more liberal definition of B-lineage patients such that a sufficient numbers of patients could be classified for statistical analysis based on the available data. Patients were typed as B-lymphoblast lineage if antigens CDIO and CD24 had levels greater than 20%, and any of CD2 or CDS or CD 7 were less than or equal to 20% ( immunophenotyping assessments were based on the percentage of blasts I expressing each particular antigen). Patients were also j classified as B-lymphoblast lineage if antigens CD2 and CDS : I and CD7 where all less than or equal to 20%. T-lineage i patients had CD24 antigen levels less than or equal to 20% 1 and any of CD2 or CDS or CD7 greater than 20%. 21 2.4 Statistical Analysis Using log minus log plots of the survivor function one can check the proportionality assumption of an independent variable on the hazard function. Let us assume a proportional hazards relationship ^(t;z )=A.o(t)exp(J3z ) for a set of covariates z=( z,,, - • ",z^) and regression coefficients B=(i3^, • • ",5^). It follows that for a covariate z^ to satisfy the proportional hazards model log(-log(Sgj (t) ) ) - log(-log(Sgjx(t ) ) ) = constant x J3- for the and values of By plotting log(- log(Sgj ( t) ) ) for j=l,2,3/' • • on the same graph and noting that the two curves are approximately parallel one can conclude that satisfies the proportional hazards assumption. Plots of estimated log minus log survivor function stratified on age at diagnosis for these ALL data could be interpreted as approximately parallel for most groups. However the one year of age at diagnosis and under group was an exception and did not exhibit the same features as the other age at diagnosis groups. | Relative risk was estimated using the age spline by ! taking the ratio of estimated hazard functions to estimate ; the proportional increase in risk of failure at any given ! time, adjusted for significant clinical variables. I i 22 i Goodness of fit for the spline model and interaction of clinical variables with the age spline were tested for significance by comparing the log-likelihoods of the fit associated with the model containing terms of interest | (likelihood ratio c h i - s q u a r e s t a t i s t i c ) . A d j u s t m e n t s i n t h e degrees of freedom associated with the likelihood ratio test due to hidden parameters caused by knot location were not made. This is consistent with the methods of Durrleman and Simon in which they demonstrated similar results between the above method and a local scoring algorithm that adjusted for hidden parameters. Clinical variables found to have significant interaction effects with the spline were used as stratification variables. A separate age spline model was developed for each stratum and relative risks were estimated as above. Univariate and multivariate survival analysis estimates without the age spline were used to compare the fit of the spline model findings. Estimates of life table outcome were plotted using the Kaplan-Meier method for censored data^^, and curves were compared using the logrank statistic^®. Also, I the number of observed to expected (0/E) events were ' calculated for each group, and used to determine estimates ' for relative hazard rates between groups (e.g., relative • hazard of group 1 compared to group 2 is estimated as the i ■ ratio of 0/E of groups 1 & 2). Expected events were based on 23: the life table estimate of the number of events in the group of interest if the null hypothesis of no difference among groups was true. Life tables were stratified over age, study and treatment groups and compared within the interaction variable groupings to determine the effects the interaction variable had on outcome. Outcome was defined as the time from initial study entry to the first major disease event (i.e., failure to achieve remission, relapse at any site, second malignant neoplasm, or death) often referred to as event-free survival (EFS). In addition, separate life table analysis was performed excluding those who failed induction (i.e., disease-free survival from end of induction). Multivariate analysis utilized the Cox proportional hazards regression model to determine adjusted relative risks (from empirical data) within age and treatment groups. 24 Chapter III RESULTS Results from the stepwise regression, outlined in the methods section are: first, second and third knots were located at 2 2 , 3 7 , and 1 6 3 m o n t h s , respectively, for t h e a g e at diagnosis spline covariate with significant clinical variables also included in the model (viz., WBC, hepatosplenomegaly, sex, race and platelet count). Using this three knot cubic spline model, a testing procedure was implemented. Nested covariates were utilized to determine the polynomial spline segment in the end pieces that most closely represented the age at diagnosis data. Using Egs. (8 & 9) the quadratic term in the first and last sections of the spline were tested for significance by comparing the log—likelihoods of the models with and without the quadratic term (Bgg) • This method of testing nested terms, as detailed in the paper by Smith^^, is made possible because of the " + function terms. The function terms in Eg. 8 only have an effect when age at diagnosis is beyond the first knot, leaving the Bqj coefficients to determine the degree of the polynomial in the first spline segment. Eg. 9 performs the same function for the last spline segment by reversing the function notation. Then the functions only have an effect on the first, second, and third spline segments, with the final segment determined by the Bq. terms. 25 Comparisons of the spline model to that of the simple polynomial model were made by testing the significance of spline coefficients as a group in the spline model (since the polynomial model with terms are nested within the spline model, see Eg. 8). Table 2, part A shows that a linear polynomial first section results in a much worse fit than a quadratic polynomial first section (p<0.0001). A linear polynomial in the last spline segment has approximately the same statistical fit as a quadratic polynomial in the last section, but uses fewer degrees of freedom (i.e., avoiding the problem of over fitting associated with more degrees of freedom; p=0.24). The last line in Table 2, part A demonstrates that the spline model gives a much improved fit to the data than simply treating the age covariate as a simple quadratic polynomial (p<0.0001). Tests for significant improvement of the cubic polynomial spline in the first and last segments are shown in Table 2, parts C & D. Part C shows that a quadratic polynomial spline in the last segment offers about the same statistical fit as the cubic polynomial spline (i.e., again with fewer degrees of freedom, p=0.57), and thus would offer no advantages over the quadratic polynomial (or linear polynomial) spline in that segment. However, the spline function has an improved fit over the simple cubic 26 Table 2. Results of fitting Cox proportional hazards models using a spline function to estimate the prognostic effect of age at diagnosis. MODEL LOG-LIKELIHOOD LIKELIHOOD RATIO Chi-SQUARE DF P-VAL PART A q"c"c"q+CL l"c"c"q+CL q"c"c"l+CL q +CL -10487.14 -10512.31 -10487.84 -10526.61 50.33 1 1.41 1 78.94 2 <0.0001 0.24 <0.0001 PART B l"c"c"l+CL 1 +CL -10520.73 -10534.49 27.52 1 <0.0001 PART C c^c^c^c+CL c"c"c"q+CL c"c"c"l+CL c +CL -10486.92 -10487.08 -10487.79 -10507.89 0.33 1 1.75 2 41.94 3 0.57 0.42 <0.0001 PART D c"c"c"l+CL q"c"c"l+CL -10487.79 -10487.84 0 .10 1 0.75 Notes : 1, q, and c represent linear, segments. quadratic and cubic spline ^ represents diagnosis. knot points at 22, 37, and 164 months after CL represents clinical covariates included in the model - WBC, hepatosplenomegaly, sex, race and platelet count. 27 polynomial(p<0.0001). Part D illustrates that the quadratic polynomial spline in the first segment also results in about the same statistical fit as the cubic polynomial (p=0.75). For completeness, part B of Table 2 shows a statistically improved fit of the spline model over a simple linear polynomial (p<0.0001). The primary conclusion from Table 2 is that the spline: quadratic'^ cubiccubic''linear is the lowest order spline (avoiding problems associated with over fitting) such that no other spline has a better fit to the data. The notation used here, and in Table 2, to represent the spline is the same as that used by Smith^^. Linear, quadratic and cubic refer to the degree of the spline polynomial segment, while denotes a segment joint or knot. Therefore, the quadratic''cubic''cubic''linear (q''c''c''l) spline model forage at diagnosis was used for the remainder of this study. Shown in Figure 2 are risk estimates based on the age spline for ALL patients relative to the median age at diagnosis (i.e., approximately 5 years or 60 months), with associated 95% confidence limits at various age values. A graphical comparison of the spline model relative risk estimates to that of simple linear, quadratic and cubic polynomial models are illustrated in Figure 3. It is important to note that even though the age spline had the ability to assume a variety of shapes, the result 28 œ CE LU > 5 LU CE 95% UPPER Ci 95% LOWER Cl 0 24 48 72 96 120 144 168 192 216 AGE AT DIAGNOSIS (Months) Figure 2. Spline estimated relative risk by age group, relative to children diagnosed at 5 yrs. 29 MODEL TYPES Spline Linear ^Q uadratic Cubic 0 24 48 72 96 120 144 168 192 216 AGE AT DIAGNOSIS (Months) Figure 3. Relative risk comparisons using linear, quadratic, cubic polynomial age covariates and the spline function estimate of the age effect. 30 was a steep monotonie decrease in the hazard function as age increases for the youngest children, with a minimum at approximately 30 months, and a gradual monotonie increase in risk for advancing age beyond 30 months. The minimum of 30 months is the absolute minimum of the spline curve, while there is a somewhat flat portion of the spline that extends from 24 to 48 months that can be considered the ages of lowest risk. The sharp peak in risk for infants was corroborated with Kaplan-Meier life table estimates for event-free survival. Table 3 demonstrates that within refined age intervals there is indeed a highly statistically significant trend (p<0.0001) of decreasing risk from age 0 to 24 months (as the spline demonstrated). The Chi-square values in Table 3 show that the linear trend effect accounts for most of the differences seen in the age groups. A Cox proportional hazards regression that included age at diagnosis in finely divided categories as a qualitative variable along with clinical variables that were found to be significant in the spline model, resulted in relative risk estimates for age that are quite similar to the spline model. Specifically, risk begins at a high level for patients under 1 year of age, drops to a minimum for ages 2- 3 years, then increases as age increases. Table 4 displays these estimates categorized by age groups, and compares them to relative risk point estimates obtained from the spline 31 o o ^ q I I V g co LJL LU o S 00 co LO Gi c\i LU CD ( D _Ü 8 CO CM CO CM 00 CO Q CL o o co co CD 0 k- co en co < Q 32 Table 4. Relative risk comparison within age groups adjusted for significant clinical variables. COX REGRESSION SPLINE MODEL AGE GROUP(Yr.) RELATIVE RISK RELATIVE RISK P-VALUE < 1 3.63 3.5 <0.0001 1-2 1.30 1.2 0.03 2-3 0.99 0.8 0.8 9 3-4 1.05 0.9 0.64 4—6 1.00 1.0 — — — 6-10 1.24 1.2 0.03 10-14 1.70 1.4 <0.0001 >14 2.04 2.0 <0.0001 Note: Spline model relative risk estimates taken at 0.5, 1.5, 2.5, 3.5, 5, 8, 12, and 17 years respectively. P-value represents significance associated with empirical data when compared to the "baseline" group of 4-6 years of age at diagnosis. 33 model at the midpoint of each age group. Note that if one attempts to model the age effect by categorical groupings, it will require numerous categories (i.e., parameters) if accurate estimation across the entire age range is desired. On the other hand, the graphical representation of the age spline model provides an accurate depiction of the risks associated with age at diagnosis without requiring the introduction of a large number of parameters. Observing the characteristics of the age spline model one can see trends associated with age at diagnosis that would be more difficult to detect using other methods. By imposing conditions on the model one can easily observe the effects these conditions have over the range of age at diagnosis. Effect modification on the age spline is one such application that can be examined. An analysis using other factors with known prognostic effects on outcome as potential interaction factors with the age spline model was performed to find possible confounding factors with the age spline. This resulted in statistically significant (p=0.02) results for only the expression of the CDIO or CALLA antigen (see Table 5). Lines 2 and 8 of Table 5 show that CALLA had a more significant effect modification on age at diagnosis when it was used in the form of a spline model (line 8, p=0.02) as opposed to a qualitative variable (line 2, p=0.07) with arbitrary categories. Thus the spline 34 Table 5. Results of interaction effects for other covariates with age at diagnosis. MODEL LOG-LIKELIHOOD LIKELIHOOD RATIO Chi-SQUARE DF P-VAL SPL+CL -5214.91 _ „ ^ -— --- +AGE * CALLA -5210.60 8.61 4 0.07 +AGE*SEX -5213.41 2.99 2 0.22 +AGE*RACE -5213.87 2.06 2 0.36 +AGE*WBC -5212.66 4.50 4 0.34 +AGE*HSM -5214.62 0 . 57 2 0.75 +AGE*PLATELET -5214.31 1.20 4 0. 88 4-CALLA*SPLINE -5209.67 10.46 3 0.02 Notes: The first line represents the baseline to which the other lines are compared. Lines 2 - 8 includes the covariates from line one in addition to those on its line. * - indicates interaction between covariates. CL - Clinical and laboratory covariates included in the model - WBC, hepatosplenomegaly (HSM), sex, race, platelet count, and CALLA. Age, WBC, CALLA, and platelet count are qualitative variables split such that each group has an equivalent number of patients (see methods section). Sex, race, and hepatosplenomegaly are qualitative variables split into two categories (see methods section). SPLINE - Representation of age using the spline model. 35 model which allows a more precise representation of age at diagnosis resulted in a greater effect modification with CALLA than when age was categorized arbitrarily. Graphically one can see this interaction effect using relative risk estimates displayed in Figure 4. A separate spline model was generated for three levels of CALLA expression. Risk of relapse relative to those at 5 years (60 months) of age was greater for those with lower CALLA expression levels when only younger patients were considered. For older patients risk was higher for those with intermediate or elevated CALLA levels (see Figure 4). To verify the results found with the spline model, univariate and multivariate analysis using age at diagnosis as a categorical variable was performed via Cox regression and Kaplan-Meier life tables. The interaction effect of CALLA with age from a Kaplan- Meier perspective for event-free survival outcome was analyzed. The aggregate observed to expected (0/E) ratios for the three categories of CALLA (CALLA grouped into approximately equal patient groups : <30%, 31%-80%, >80%) were greatest for lower expression levels of CALLA after adjustments for the age at diagnosis groups were considered (logrank p=0 . 0001, trend p<0 . 0001 ) . Within age groups, those under 6 years continued to exhibit statistically significant higher 0/E values for depressed CALLA expression levels (see Table 6). However, for age groups over 6 years the 36 CALLA STRATA > 80 % 31 - 80 % ^ < 31 % > 2 0 24 48 72 96 120 144 168 192 216 AGE AT DIAGNOSIS (Months) Figure 4. Estimated relative risk, using spline techniques stratified by CALLA expression levels. 37 < _J < ü M— O c / ) ü CD ît CD ü œ o c D) o Q_ O H— CO u_ LU c / ) CD 1o E w CD CD JD CO +-* CD CD O) CO 0) CD ^ -O ~ H— CO +3 Q_g (d _ 0 ) . C O Q Z LU EC § A g LU O § CO V I < ü o oo A g co g VI < ü C/D CO II < O o c >- ET S ' oT M 5T o' co O O o C D D co C D ) é Si CM O C D D ;= o 00 C D D CM ID M C) CD CD d d d d d co o' V CD 00 lO M CM N CD CM a LO 00 ■ < — CD LO CD CD CD co O CM T — O c o " c d d" CO CO N CD 00 T— S O) o co CM CO CD O CD G i C M lO 00 00 A o o o CD V o o o s: 00 co iq co iq % N C D D s p a Z Z ' c. ô C, o r> - co lO C M 00 LO CO 00 N co CD p C D ) OO d T - ^ d d d ' T- d d ID co cT C D D oT p 6T M o ' co à C - 00 CD CD co 1 — lO CD p CD C D D C M C D D C D ) d d d T— d d O CD o" LO co c d d" lO" iq od" C D D s lo " p T - : T - ^ T - ^ T-‘ d d d N 00 N CD S8 M CD < CE Ul B (D 73 0) £ c (D C 0 D 1 < ü O < A ) ■O i S I >> (D O Ci D- (/) 0 ) 1 1 û 5 Q ) c (D W 0) Q . 0) (D i C w co d ) X 0) s JC D î ( 0 J C II 38 statistical significance was lost and in fact a different pattern within CALLA levels was observed (i.e., those patients with intermediate CALLA expression levels achieved the highest 0/E values with the low CALLA expression patients now having the s m a l l e s t Q/E). Due to small sample sizes in many groups and/or random variation, the p-values fluctuate from group to group and would not be expected to exhibit the same level of statistical significance as the overall adjusted value. A more representative statistic may be the life table estimated relative hazard (as defined in the methods section) shown in Table 6. One sees that the relative hazard of the low CALLA expression group to that of the intermediate and high groups displayed the same characteristics as mentioned above from the spline analysis. To ensure that early induction failures (failure to respond or death in induction) did not have an important effect on our results, Kaplan-Meier life table analysis was repeated excluding patients that never completed induction successfully. The results indicated no significant change from the CALLA analysis of event-free survival from study entry discussed earlier. This is expected considering the small percentage of induction failures within our population. In a multivariate analsis, using a Cox regression model with the same clinical variables as covariates, CALLA level 39 relative risk estimates within age groups displayed the same characteristics as outlined in the Kaplan-Meier life table analysis (see Table 7). Therefore, both the Kaplan-Meier and Cox regression analysis agreed with the interaction effects demonstrated in the spline model. Adjustment (i.e., stratification) of the Kaplan-Meier life table analysis of CALLA over treatment type resulted in the same overall trend (ie. lower CALLA expression associated with a poorer prognosis, global logrank test, p=0.0001; trend test, p<0.0001, see Table 8). However, patients receiving intensive regimens (those classified as intensive and "lymphoma-like” comprising a majority of ALL patients) had statistically significant logrank tests for CALLA, generally responsible for producing this overall trend effect. One notes that in both groups of patients receiving standard non-intensive chemotherapy, the CALLA effect was very weak. Adjusted CALLA life table analysis (using only patients treated with intensive and "lymphoma-like" regimens) resulted in statistically significant higher risks for lower levels of CALLA expression for patients under 6 years of age at diagnosis (see Table 9). Patients over 6 years had similar or slightly greater risks for the intermediate and high CALLA e x p r e s s i o n levels (as with the previous analysis, no statistical significance was achieved in the older age 40 Table 7. Relative risk of CALLA within age groups. COX REGRESSION AGE GROUP(Yr.) CALLA(%) RELATIVE RISK < 1 <30 vs. >80 2.81 31-80 vs. >80 1.84 1-2 <30 vs. >80 1.48 31-80 vs. >80 0.63 2-3 <30 vs. >80 1.59 31-80 vs. >80 1.15 3-4 <30 vs. >80 1.56 31-80 vs. >80 1.44 4 — 6 <30 vs. >80 1.77 31-80 vs. >80 1.11 6-10 <30 vs. >80 0.81 31-80 vs. >80 1.09 10-14 <30 vs. >80 0. 78 31-80 vs. >80 1.12 > 14 <30 vs. >80 0.84 31-80 vs. >80 1.23 OVERALL <30 vs. >80 1.92 31-80 vs. >80 1.13 41 < _J < ü H— O ü C D (D ü C O O C D) O 1— ÛL 1— O M— C O L i _ L U C O C D C O E Q. 3 O c o L_ C D U) C D c 0 g E C D c o 0 0 ‘o n u 0 C C O Q . 0 C O +-» b d 0 DO C D _o .C O H LU C E t o o 00 A s lU « o g co V I S § A § CO § V I < Ü h - z LU § o H O c o o o o (M O o o o o CO N s 2. 8 S O S e N CD O O O S- § CVJ o o O O O CD CD CD CD CD CD CD 8 LO* g S c v T CD 6^ ZZ' Ebl El — ^ CD O) Gi CD CD N S p ? S O O O o o CD CD - - - S o' (J) S N CD CD p ô c. zz O i o CO g CD p o p CD CO 00 p T-" 1 —‘ o 1 —’ 1-^ O o 8 c\T o s CD O o o " g î S CD CVJ LO g 00 CVJ CVJ 2 CD S LO M GÎ ID o o " N ID fe S I N 00 CO (J) (M É g CD 00 ID < Q < c e s o < Q < OC s O < Q < OC < Q < OC < Q < OC Û o c o c o c z o z < z < co < > < J i i c o ^ LU > c o z LU < z il o c CL >- < il Ou o c < Q < DC CO Û_ Z) o o c ü a > % y ( D £ o c 0 ) > 0 ) c o c o (O 0 ) Œ < Ü o w -o c ô > to > ( D > ü 0 ) Q. ü ) 0 ) S “ 0 ) (/> _ 0 ) g - 1 li .£ • §> w y 1 1 42 Q (/) (/) UJ 0 Q_ CL CO CO CO 0 13 13 2 2 o o N CD 0 ^ _l y o> O) UJ d G) d 0 0 ■§' o d CD d E 0 'ce tî o _j ■ _c o c O 0 > o o' <q> « A +- 0 0 C 0 > 0 0 0 ^ 0 0 n > 0 0 C ^ -Ï § CO Z § in CM CO CM in % K l_ — s § 11 2 # = .E CO V I CM CM IQ CM o CO CO 0 ^ 0 JO < CO m — 1 * _j 0 ■ u _j < Ü I s 0 ^ .S-& Q- S w !c O) UÜ 0 Ql 3 ^ 2 g CO CO o o l l < O ^ V CO CO A 0 ' — ' _a .0 1- 43 groups). These are the same effect modification results observed in the age spline model. Thus, it appears that patients in the intensive treatment group were the primary cause for the interaction effect. Confirming the CALLA-AGE interaction effect using multivariate Cox regression, with age at diagnosis represented as a quantitative variable (not a spline) and adjustment for clinical variables, a strong interaction effect was observed. Table 10 illustrates that the difference in likelihoods between models containing a CALLA- AGE interaction and models without it had a chi-square value of 13.20 on 2 degrees of freedom with a p-value of 0.001. Since CALLA expression does not indicate a specific cell lymphoblast lineage (although it is much more common in B-lineage patients), Kaplan-Meier life table analysis was performed within B and T cell subtypes. Due to the small percentage of patients that could be classified into lineage types because of missing data for immunophenotyping in many patients, age groups were combined such that all patients under 6 years of age at the time of diagnosis were categorized into the first group and those over 6 years where placed in the second group. This categorization was chosen based on CALLA’s similar life table outcomes within these two groups in previous analyses (see Table 6). Table 11 shows that within B-cell patients both the over and under 44 Table 10, Significance of CALLA - AGE interaction after adjustment for clinical variables. df LL CLINICAL VARIABLES+ CALLA 14 -5211.27 Multiplicative model with qualitative clinical var. CLINICAL VARIABLES^ CALLA+CALLA*AGE 16 -5204.67 Quantitative linear * linear interaction of CALLA with age CHI-SQUARE = 13.20 on 2 degrees of freedom P-val = 0.001 Note: Clinical variables are categorized as qualitative variables. CALLA and age are quantitative variables. 45 LU U_ g g S ’ ! CL CD O 00 LL JQ û. g o 00 00 o co O) s i < û jQ 0 CD ( C ( D C C O N â LO d 00 o co CD d o' C V J co N CO V I o S' S' CM o' co CD CD CO d d CM CM N c o CD CD CD CD CD d d d d d S' S' S' S' co CO N CO q d d c o N o CO o q CD co 1 —_ q d d d c ÿ P O S' S' S' CD CO CM CD q d c^ d f CD co N co LO CD q q (D d d d S S O) CD co o CD o o N 00 CM •« - co CM LO O S s co co" CD CM co CM CM cü co LO CO r^ CM N cd" T f - q CO CM lO CD • « — CM CD A < OC LU > O 0 CD CO 0 C co V I co A < OC LU > O 0 0 JJ 0 E 0 c 0 > 0 ) c o 0 $ o. s < ü o 0 I I 0 - > 0 1 1 0 0 il s i l i 5 o 0 d 11 46 6 years of age at diagnosis groups and the adjusted summary life tables all displayed similar characteristics (intermediate to high CALLA expression group had the highest risks). However, we should be cautious about the interpretation of these results due to the small number of B-lineage specific patients in the under 31% CALLA expression level. Patients with T-cell lymphoblast lineage exhibited higher risks with lower CALLA expression levels, with the adjusted summary life table resulting in higher risks for lower CALLA expression levels (see Table 11). Again, caution must be taken with these results and confirmation with a larger number of lineage classifiable patients should be attempted, such that this interesting issue can be more definitively determined. 47 Chapter IV DISCUSSION This study has demonstrated the usefulness of the incorporation of spline functions into Cox proportional hazard r e g r e s s i o n m o d e l s a s a tool for recognizing risk trends associated with the age effect in childhood acute lymphoblastic leukemia. The primary advantages associated with the spline procedure are the less restrictive assumptions concerning the underlying form of the "true model". As detailed in the results section, where the spline model had a much improved fit to the data over that of conventional (linear, quadratic and cubic) polynomial models, traditional regression techniques can lead to unreliable estimates. The basic shape of the relative risk curve using the age spline model shown in Figure 1, corresponds well to observations reported in other studies^"^^'^^'^^. These researchers have reported a very high risk of relapse for ALL patients under 1 year at diagnosis, falling to a minimum for ages 2 to 4 years, then gradually increasing with advancing age beyond 4 years. The cubic spline model replicates these characteristics quite closely, while the linear, quadratic and cubic polynomial models do not. The smooth age spline function provides a more accurate representation of risks associated with ALL as a function of 48 age at diagnosis than more traditional methods. Risk analysis using groupings of arbitrary age at diagnosis intervals produces results that vary greatly between groups. This variation is usually based on the intervals selected and do not have any biological foundation. The age spline function has the effect of smoothing these spurious points and producing a more accurate representation of relative risk over the range of age at diagnosis. Moreover, using numerous groupings to accurately represent the effect of a quantitative variable will require several additional parameters to be introduced into any Cox regression procedures that are being considered for analysis. Therefore, the spline approach is a modeling strategy that avoids excessive parameterization for multivariate analysis. The poor outcomes for infants as compared to older patients, as shown in the relative risk spline curve, is similar to that reported in earlier studies^^. A plausible explanation for this steep gradient may be found in the way infants respond to treatments and disease processes differently than older populations, due to unique biological traits associated with infants. By 18 months of age at diagnosis the spline function demonstrates that the rate of increase of the relative risk is quickly declining, approaching a region that can be considered "at lowest risk" from 24 to 48 months. Analysis 49 of the spline' function resulted in an absolute minimum occurring at 30 months of age at diagnosis. Beyond 48 months a smooth gradual increase in the hazard function is apparent, regardless of the ability of the spline to assume a variety of shapes. There has been considerable speculation and research^^'^^ concerning the increased risk associated with older children. Through blood tests, urinary steroid analysis, and interviews of parents and patients it has been theorized that patient noncompliance with self-administered therapy is the cause of the increased risk among adolescent children^^'^^. Compliance was found to be closely related to the degree of confusion concerning the transfer of responsibility to administer the medication from the parent to the adolescent^^. Noncompliant patients reported disagreements between parent and adolescent patients when asked who was responsible for administering the medication. Also busy schedules and forgetfulness were stated as reasons for noncompliance. It would obviously be interesting to examine whether the gradual increase in risk among the older patients could be associated with measures such as compliance. This would be a worthwhile study design consideration for investigation in future childhood ALL studies. 50 As an application using the spline function we found the age spline had an effect modification with CALLA. Stratification of the age spline model over three levels of CALLA expression indicated varying failure rate curves for each CALLA level. All three levels of CALLA (<30%, 31%-80%, >80%) had the same general shape to their relative risk curves as that detailed above. However, for younger patients their rate of failure was greater for lower levels of CALLA expression (or CALLA negativity). This trend reversed for older patients such that intermediate to high CALLA expression patients (or CALLA positivity) now had the highest risk for poor outcomes. Past research has established CALLA as a good prognostic indicator for ALL disease outcome. However, no studies thus far have investigated the prognostic effect of CALLA within refined age groups. Studies have found CALLA negativity to be an unfavorable prognostic factor when all age groups were considered^®. Some researchers qualified this statement to pertain to patients with B-cell lineage leukemia. However, they also found that no difference between CALLA groups existed once patients reached consolidation (i.e., duration of complete continuous remission was the same between CALLA groups, but more CALLA negative patients failed to reach complete remission^^) . Unfortunately, we were unable to confirm the CALLA 51 interaction effect within B-cell lymphoblast lineage patients, possibly stemming from a lack of sufficient number of specific lineage subtype patients classifiable into each CALLA category (T-cell lymphoblast lineage patients did experience the CALLA-age interaction effect, although it was statistically non-significant due to small patient counts in some CALLA groups). Also, no difference in our results were found when only those patients who reached complete remission were considered. However, we did find that when we considered all age groups, CALLA negativity was a statistically significant unfavorable prognostic factor, even after adjustment for treatment and study groups. Children in the intensive and "lymphoma-like" regimen treatment groups were found to have the greatest prognostic association with CALLA. Also, both treatment groups displayed the CALLA-AGE interaction effects described earlier. However, patients in the non-intensively treated regimens did not show the aforementioned relationship of CALLA expression levels to outcome. In conclusion, for these 3801 patients with ALL, the spline function was found to more accurately represent relative risk over the range of age at diagnosis than traditional methods using age categories. The age spline corroborated many of the age at diagnosis characteristics found in previous studies (i.e., very high risks for 52 infants, lowest risks for patients between 24 and 48 months, gradual increasing risks for older patients) while providing a much clearer depiction of risks associated with age at diagnosis for ALL patients. In addition we found CALLA negativity to be an adverse prognostic factor for disease outcome. However when stratified within age at diagnosis groups we found CALLA negativity to have a better outcome (although statistically nonsignificant) in older patients. We also found this effect to occur predominantly in patients in the intensive and lymphoma type treatment groups. Although the spline model preformed well, it is worth noting that as Durrleman and Simon point out more research is warranted in such areas as: optimal choice of knot location, development of nested spline models, measures of influence and multivariate splines for interaction effects. 53 REFERENCES 1. Pierce, M., Borges, W., Heyn, R., Wolff, J.A., Gilbert, E.S.: Epidemiological factors and survival experience 1770 children with acute leukemia treated by members of the Children's Study Group A between 1957 and 1964. Cancer, 23:1296-1304, 1969. 2. Committee on Leukemia and Working Party on Leukemia in Childhood: Duration of survival of children with acute leukemia. Br. Med. J., 4:7-9, 1971. 3. Tivey, H.: The natural history of untreated acute leukemia. Ann. NY Acad. Sci., 60:322-358, 1954. 4. Poplack, D.: Acute Lymphoblastic Leukemia in Principles and Practice of Pediatric Oncology: Pizzo, P., Poplack, D.: pp 431-481. Philadelphia, J. B. Lippincott Co., 1989. 5. 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Richardson, J., Marks, G., Levine, A.: The Influence of Disease and Side Effects of Treatment on Compliance with Cancer Therapy. J. of Clinical Oncology, 6:1746 -1752, 1988. 38. Sallan, S., Ritz, J., Pesando, J., Gelber, R., O'Brien, C., Hitchcock, S., Coral, F., Schlossman, S.: Cell surface antigens : Prognostic implications in childhood acute lymphoblastic leukemia. Blood, 55: 395-401, 1980. 39. Pullen, J., Boyett, J., Borowitz, M., Dowell. B., Falletta, J., Krejmas, N., Sexauer, C., Crist, W.: How important is common acute lymphocytic leukemia antigen (CALLA) negativity as a prognostic factor in children excluding infants with B-precursor acute lymphocytic leukemia (ALL)? A Pediatric Oncology Group (POG) Study [abstract]. Proc Am. Soc. Clin. Oncol. 6:151, 1987. 57</q>

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Creator Ruel, Christopher James (author)

Core Title The use of cubic splines for estimating the prognostic effect of age at diagnosis in childhood acute lymphoblastic leukemia

School Graduate School

Degree Master of Science

Degree Program Biometry

Degree Conferral Date 1994-08

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag biological sciences,health and environmental sciences,OAI-PMH Harvest

Format application/pdf (imt)

Language English

Contributor Digitized by ProQuest (provenance)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c37-199062

Unique identifier UC11647973

Identifier EP54951.pdf (filename),usctheses-c37-199062 (legacy record id)

Legacy Identifier EP54951.pdf

Dmrecord 199062

Document Type Thesis

Format application/pdf (imt)

Rights Ruel, Christopher James

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