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Essays in pharmaceutical and health economics
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Essays in pharmaceutical and health economics
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Essays in Pharmaceutical and Health Economics by Jaehong Kim A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY HEALTH ECONOMICS August 2021 Copyright 2021 Jaehong Kim Acknowledgments I am grateful to Professor Darius Lakdawalla for his guidance, support and encouragement in completing this dissertation. I am fortunate to have a great mentor who invested so much time, resources and goodwill into my academic and personal growth. My sincere gratitude also goes to Professor John Romley. He always had an open door and taught me the essence of great research. Furthermore, I want to thank Professor Neeraj Sood and Professor Seth Seabury for being my mentors throughout my academic research. I have beneted immensely from discussions with them. To my mom and brother in Korea { none of this work would have been possible without the unconditional support you've given me. Thank you for always being there for me. Without you, I would not be the person I am today. I hope that I have made you proud. My special love is saved for my wife and daughter. To my wife, Eunhae { you have been supportive of me throughout this entire process and have made countless sacrice to help me get to this point. But, most of all, thank you for being my best friend. I owe you everything. To my daughter, Jua { you have been the light of my life for the last three years and have given me the extra strength and motivation to get things done. I love you to the moon and back. Finally, to my dad who never saw this adventure, this dissertation is dedicated to you. ii Table of Contents Acknowledgments ii List of Tables v List of Figures vi Abstract vii 1 Patent Race and Heterogeneous Innovations 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Key features of the heterogeneous patent race . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Incomplete information on R&D technology . . . . . . . . . . . . . . . . . . . 4 1.2.2 Heterogeneous patent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Non-cooperative game of R&D investment . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Normative economics of R&D investment . . . . . . . . . . . . . . . . . . . . . . . . 17 1.5 Social benet appropriation and market eciency . . . . . . . . . . . . . . . . . . . . 21 1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2 Pharmaceutical R&D Competition: Application of Heterogeneous Patent Race 24 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Pharmaceutical innovation and development . . . . . . . . . . . . . . . . . . . . . . . 26 2.3 Introduction of key concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5 Empirical framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5.1 Estimation of the drug quality-adjusted market share distribution . . . . . . 30 2.5.2 Estimation of the eect of the drug quality-adjusted market share distribution on the R&D investment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.6 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 iii 3 Association between Verapamil Use and Serious Hypoglycemic Events among Persons with Type 1 Diabetes: A Retrospective Cohort Analysis 53 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Bibliography 65 A. Appendix to Chapter 1 76 A.1 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 A.2 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 A.3 Proof of Proposition 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 B. Appendix to Chapter 2 81 C. Appendix to Chapter 3 83 iv List of Tables 2.1 NDA classication codes (1996-2015) . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2 Distribution of the markets and the average of the realized market shares by the number of NMEs (1996{2015) . . . . . . . . . . . . . . . . . . . . . . . 42 2.3 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.4 Estimation results of the drug quality-adjusted/unadjusted market share distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.5 Estimation results of the eect of the drug quality-adjusted market share distribution on the R&D investment . . . . . . . . . . . . . . . . . . . . . . . . 45 2.6 Robustness check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.7 Proportion of therapeutic classes where early mover advantage is identi- ed, by therapeutic group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.1 Characteristics of study population . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2 Poisson regression results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 B.1 Time windows for measuring the market share distribution and the future market size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 B.2 List of therapeutic classes and groups in the study sample . . . . . . . . . 82 C.1 Poisson regression results of comorbidities . . . . . . . . . . . . . . . . . . . . 85 v List of Figures 2.1 Time schedule of R&D decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.2 Comparison of drug quality-unadjusted versus quality-adjusted market shares of early movers, by the number of drugs . . . . . . . . . . . . . . . . . 49 2.3 The number of therapeutic classes where at least one drug is intro- duced and the number of therapeutic classes where early mover advantage (EMA) is identied, by therapeutic group and 10-year window . . . . . . . 50 2.4 Genitourinary product group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.1 Predicted number of hospital admissions / ED visits for hypoglycemia per 1,000 person-years, according to number of verapamil lls . . . . . . . 63 3.2 Predicted change in hospital admissions / ED visits for hypoglycemia per 1,000 person-years with an additional verapamil ll beyond the median quantity, by subpopulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 C.1 CONSORT diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 C.2 Empirical cumulative density functions of the predicted probability of being a non-user, a low user, or a high user . . . . . . . . . . . . . . . . . . . 84 vi Abstract This dissertation comprises three essays in pharmaceutical and health economics. The rst paper studies the structure of research and development (R&D) competition in an industry where hetero- geneous technologies with the same innovative contribution are patented and launched on the same market. In such industries, R&D competition does not end up with winner-takes-all as is implicitly assumed in the conventional theory of innovation investment. This paper suggests an alternative framework to incorporate such a market structure into R&D competition: the heterogeneous patent race. In this framework, the industry equilibrium of R&D increases as the higher market share is predicted for the early mover, i.e. the winner of the competition. Contrary to the conventional theory that necessarily results in overinvestment, R&D can be over- or underinvested depending on whether early mover advantage or disadvantage is expected. The second paper explores pharmaceutical R&D competition applying the heterogeneous patent race model. An empirical study of pharmaceutical expenditures and pipelines in 1996{2016 shows that the R&D eort, measured by the number of drugs in clinical trials, increases by 1.5%{2.0% in response to a 1% point increase in the expected market share of early movers. The estimated market share distribution suggests that in 14.2% of the therapeutic classes, too many resources were invested in clinical trials beginning between 2005 and 2015. The last paper performs a retrospective cohort study of fee-for-service Medicare beneciaries with type 1 diabetes to determine whether the use of verapamil by persons with type 1 diabetes is associated with a lower risk of serious hypoglycemic events. It shows that an additional 30-day- equivalent ll of verapamil beyond the median quantity during the 12-month exposure period was associated with a 5.0% reduction in the number of acute hospital admissions and emergency de- partment visits during the 12-month follow-up period. This evidence is consistent with the ndings from a small trial of the eect of verapamil on pancreatic cell survival in newly diagnosed adults. vii Chapter 1 Patent Race and Heterogeneous Inno- vations 1.1 Introduction This paper presents a model of the research and development (R&D) competition of an industry in which heterogeneous technologies with the same innovative contribution are patented and launched on the same market. In such industries, patent does not guarantee eective market exclusivity. For example, in the pharmaceutical industry, even if a pioneer rm has already developed an innovative molecule introducing a new mechanism of action for a certain indication, a distinct molecule can be introduced into the same therapeutic class market. This is because, just as with the pioneer drug, the intellectual property of the new molecule can be protected by patent. This implies that the R&D competition in this industry does not end up with winner-takes-all; instead, the followers, who are the losers in the competition, can bring their own molecules into the same therapeutic class market and share the market rents (Berndt, 2002; Lakdawalla, 2018). In this study, the R&D competition structure in such industries is referred to as heterogeneous patent race. The heterogeneous patent race model introduces the oligopoly structure of the product market into the conventional patent race framework. The reward of the competition is not monop- olized by the player who reaches the nishing line rst. Even if a rm fails to beat its competitors to market, it does not drop out of the R&D race, as the loser has the chance to partake in the 1 reward in the form of market share. Although there are two lines of research on the theory of innovation investment, they do not address the characteristic feature of the reward system of the heterogeneous patent race. They assume that rms pursue homogeneous technology and only one technology is patented. Naturally, the winner of the competition, the one and only provider in the market, reaps the reward in the form of monopoly rent. The models in the rst line are designed in such a way that action{reaction among the players in the middle of the race is absent, hence the previous strategies are inherently inhibited from aecting consecutive decisions (Loury, 1979; Lee and Wilde, 1980; Dasgupta and Stiglitz, 1980; Reinganum, 1981, 1982; Zeira, 2011). In this environment, competition always re- sults in excessive R&D investment due to duplicated eort. The studies in the second line focus on the dynamics of the equilibrium rather than normative implication (Fudenberg et al., 1983; Harris and Vickers, 1985a,b, 1987; Budd et al., 1993; Doraszelski, 2003; Cao, 2014). In the multistage race, rms check their positions in the race before making a decision, which results in an increase in leader dominance or catch-up behavior of followers. 1 In order to bridge the gap between the theoretical framework of the patent race and the compe- tition structure of pharmaceutical R&D, the heterogeneous patent race model is developed based on the model suggested by the rst line of literature. The model of the second line is hard to apply because it assumes the history of the competitors' strategies and their results to be observable during the race. This assumption is controversial in the sense that secrecy is one of the foremost strategies to preserving competitive advantage created by innovation in most industries (Cohen et al., 2000; Arundel, 2001; Hannah, 2005). For example, in the pharmaceutical industry, during clinical tests of substances, rms classify method or process, as well as the safety and ecacy of the substance, into trade secret. Therefore, they rarely unveil the progress and the results of each step before marketing; regulatory authorities also prohibit agents from divulging information gained during the review process (Medawar, 1993; Kesselheim and Mello, 2007). Due to its reward system characterized by the oligopoly structure of the product market, the heterogeneous patent race model has a competition structure distinctive from that of conventional 1 In another line of literature investigating sequential innovation (Green and Scotchmer, 1995; Scotchmer, 1996; O'Donoghue, 1998; Denicol o, 2000; Bessen and Maskin, 2009), the socially optimal patent breadth/length is examined. However, the nature of the R&D race is not inherent in the study setting; it does not consider the market uncertainty inherited by the eort made by rivals. 2 models. First, since a loser keeps running in the race until reaching the nish line, any rm partic- ipating in a race bears risk not only ex-ante its arrival at the market but ex-post. Even once the winner is determined, a rm still running R&D to launch a competing product (ex-ante market entry) is exposed to the same structure of market uncertainty as before the winner was announced. For example, even if it is expected that the reward always splits evenly to all rms whose innovations are on the market, the return to the second-to-market is higher than that to the third-to-market insofar as the second rank (the rst follower) earns in the duopoly market. The market uncertainty on the market position (whether to the second or the third ranks) results from the stochastic oc- currence of success and the amount of investment made by the rivals still competing with the rm in the race. Additionally, if a rm has already entered the market (ex-post market entry), whether it is the winner or not, it faces market uncertainty from about when its stake is encroached on by subsequent rms coming into the market, proportional to how much eort is made by the rms remaining in the race. The conventional patent race framework considers the market uncertainty ex-ante market entry of the rst rm only. The second distinction from the conventional approach is that patent does not work as a barrier to market entry. Instead, two types of R&D technology that are randomly assigned and unknown before the race starts are introduced into the model: one that results in a patentable invention at a random point of time, and the other that results in no output and failure of the project. Incorporating a competition structure characterized by these two features into the theory of in- novation, this paper rst theoretically shows that the expectation of time advantage/disadvantage in market share, that a rm gains by arriving early at the market, plays a key role in the rm's R&D decision and in the market eciency of the R&D investment. Specically, rst, the mar- ket equilibrium level of R&D investment is higher where more market share is anticipated for the player who makes a successful run on R&D ahead of the others (Proposition 1). Second, early mover advantage 2 is a sucient condition for overinvestment (Proposition 2). Third, if early mover disadvantage is expected, the industry equilibrium can achieve or fall below the market ecient level in a quickly growing market (Proposition 3). This paper is outlined as follows. Section 1.2 explains how to address the key characteristics of the heterogeneous patent system in the theory of innovation. Section 1.3 models the heterogeneous 2 The general mechanism of early mover (dis-)advantage is documented in Lieberman and Montgomery (1988). 3 patent race and presents the market equilibrium of the model. Section 1.4 provides normative implications. Section 1.5 discusses how the positive and normative implications change in a case where rms fail to completely appropriate the social benets of innovation. Section 1.6 concludes. 1.2 Key features of the heterogeneous patent race Innovators decide how much investment to make per period x for a given per-period market value or reward v t that is split between those arriving at the market with new technologies. Starting fromv 0 (hereafter, absolute market size), the market value evolves at the rate of (market growth rate), i.e. v t =e t v 0 . Since successful R&D is assumed to follow a Poisson process, time-to-invent is exponentially distributed with a rateh(x) that represents a success rate or productivity of R&D. The heterogeneous patent race model distinguishes itself from conventional models by its unique market structure. First, a rm makes a decision on R&D based on incomplete information on the type of its R&D technology. Second, since heterogeneous technologies are introduced into the same market, even after the winner of the patent competition is determined, the other rms continue to carry out their R&D projects with the goal of sharing the reward. These are the characteristic features of the heterogeneous patent race that must be addressed in the model. 1.2.1 Incomplete information on R&D technology As opposed to the conventional framework in which patent allows the reward to be completely exhausted by the winner by restricting the losers from entering the market, the heterogeneous patent race model assumes that the success or failure of R&D is determined by the types of R&D technology exogenously given with a common prior: \patentable R&D technology" and \null R&D technology" with a set of beliefsfq; 1qg. Patentable R&D technology is such that investment ultimately results in patentable inventions. It is represented by the success rate h(x) which is strictly increasing and concave. In the case of null R&D technology, investment incurs cost C(x) only, without any output. The cost function is strictly increasing and convex. Hence,q is referred to as patentability. The probability of success of patentable R&D follows an exponential distribution with the rate h(x) supported on an interval of time t2 (0;1). Consider an industry withM rms. Then, a representative rm has the following lifetime payo 4 function: E(x; ^ x) =q M X N=1 M 1 N 1 q N1 (1q) MN E N (x; ^ x) (1q)C(x) = M X N=1 P N E N (x; ^ x) (1q)C(x) (1) where ^ x is a selection of the competitors' strategies. The rst term on the second line of (1), the lifetime expected prot by patentable R&D technology P M N=1 P N E N (x; ^ x), is made up of two parts. The rst part is the probability that there are N rms (including the representative rm itself) whose R&D technologies are patentable, P N M1 N1 q N (1q) MN . In other words, it means the probability that the market nally ends up withN products (hereafter,N-rms market) including the representative rm's product. The other part is the lifetime expected prot ofN-rms market, E N . The second term in (1), (1q)C(x), is the expected cost of null R&D technology. 3 1.2.2 Heterogeneous patent Innovators competing in the conventional patent race exert themselves to reach the market rst to seek the monopoly rent generated by market exclusivity if the positive producer surplus is anticipated. In the heterogeneous patent race framework, however, the rm's decision-making process becomes more complicated because the expectation of reward allocation and the market uncertainty change as the race progresses. 1.2.2.1 Reward scheme As opposed to the conventional model whereby the market entry is restricted only to the winner, the distribution of the market shares of the winner versus the losers comes into play in the heterogeneous patent race framework. The winner takes whole market value only until the next rm (the second rank) brings its invention into the market. Meanwhile, the losers continue R&D. After the arrival of the second rank, the market share of the winner shrinks to 1 and the second gets 1 1 . After the n'th rm's arrival, the rst rm occupies n1 and the other n 1 rms share the rest 3 The cost function C(x) of null R&D technology may have a specic form. For example, if a rm recognizes the type of its R&D technology at a random point of time tc that follows an arbitrary distribution whose expectation is dened, then the cost function is represented by a quasi-convex function, C(x) = E[tc]x. 5 1 n1 . A set or sequence of the winner's market shares is dened by the reward scheme and each element n represents a stage of the reward scheme. Also, the reward scheme is assumed to be predetermined and announced before the race. =f n1 j 1nM; 0 = 1g There are some remarks regarding the reward scheme. First, the reward scheme in the conven- tional framework is a singletonf 0 g which is always 1. Intuitively, the rms in the heterogeneous patent race are not motivated to win the competition as much as in such winner-takes-all setting. Second, the sequence of rewards that is realized over time to each strategy is a stochastic function of the R&D eorts made by the rivals. This is discussed in detail in the following section. 1.2.2.2 Market uncertainty The heterogeneous patent system changes the form of the market uncertainty which fundamentally stems from the stochastic nature of the earliest competitor arrival time. In conventional models, since market entry is restricted only to the winner, a rm faces the risk in predicting the probability of being rst to market before anyone, including itself, reaches the market. The risk is identied simply by an unconditional distribution of the earliest time-to-invent of all N 1 rivals. However, in the heterogeneous patent race where market entry is exogenously determined by the randomly assigned types of the R&D technology and no one withdraws from the race after the winner is decided, a loser is still exposed to market uncertainty induced by rival R&D eorts made by those still competing with her in the race until she arrives at the market. This market uncertainty is represented by the conditional distribution of the earliest time-to-invent of these rms after the latest event of arrival, and must be updated with every arrival event. Before anyone enters the market, the market uncertainty has the form of the unconditional distribution as in the conventional models. These unconditional and conditional distributions are denoted by ex-ante market uncertainty. The lifetime payo is heavily dependent on the ex-ante market uncertainty in the sense that the uncertainty plays a pivotal role in determining the rank of the players, which in turn determines player revenue every period as scheduled by the reward scheme. Consider the case where three 6 rms have patentable R&D technologies (N = 3). The winner takes the whole market until its market share falls to 1 each period with the arrival of any of the other rms. After the last rm enters, the winner takes 2 and the two followers share the rest. For every strategy, the ex-ante market uncertainty aects the likelihood that a rm will be able to enjoy the revenue streams of the winner, of the second ranking, and of the third, thereby aecting the lifetime payo. In addition to the ex-ante market uncertainty, there exists another type of market uncertainty. Permitting a continuous in ow of new innovations, the heterogeneous patent system forces a rm to face market risk even after successful completion of the project (hereafter, ex-post market uncer- tainty). Specically, for a rm that has already entered the market, how fast its market share will shrink depends on how quickly its opponents still out of the market complete development. In other words, the ex-post market uncertainty determines the duration of each stage of the reward scheme. Therefore, just as the ex-ante market uncertainty, the ex-post market uncertainty contributes to the lifetime payo but not to market entry. In the three rms example, the ex-post market uncertainty determines how much time the winner can enjoy monopolistic status and how early its share falls to 1 and to 2 , and how much time the second rank can gain 1 1 before sharing 1 2 with the third rank. To see how to incorporate the market uncertainty ex-ante and ex-post market entry into the model, pick any rm among N rms assigned patentable R&D technology and suppose that n 1 of its N 1 opponents have already made a successful run on R&D. Then, no matter whether the rm has launched its innovation or not, the time-to-invent of the rst rank among the Nn (= (N 1) (n 1)) opponents still performing R&D is denoted by: ^ N n min ^ T N n where ^ T N n is a set of time-to-invent of the Nn opponents. Under the independence assumption of across the rms, ^ N n follows the exponential distribution of a rate a N n (^ x) P h2 ^ H N n h(^ x) where ^ H N n is a set of the R&D productivity of the Nn rms. p(^ N n =t) =a N n (^ x)e a N n (^ x)t p(^ N n t) = 1e a N n (^ x)t 7 Denote t N n as the time t when the n'th rank among N 1 opponents completes its R&D project. Then, the memoryless property of the exponential distribution indicates that the market uncer- tainty that is updated after t N n1 observed is identied by the following form: p(^ N n =tj ^ N n >t N n1 ) =a N n (^ x)e a N n (^ x)(t N n t N n1 ) (2) This implies ^ N n ^ N n1 Exp(a N n (^ x)). For a rm that has already reached the market, (2) is the ex-post market uncertainty. Otherwise, it is the ex-ante market uncertainty. When no rms have yet completed R&D projects, the ex-ante market uncertainty is represented by the unconditional distribution, ^ N 1 Exp(a N 1 (^ x)). Indeed, in the conventional model, the ex-ante market uncertainty is a key component demon- strating the competition structure. However, as explained previously, it does not need to be updated because the competition ends as soon as the winner is decided. By the same logic, the ex-post risk does not exist. Therefore, market uncertainty in the conventional model is composed only of the unconditional distribution. The Poisson process of a successful discovery gives an important implication associated with the dynamics of market uncertainty. Consider the two cases, n =n 0 versusn =n 1 wheren 0 <n 1 . Then, a N n 0 (^ x) = X h2 ^ H N n 0 h(^ x)> X h2 ^ H N n 1 h(^ x) =a N n 1 (^ x); 8^ x2R N1 + \ 0 c holds by ^ H N n 1 ^ H N n 0 . This implies that the dispersion of ^ N n increases as n decreases. The number of ongoing R&D projects changes fromNn 0 toNn 1 because the number is weakly decreasing by time. Therefore, the magnitude of market uncertainty is amplied as the race progresses. 1.3 Non-cooperative game of R&D investment Non-cooperative rms maximize the lifetime expected prots (1) based on the common knowledge summarized by an information set =f;v 0 ;q;h();C();P;;r;Mg where P =fP N j 1 N 8 Mg and r is interest rate. 4 max x E(x; ^ xj ) = M X N=1 P N E N (x; ^ x) (1q)C(x) s:t: x 0 where E N (x; ^ x) =W mono N (x; ^ x) +W win N (x; ^ x) +W lose N (x; ^ x)VC(x)F (3) The expected prot of N-rms market, E N , is composed of three parts. The rst part is the expected monopoly rent W mono N that is equivalent to the winner's expected revenue generated only until any of the followers enter into the market. The second part is the rent-sharing of the oligopolists which consists of W win N and W lose N . They are the expected revenue in the oligopoly market for the winner and a loser, respectively. Both are zero when N = 1. The last parts are the variable cost VC and the xed cost F . For a representative rm, the expected monopoly rent is: W mono N (x; ^ x) = Z 1 0 p(^ N 1 =t N 1 )p( <t N 1 ) mono N (x)dt N 1 Since no competitors have arrived at the market, the market uncertainty is represented by the unconditional distribution, p(^ N 1 =t N 1 ). The revenue of the monopolist given an assumption that the second rank completes the project at t N 1 is denoted by mono N : mono N (x; ^ x) = Z t N 1 0 p( =sj <t N 1 ) Z t N 1 s v 0 e Rz dz ! ds The interest rate net of the market growth rate is denoted by Rr. The term in the bracket represents the cumulated market value that the winner gains until the second rank enters the market: Z t N 1 s v 0 e Rz dz 4 In order to focus on the roles that the key characteristics of the heterogeneous patent race framework have in the market equilibrium and market eciency, I make assumptions about other factors of the market environment, such as an innite patent length and 2 [0;r). 9 If the winner is one and only that one rm has patentable R&D technology (N = 1), thent N 1 is set to innity, and thus there is no market uncertainty inherent in the winner's revenue stream. W mono 1 (x) = Z 1 0 p( =t) Z 1 t v 0 e Rz dz ! dt After the entry of the second rank, the expected revenue of the winner is transformed from the monopoly rent to the oligopoly rent allocated to her. W win N (x; ^ x) = Z 1 0 p(^ N 1 =t N 1 )p( <t N 1 ) win N (^ x)dt N 1 (4) where win N is the oligopoly rent for the winner after t N 1 : win N (^ x) = Z 1 t N 1 p(^ N 2 =t N 2 j ^ N 2 t N 1 ) Z 1 t N N2 p(^ N N1 =t N N1 j ^ N N1 t N N2 ) ( N2 X i=1 Z t N i+1 t N i i v 0 e Rz dz + Z 1 t N N1 N1 v 0 e Rz dz ) dt N N1 dt N 2 (5) The product of the conditional probabilities representing the updated ex-post market uncertainties describes the likelihood that a particular sequence of rewards is realized over the period: p(^ N 1 =t N 1 ) N1 Y i=2 p(^ N i =t N i j ^ N i t N i1 ) The rst term in the brace of (5) is the sum of the revenue produced during the interval between two consecutive stages of the revenue scheme (i.e. between two consecutive follower arrival events): N2 X i=1 Z t N i+1 t N i i v 0 e Rz dz The other term is the revenue after the last product comes into the market: Z 1 t N N1 N1 v 0 e Rz dz 10 If N = 2, there is no ex-post market uncertainty to be updated. Therefore, in this case, (4) is rewritten as: W win 2 (x; ^ x) = Z 1 0 p(^ 2 1 =t 2 1 )p( <t 2 1 ) Z 1 t 2 1 1 v 0 e Rz dz dt 2 1 For the representative rm, its expected revenue in a case of defeat in the competition is: W lose N (x; ^ x) = Z 1 0 p(^ N 1 =t N 1 )p(t N 1 ) lose N (x; ^ x)dt N 1 (6) where lose N is the oligopoly rents it shares with other followers in the market: lose N (x; ^ x) = Z 1 t N 1 p(^ N 2 =t N 2 j ^ N 2 t N 1 ) Z 1 t N N2 p(^ N N1 =t N N1 j ^ N N1 t N N2 ) " N2 X i=1 Z t N i+1 t N i p( =sjt N 1 ) ( Z t N i+1 s ~ i v 0 e Rz dz + N2 X k=i+1 Z t N k+1 t N k ~ k v 0 e Rz dz + Z 1 t N N1 ~ N1 v 0 e Rz dz ) ds + Z 1 t N N1 p( =sjt N 1 ) ( Z 1 s ~ N1 v 0 e Rz dz ) ds # dt N N1 dt N 2 (7) The product of the updated market uncertainties is involved in the rent function in the same manner as in W win N (x; ^ x). The market uncertainty is either the ex-post or the ex-ante depending on whether the rm has arrived at the market or not. The loser's market share denoted by ~ n is a function of n . Precisely, if uniformity of the market share among the losers is assumed, it follows that after the n'th rm's arrival, the winner occupies n1 and each of the other n 1 rms takes the rest equally per period. ~ n1 1 n1 n 1 ; 8n where 2nM The expected revenue of the loser has a dierent form according to whether the loser is the latest in the race or not. The term in the square bracket of the last line of (7) describes the expected 11 revenue of the last arrival: Z 1 t N N1 p( =sjt N 1 ) ( Z 1 s ~ N1 v 0 e Rz dz ) ds If the representative rm is not the last, its expected revenue when its invention is anticipated to come right after i'th invention is described on the third line of (7): N2 X i=1 Z t N i+1 t N i p( =sjt N 1 ) ( Z t N i+1 s ~ i v 0 e Rz dz + N2 X k=i+1 Z t N k+1 t N k ~ k v 0 e Rz dz + Z 1 t N N1 ~ N1 v 0 e Rz dz ) ds Specically, the rst, the second, and the third terms in the brace represent the rents that the rm collects until the next rm arrives, from then until the latest rm enters, and after then, respectively. ForN = 2, with the same argument as W win N , the second and third lines of (7) are omitted and the market risk consists only of the unconditional probability. W lose 2 (x; ^ x) = Z 1 0 p(^ 2 1 =t 2 1 )p(t 2 1 ) Z 1 t 2 1 p( =sjt 2 1 ) Z 1 s ~ 1 v 0 e Rz dz ds dt 2 1 For N = 3, the second term in the brace on the third line of (7) does not appear because the line represents the expected revenue of the second rank and there are no arrival events between the second and the third ranks. W lose 3 (x; ^ x) = Z 1 0 p(^ 3 1 =t 3 1 )p(t 3 1 ) lose 3 (x; ^ x)dt 3 1 where lose 3 (x; ^ x) = Z 1 t 3 1 p(^ 3 2 =t 3 2 j ^ 3 2 t 3 1 ) " Z t 3 2 t 3 1 p( =sjt 3 1 ) ( Z t 3 2 s ~ 1 v 0 e Rz dz + Z 1 t 3 2 ~ 2 v 0 e Rz dz ) ds + Z 1 t 3 2 p( =sjt 3 1 ) ( Z 1 s ~ 2 v 0 e Rz dz ) ds # dt 3 2 12 The variable cost of the patentable R&D technology is incurred until a rm completes the project. VC(x) = Z 1 0 p( =t) Z t 0 xe rz dz dt Since the lifetime expected prot function of the N-rms market E N is continuous on the compact set, R + , for all N, the existence of the solution is guaranteed by the extreme value theorem. Under an assumption of quasi-concavity of E N , the second-order condition is always negative at the maximizer because the objective function is twice continuously dierentiable on its domain. Under the assumption that rms pursue a symmetric strategy, I characterize a functional form of the Bayesian-Nash equilibrium x by substituting a n with (Nn)h in the rst-order condition of the lifetime expected prot for all N: 5 M X N=1 P N ( w mono N (x) +w oligo N (x) ) q ( 1 h +r xh 0 (h +r) 2 ) (1q)C 0 (x) 0 (8) The equality holds if x is strictly positive. The rst part, P M N=1 P N fw mono N (x) +w oligo N (x)g, repre- sents the lifetime expected marginal revenue. It is composed of the expected marginal rents in the monopoly market w mono N and in the oligopoly market w oligo N : w mono N (x)W mono0 N (x) = 1 fNh +Rg 2 v 0 h 0 (9) w oligo N (x) =W win0 N (x) +W lose0 N (x) = N1 X n=1 1 n ( f1 (n + 1) n gf(N 1)h +Rg f(Nn 1)h +Rg(Nh +R) | {z } (i) + n X k=0 1 n (Nk)h +R | {z } (ii) ) 1 Nh n Y k=0 (Nk)h (Nk)h +R ! v 0 h 0 (10) 5 The argument of h(x) is omitted to simplify the notation. 13 where w oligo 1 (x) = 0. The second part of (8) is the expected marginal variable cost: q ( 1 h +r xh 0 (h +r) 2 ) Along with the lifetime expected marginal revenue, it composes the lifetime expected marginal prot generated by the patentable R&D technology. The last part of (8) is the expected marginal cost incurred if the R&D technology is not patentable. From (9) and (10), we see that the lifetime expected marginal revenue in (8) is made up of three components. The rst component is the expected marginal monopoly rent. (a) Marginal eect of the R&D investment on the expected monopoly rent ( P M N=1 P N w mono N (x), hereafter, extensive margin eect in monopoly market): The marginal increment of R&D enables an invention to be introduced into the market earlier, thereby raising the likelihood of being rst-to-market and helping the winner to start harvest- ing the monopoly rent earlier. This indicates that the investment contributes to expansion of the extensive margin of the expected monopoly rent. This is always positive. The other two components of the lifetime expected marginal revenue in (8) describe the expected marginal rent shared by oligopolists, P M N=2 P N w oligo N (x). In the oligopoly market, the marginal eects of R&D are not the same between the winner and the losers because both the ex-ante and the ex-post market uncertainties are inherited in the losers' revenue function, meanwhile only the ex-post uncertainty is in the winner's function. To help understand the logic, recall the general form of the expected oligopoly rent of anN-rm market. For the winner's case, take the derivative (4) with respect to x. W win0 N (x; ^ x) = Z 1 0 p(^ N 1 =t N 1 ) dp( <t N 1 ) dx win N (^ x)dt N 1 Intuitively, the chance to win the race, presented byp( <t N 1 ), is enhanced by R&D. Therefore, this equation implies that the expected oligopoly rent of the winner always increases as R&D increases. 14 For the losers' case, take the derivative (6) with respect to x. W lose0 N (x; ^ x) = Z 1 0 p(^ N 1 =t N 1 ) ( p(t N 1 ) d lose N (x; ^ x) dx + dp(t N 1 ) dx lose N (x; ^ x) ) dt N 1 The rst term in the brace raises the possibility that R&D increases the loser's expected rent; even if the marginal eort fails to result in winning the race, it moves up the launch of a loser's product and thereby allows the loser to enjoy the oligopoly rent earlier. This is presented in the equation by: d lose N (x; ^ x) dx > 0 On the contrary, as the second term in the brace implies, R&D simultaneously reduces the proba- bility to lose: dp(t N 1 ) dx < 0 Hence, it can decrease the expected rent. The marginal eect of R&D on the expected revenue in the oligopoly market is rearranged as: M X N=2 P N w oligo N (x; ^ x) = M X N=2 P N n W win 0 N (x; ^ x) +W lose 0 N (x; ^ x) o = M X N=2 P N Z 1 0 p(^ N 1 =t N 1 ) " dp( <t N 1 ) dx win N (^ x) lose N (x; ^ x) + 1p( <t N 1 ) d lose N (x; ^ x) dx # dt N 1 M X N=2 P N n w ints N (x; ^ x) +w exts N (x; ^ x) o Under the symmetry assumption,w ints N (x; ^ x) andw exts N (x; ^ x) in the equation correspond to the terms related to (i) and to (ii) of (10), respectively: w ints N (x) = N1 X n=1 1 n f1 (n + 1) n gf(N 1)h +Rg f(Nn 1)h +Rg(Nh +R) 1 Nh n Y k=0 (Nk)h (Nk)h +R v 0 h 0 w exts N (x) = N1 X n=1 1 n n X k=0 1 n (Nk)h +R 1 Nh n Y k=0 (Nk)h (Nk)h +R v 0 h 0 15 The marginal eects associated with w ints N (x) and w exts N (x) are explained in (b) and (c) below. (b) Marginal eect of the R&D investment on the marginal benet of being the winner in the oligopoly market ( P M N=2 P N w ints N (x), hereafter, intensive margin eect in oligopoly market): In the oligopoly market, the winner's rent exceeds (falls below) the loser's proportionally to the discrepancy in the market shares between them. Accordingly, by enhancing the chance of winning the race, the marginal investment increases the magnitude of the expected net benet of being the winner. It is positive (negative) if and only if the winner's share is larger (smaller) than the loser's. In this context, the incremental loser's rent is the opportunity cost of the marginal investment. (c) Marginal eect of the R&D investment on the loser's rent ( P M N=2 P N w exts N (x), hereafter, extensive margin eect in oligopoly market): This is an increase of the expected revenue in the oligopoly market that an additional input causes by bringing forward the launch of the loser's invention. This is always positive as long as the loser's market share is not zero. The three marginal eects (a){(c) demonstrate the mechanism of how the industry equilibrium is determined. To see the role that patentability q plays in the market equilibrium, consider the case of x = 0 in the rst-order condition. Since P N is summed to q for any M, (8) is rewritten as: q C 0 (0) R 2 v 0 h 0 (0)r 1 +C 0 (0) q (11) The implication of (11) is that positive investment is not made as long as q does not exceed the threshold q. For a class of products requiring riskier R&D technology (lower q), rms are more reluctant to settle investment. The threshold has nothing to do with the number of rms in the industry. On the other hand, it is positively associated with the future market value; rms are more willing to accept the risk of failure if the absolute market size is large or the market is predicted to grow quickly. The reward scheme has no impact on the threshold, hence on the decision of whether to invest. This means that when deciding on participation in the competition, rms do not care about the intensive margin of the market value, but care about the extensive margin. 16 Once the decision on participation is made, the reward scheme comes into play; rms are en- couraged to put more resources into R&D as higher market share for the winner is anticipated because of the value of being rst-to-market. Proposition 1. Assume = f 1 ; ; M1 g f 0 1 ; ; 0 M1 g = 0 and 6= 0 . Then, x ()>x ( 0 ) holds. Proof. See A.1. For any given x, as the reward is allocated more to the winner, the extensive margin eect re- mains constant in the monopoly market whereas the extensive and the intensive margin eects in the oligopoly market are decreasing and increasing, respectively. Proposition 1 holds because the intensive margin eect is more responsive to the market share than the extensive margin eect. For instance, consider the case of N = 2. In the oligopoly market, if 1 gets larger, the increment of the intensive margin eect is double of the decrement of the extensive margin eect. This is because the change of 1 has eects on both the winner's and the loser's revenue functions in the same magnitude but in the opposite direction. 1.4 Normative economics of R&D investment This section examines the market eciency of R&D investment by comparing the optimal strategy of the non-cooperative game to the social optimum under the assumption of symmetry. As will be shown later, early mover advantage (hereafter, EMA) and early mover disadvantage (hereafter, EMdA) play key roles in drawing normative conclusions. 6 For allN where 2NM,a n is replaced by (Nn)h in the lifetime expected prot function (3). Then, the social planner solves: max x M X N=1 P N n 1 R(Nh +R) v 0 hVC(x)F o (1q)C(x) s:t: x 0 6 In this study, equal market share is denoted by =f n1j =n 1 ; 2nMg The presence of EMA is identied by such that and 6= ;M A =fj and 6= g The opposite case, and 6= , is denoted by EMdA;M D =fj and 6= g 17 In the social planner's problem, the per-period market value or reward v t means the per-period social benets by innovation. The objective function multiplied by the total number of rms M is equivalent to the lifetime social net benet function. To see this, let N 0 denote the minimum time-to-invent of N rms and p( N 0 =t) denote the probability of the rst of theN technologies being introduced into the market at t: p( N 0 =t) =Nhe Nht Then, the substitutions of q M1 N1 q N1 (1q) MN for P N , of N M M N for M1 N1 , and of N 1 Z 1 0 p( N 0 =t) Z 1 t v 0 e Rz dz dt forfR(Nh +R)g 1 yield the following form of the lifetime social net benet function: SB(x)MqfVC(x) +FgM(1q)C(x) (12) where SB(x) M X N=1 M N q N (1q) MN Z 1 0 p( N 0 =t) Z 1 t v 0 e Rz dz dt is the lifetime social benets generated after the rst invention is introduced. The second term of (12) is the expected social cost made by the eective R&D investments, MqfVC(x)+Fg. The last is the expected social cost incurred by the null R&D technology, M(1q)C(x). It is noteworthy that the Pareto-optimality does not depend on the reward scheme. The social planner does not have any preference on who gets how much rent because it does not aect the extensive margin of the lifetime social benets. The socially optimal level of R&D, x e , satises: M X N=1 P N 1 fNh +Rg 2 v 0 h 0 q ( 1 h +r xh 0 (h +r) 2 ) (1q)C 0 (x) 0 (13) 18 where equality holds if x is strictly positive. It is exactly the same as the rst-order condition of the prot maximization problem (8), without the marginal revenue expected in the oligopoly market P M N=2 P N w oligo N . This indicates that the oligopoly rent is the source of the market in- eciency. The rst term of (13), representing an increase of the lifetime social benets by an individual rm's marginal eort in R&D (M 1 SB 0 (x); hereafter, lifetime marginal social benets of individual R&D), is equivalent to the lifetime expected marginal revenue in the monopoly market P M N=1 P N w mono N . The intuitive reason is that the social planner is interested only in how early the industry can start to harvest the surplus (prots) as if a monopolist carrying out M parallel R&D projects. For a detailed discussion of normative implications, consider the benchmark case where all inno- vators always occupy the market share equally ( = ). In the oligopoly market, since the benet of being the winner is oset by its opportunity cost (the loser's market share), the intensive margin eect is zero. So, the expected marginal revenue is always larger than the lifetime marginal social benets at any point ofx due to the presence of the extensive margin eect in the oligopoly market which is positive as long as the reward is not fully exhausted by the winner. Accordingly, even though the time value is zero (i.e. equal market share), the industry equilibrium is higher than the socially desired level. In other words, although there is no advantage to be rst-to-market, the potential marginal benet of R&D in the oligopoly market that is made by the earlier introduction of loser's innovation attracts excessive R&D eort. Combined with proposition 1, this indicates that the expectation of EMA or equal market share is a sucient condition for overinvestment. Proposition 2. If 2M A [f g, then x >x e holds. Proof. See A.2. In the case of EMdA, R&D competition can achieve the market eciency or end up with underinvestment. The fundamental reason is that, the intensive margin eect is amplied in a rapidly growing market. The revenue gap between the winner and the loser generated every pe- riod by the discrepancy in the market shares is cumulative as time elapses and the accumulation rate is proportional to the market growth rate. However, since the extensive margin eects in the monopoly and the oligopoly markets are created insofar additional investment brings forward the 19 launch of inventions and thereby enables to harvest the rents earlier, the eects are responsive less to the market growth than the intensive margin eect. Therefore, for a high enough market growth rate, the magnitude of the intensive margin eect made negative by EMdA becomes equal to or greater than that of the extensive margin eect of the oligopoly market. Since the marginal revenue of R&D in the oligopoly market is then non-positive, the industry equilibrium is equal to or smaller than the socially optimal level by concavity of the lifetime expected prot function. Proposition 3. For any 2M D , there always exists at least one interval of , close to r, such thatx ()<x e () is satised. For some2M D close to , there is that makesx () =x e () hold. Proof. See A.3. The intuitive reason for the existence of underinvestment is as follows. When the winner's market share is below the loser's, this situation encourages a rm to delay its market entry. This tendency is reinforced by rapid market growth because it reduces the relative size of the reward in the near future against the reward in the distant future and thereby makes early entry even less attractive. Accordingly, if the market is predicted to grow quickly enough, then rms slow down the pace of their R&D eorts below the socially desired level. As in the conventional model, the market ineciency of R&D that arises in the heterogeneous patent race is fundamentally due to the market uncertainty that a rm cannot control. However, propositions 2 and 3 demonstrate that the mechanism by which market uncertainty operates and the result that it produces are quite dierent between the two frameworks. In the conventional winner-takes-all setting, the winner is the one and only provider, and thus the marginal value of the eort to be rst-to-market is positive. For this reason, the market uncertainty caused by the negative relationship between the probability of entering the market and the opponents' eorts al- ways makes a rm exert itself more than the socially desirable level. However, in the heterogeneous patent race framework, market uncertainty is associated not with market entry, but with a rm's position in the competition and the prot erosion after entry. Accordingly, the industry equilibrium of R&D can be larger or smaller than the socially optimal level depending on whether and to what degree the marginal eort to reach the market early is valuable, which is a function of the reward 20 scheme and the market growth rate. 1.5 Social benet appropriation and market eciency So far, the discussion is based on the implicit assumption about Schumpeterian rent, full appropri- ation (or extraction) of the social benets by innovators. This section considers the other case in which they fail to fully incorporate the social benets into prots due to the absence of rst-degree price discrimination. 7 Under the imperfect appropriation assumption, the per-period social benets v t is replaced byv t in the prot maximization problem (in the fashion of Loury (1979) and Shapiro (2007)) where 2 (0; 1) is the innovator's appropriation rate, the ratio of the rewards provided to the innovator to the social contribution of her invention (Shapiro, 2007). Full appropriation is presented by = 1. The rst-order condition of the prot maximization problem (8) is rewritten as: M X N=1 P N ( w mono N (x) +w oligo N (x) ) q ( 1 h +r xh 0 (h +r) 2 ) (1q)C 0 (x) 0 (14) The incomplete extraction of the social benets makes signicant changes in the positive and normative implications. First, rms become more cautious about participating in the race. To see this, rearrange (14) at x = 0 as in (11). q C 0 (0) R 2 v 0 h 0 (0)r 1 +C 0 (0) q() This indicates that the threshold of patentability for non-zero R&D, q(), decreases as increases. Therefore, q(< 1)> q( = 1) holds. Second, compared to full appropriation ( = 1), the privately optimal level of R&D decreases. This is because the lifetime expected marginal revenue, the rst term of (14), does not fall below zero systematically and is homogenous of degree 1 with respect to , hence: dx d > 0 7 For simplicity of discussion, the case of the negative expected marginal revenue in the oligopoly market, P M N=2 PNw oligo N < 0, is ruled out. 21 holds by the implicit function theorem. Third, for given reward scheme and market size that R&D competition results in overinvestment if the per-period social benets is fully captured by innovators ( = 1), the competition can end up with underinvestment if partially captured ( < 1). To understand this argument, compare the prot maximization problem with imperfect appropriation of the social benets and the social planner's problem by combining the left-hand side of (13) with that of (14). Denote the lifetime expected marginal prot with at x e as: G(x e j) M X N=1 P N ( (1)w mono N (x e ) +w oligo N (x e ) ) (15) Although G(x e j = 1) = P M N=1 P N w oligo N 0 holds (i.e. overinvestment), it is possible that G(x e j< 1) falls below zero (i.e. underinvestment) for a small enough because: @G(x e j) @ > 0 and lim !0 G(x e j) = M X N=1 P N w mono N (x e )< 0 hold for anyx e . Therefore,x <x e holds for a low by concavity of the lifetime expected prot. 1.6 Conclusions To investigate how a market structure that does not guarantee winner-takes-all aects R&D compe- tition, this paper suggests the heterogeneous patent race by addressing the following characteristic features in the model. First, before completing development (no matter whether the winner of the race is decided or not), a rm faces market risk that stems from the association between the likelihood of being the next rank and the amount of R&D eort made by rivals. Second, once a rm reaches the market (no matter whether it is the winner or not), it is still exposed to market uncertainty because its revenue ow depends on the strategies of the other players still performing R&D. Both types of uncertainty are updated with every subsequent arrival event. Last, market 22 entry is exogenously determined by patentability, regardless of how much eort is made. The heterogeneous patent race model demonstrates that the industry equilibrium and market eciency are largely dependent on time advantage/disadvantage in market share. First, the expec- tation of the higher market share for the winner encourages rms to devote more eorts to R&D. Second, the expectation of early mover advantage or equal market share is a sucient condition for overinvestment. Third, in the case of early mover disadvantage, rms invest too little in R&D if the market grows quickly. If the market share for the winner is not too low, there exists a certain level of the market growth rate at which the industry equilibrium achieves market eciency. An empirical justication of the model requires an appropriate test for the positive implication on how the rm's R&D changes according to the market share distribution. This is an avenue for future research. 23 Chapter 2 Pharmaceutical R&D Competition: Ap- plication of Heterogeneous Patent Race 2.1 Introduction Kim (2021) suggests an alternative framework to the conventional theory of innovation investment, heterogeneous patent race, to consider rent-sharing by oligopolists in the reward of R&D compe- tition. The heterogeneous patent race model addresses how the expectation of the market share distribution aects the rm's R&D decision. The pharmaceutical industry is an obvious case t- ting to the framework of heterogeneous-patent race in the sense that multiple molecules (innovative products), protected by patent (and regulatory approval), compete for market shares within the same therapeutic class. Applying the theory to the pharmaceutical industry, this paper i) presents empirical evidence of the positive implication, the positive eect of the expected market share of the winner in R&D competition on the rm's R&D eort (proposition 1), and ii) discusses the normative implication on the market eciency of the R&D investment in the industry (proposition 2 and 3). The success of a pharmaceutical rm largely depends upon the success of the R&D investment (Cockburn and Henderson, 1994). This is because while the development of a new medical product brings a substantial \reward" (if successful), it requires considerable resources and eorts compared to the high uncertainty of success inherent in the process. The median R&D expenditure of can- 24 cer drugs that obtained FDA approvals from 2006{2015 is estimated at $648 million in 2017 US dollars (Prasad and Mailankody, 2017). This gure accounts for 17.1{19.7% of the total revenue of an average pharmaceutical rm. 1 However, only 10.4{11.8% of the initial pipelines endure the successive drug development process that necessitates 10{12 years to nally end up on the market (Hay et al., 2014; DiMasi et al., 2016). These facts imply that, with a probability of about 89%, a rm fails in drug development and suers the enormous economic/nancial loss due to the large sunk cost and the depreciation of the market value of the rm (P erez-Rodr guez and Valcarcel, 2012; Hwang, 2013). The \reward" motivating pharmaceutical rms to run this signicant risk is the market exclu- sivity granted by the patent and regulatory authorities. No rms are willing to commit to R&D without market exclusivity due to the considerable sunk cost of R&D and the trivial marginal cost of production (Morton and Kyle, 2011; Boldrin and Levine, 2013). However, market exclusivity does not mean that a new molecule can avoid competing against other innovative molecules in the same therapeutic class because market exclusivity aims to protect a new molecule (i.e. a brand-name drug) only from competition with generic versions of the same molecule. In other words, the market exclusivity of the rst molecule cannot deprive other rms of their right to bring distinct molecules to the same therapeutic class (Berndt, 2002; Lakdawalla, 2018). For example, Victrelis and Incivek were two drugs that introduced a new generation of hepatitis C treatment in 2011. Before their market exclusivity expired, other branded drugs arrived successively at the same market in 2013 (Sovaldi) and 2014 (Harvoni). This illustrates that the market structure of innovative pharma- ceutical products is characterized as an oligopoly market rather than a monopoly (Berndt, 2002), and thus the reward to the successful innovation should also be explained in terms of oligopoly rent. To my knowledge, this point is not addressed in the literature studying the determinants of pharmaceutical R&D (Acemoglu and Linn, 2004; Blume-Kohout and Sood, 2013; Dubois et al., 2015). They focus only on the eects of the extensive margin of the reward, represented by the market size itself. To consider the oligopolistic nature of the brand-name drug market in the analysis of the phar- maceutical R&D competition, this paper relies on the heterogeneous patent race framework. The 1 PhRMA, Annual Membership Survey (2019), https://www.phrma.org/-/media/Project/PhRMA/ PhRMA-Org/PhRMA-Org/PDF/P-R/PhRMA2019membershipsurveyFinal.pdf. 25 remainder of this paper is organized as follows. Section 2.2 provides background on pharmaceutical innovation and the development process. Section 2.3 introduces how to dene key concepts used in the empirical study and how to incorporate the concepts into the analytic framework. Section 2.4 explains data sets. Section 2.5 presents an identication strategy to examine the positive im- plication suggested by proposition 1 of the theory. Section 2.6 summarizes the empirical results. Section 2.7 discusses the empirical implications on the market eciency of the pharmaceutical R&D investment based on proposition 2. Section 2.8 concludes. 2.2 Pharmaceutical innovation and development Although there is little consensus on how to measure pharmaceutical innovation, new molecular entity (NME), dened as an \active ingredient that contains no active moiety that has been previ- ously approved by a regulatory authority" by the US Food and Drug Administration (FDA), 2 has frequently been used (Acemoglu and Linn, 2004; Lanthier et al., 2013; Blume-Kohout and Sood, 2013). 3 A branded drug is identied as an NME by the new drug application (NDA) classica- tion codes that categorize drugs based on their characteristics, such as whether they contain new molecules or how the drug is related to previously approved drugs. Table 1 documents the dis- tribution of classication codes used for branded drugs that obtained NDA approval by the FDA between 1996 and 2015 (1,871 drugs in total). Following the conventional approach, this study denes innovative pharmaceutical products as NMEs; more precisely, the drugs classied as type 1 (NME; 496 drugs) or type 1/4 (combination of preexisting drugs and NME; 23 drugs). NMEs are awarded 5 years of market exclusivity, which is separate from the 20-year patent period. There are 1,252 non-NMEs, branded drugs developed during the study period from preexisting NMEs. By denition, a non-NME must have the same active ingredient of its original NMEs; phys- ical and/or chemical changes are forced into the original NMEs with the purpose of, for example, modifying release formulations, changing administration route, or combining multiple preexisting drugs. Pharmaceutical rms are incentivized to develop non-NMEs despite their shorter market exclusivity (3 years) because the non-NME NDA approvals do not require the full test sequence of 2 Center for Drug Evaluation and Research (CDER), NDA Classication Codes, https://www.fda.gov/media/ 94381/download. 3 Dubois et al. (2015) uses new chemical entity (NCE) and Krieger et al. (2018) calculates the novelty of drugs based on molecularly distance from prior drugs. 26 pharmaceutical development, therefore enabling rms to save R&D costs and enhancing the chance of R&D success. In general, the NME development process involves discovery of a new molecule, preclinical test- ing in non-human subjects, three phases of clinical trials to prove safety and ecacy of the substance in the human body, and a regulatory evaluation. On average, this successive process takes 10.7 years: 31.2 months for initial discovery and preclinical testing; 19.8 months for phase 1 of clinical trial; 30.3 months for phase 2; 30.7 months for phase 3; and 16.0 months for regulatory evaluation (DiMasi et al., 2016). The patent ling takes place after the initial discovery, before the preclinical testing. However, the monopoly or the oligopoly rents, the rewards of the R&D competition, do not benet rms before the launch of the products. Therefore, the pharmaceutical R&D strives to get regulatory approval rather than to obtain a patent itself. In this context, the patent race in the theory corresponds to the competition for regulatory approval. 2.3 Introduction of key concepts In light of the eective period of patent/regulatory exclusivity expected after launch, a market in this study is dened as a set of NMEs that are newly launched in a therapeutic class for 10 years. A market is sometimes called a window-class or an N-drugs market when the number of drugs in a market is highlighted. Consistent with the concept of market, I dene early mover as the NME that is launched earlier than any other NMEs in the relevant therapeutic class within the 10-year window. Market size is measured as the cumulative sales revenue of all NMEs introduced into a therapeutic class over the 10-year window, and market share refers to the ratio of the NME's sales revenue accumulated over the window compared to the market size. The sales revenue is adjusted by the 2018 Consumer Price Index of the US. The theoretical model implies that a pharmaceutical rm makes an R&D decision based not only on how large the market size will be, but on how benecial it will be to arrive at the market early, which is represented by the future market share of the early mover. ch2Figure 1 depicts the structure of the rm's R&D decision. Suppose that a rm determines how much investment to make in yeart. I assume that a rm uses the market share distribution observed over the previous 10 years (t 9 tot) in the relevant therapeutic class to adjust its expectation on the market share distribution for the future 10 years from the expected launch year (adaptive expectation). The 27 time framework for the prediction of the future market size diers by the rm's development stage. If a rm makes a decision on the investment in the phase 3 trial, it measures the 10-year market size of t + 4 to t + 13 because the expected market date starts after 46.7 months from year t. By the same logic, a rm anticipates the future market sizes of t + 6 to t + 15, t + 8 to t + 17, and t + 10 tot + 19 for the investment in the phase 2 trial (after 78.0 months from year t), the phase 1 trial (after 97.8 months), and the preclinical testing (after 129.0 months), respectively. Although non-NMEs are not included in the study sample, their sales records may contain important information on the market value of a pharmaceutical innovation because revenue from an NME is generated not only from sales of the NME itself, but also from sales of the NME's derivatives, non-NMEs. For example, a rm is inclined to introduce a line extension, a non-NME developed by the same rm of the original NME, with the goal of extending the eective period of market exclusivity of the original NME (Fowler, 2017). Alternatively, a rm may earn revenue by licensing out its NME to other rms. To address this point, I link each non-NME to its NME(s) using the active ingredient name, and incorporate the revenue of the non-NME into that of the original NME(s). For example, if drug A has a new dosage form (type 3) of preexisting NME B, then 100% of the sales revenue of drug A is allocated to NME B. If drug C (type 4) is a combination of NMEs D and E, then NMEs D and E share the revenue of drug C equally. Therefore, drugs A and C do not appear on the data. The same method is applied to the type 1/4 drugs; preexisting type 1 NMEs contained in a type 1/4 drug are matched to themselves, and a part of the sales revenue of the type 1/4 drug is incorporated into the sales revenue of the type 1 NMEs. For example, if drug F is made up of type 1 NMEs G and H as well as drug F's own active ingredient, then two-third of the revenue of drug F is distributed to NMEs G and H, and drug F has only one-third of its revenue. By the revenue reallocation process, I identify the gross market value of the pharmaceutical innovation. 2.4 Data Various data sources of pharmaceutical market and development information are combined for the empirical analysis, namely the Drug Databases of FDA, 4 Pharmaprojects, First Databank, and 4 Food and Drug Administration, Drugs@FDA: FDA-Approved Drugs, https://www.accessdata.fda.gov/scripts/ cder/daf/index.cfm. 28 the Medical Expenditure Panel Survey (MEPS). First, for every drug that obtained NDA approval from 1996{2015, I use the Drug Databases of FDA to retrieve the NDA approval date and other necessary drug-specic information, such as the NDA classication code, the priority review, and the orphan drug status. Second, I obtain the number of drugs in each stage of the drug development process from Pharmaprojects. This database publishes annual trends of the pharmaceutical R&D pipelines, or- ganized by therapeutic class, from 1995 to present. The therapeutic classes provided by Pharmapro- jects (208 in total) are assigned to the NDA-approved drugs. Since the classication system is con- structed based on the general therapeutic area and therapeutic strategy/type, it is common for one drug to have multiple therapeutic classes assigned. In this case, I use the primary therapeutic class to prevent drugs being counted multiple times. Pharmaprojects categorizes the 208 therapeutic classes into 16 therapeutic groups. Third, I nd the rst date when each NME was launched on the US market from the First Databank. The market date is used to identify the early mover of each market. To precisely sort out the NDA-approved drugs to be used in the study from the prescribed drugs recorded in the MEPS, I extract the labeler and product code list from the National Drug Code (NDC) of the NDA-approved drugs from First Databank. Fourth, based on the labeler-product code list, I merge the information of each NDA-approved drug with the Prescribed Medicines les of the MEPS to estimate the survey-weighted expenditure on each drug (adjusted by the 2018 US Consumer Price Index). Using the unique person identier, I link the merged le to the Full-Year Consolidated Data les of the MEPS for the user population composition for each drug. Since the MEPS data les start from 1996 and the extract le of the First Databank ends in 2015, the rst 10-year window for the estimation of the market share distribution is 1996{2005 and the last window is 2006{2015 (Table B.1). The reference year t, when an R&D decision is made, is the last year of each of these windows: 2005, , 2015. The 10-year windows used in the calculation of the market size begin from 2009{2018 for phase 3 clinical trials, 2011{2020 for phase 2, 2013{2022 for phase 1, and 2015{2024 for preclinical testing. The windows for each of these development stages last until 2019{2028, 2021{2030, 2023{2032, and 2025{2034, respectively. Among 519 NMEs obtaining NDA approvals from the FDA between 1996 and 2015, 233 NMEs 29 in 72 therapeutic classes (14 therapeutic groups) appear in the MEPS. They make up 543 window- classes (i.e. markets) and 1,164 window-drugs. Since the markets with only 1 drug (i.e. 1-drug markets) do not contain any information regarding the market share, they are not included in the analysis. This therefore excludes 60 NMEs in 69 therapeutic classes, which form 255 markets and window-drugs. Dropping these 1-drug markets, the nal dataset includes 288 markets composed of 204 NMEs in 46 therapeutic classes (13 therapeutic groups). The therapeutic classes and groups are listed in Table B.2. The 204 NME samples provide the estimation of the market share distribution with 909 window-drugs and the estimation of the eect of the market share distribution on the R&D investment (a test for proposition 1) with 288 markets. The market distribution with respect to the number of NMEs, i.e., the distribution of the N-drug markets, is displayed in Table 2. The number of markets decreases as the number of NMEs increases overall. About three quarters of the markets have only 2 or 3 NMEs (2 N 3). Each of the markets with 10 or more NMEs (N 10) occupies only less than 1% in the total number of the markets. 5 2.5 Empirical framework 2.5.1 Estimation of the drug quality-adjusted market share distribution To begin with, I estimate the early mover's market share while controlling for the drug quality. This estimate will be used as the key variable in examining how rms' R&D decisions respond to their expectations of the future market share distribution. I make two assumptions to ensure that the estimated model re ects how rms measure the market share distribution in a practical way. First, since a rm cannot identify the \true" quality of a drug that was introduced in the past, the rm relies on the information from the drug's clinical trials. This indicates that when measuring the market share distribution, rms can adjust for the drug quality that is revealed by clinical tri- als only, but not for the \true" quality. Second, when estimating the market share distribution, a rm does not control for the drug quality improvement resulting from technological progress in the pharmaceutical industry. This is reasonable because such improvement is the nature of the industry (as in other industries) that all rms will face when launching products in the future. Accordingly, I aim to measure the market share distribution adjusted for the drug quality as disclosed by clinical 5 Antiviral, anti-HIV in the windows 1996-2005, 1997-2006, 1998-2007, and 1999-2008. 30 trials, but, the natural improvement of the drug quality by technological progress is re ected. In this study, the estimated market share is referred to as a drug quality-adjusted market share. For every 10-year window (1996{2005, , 2006{2015), the quality-adjusted market share dis- tribution of the drugs introduced into a therapeutic class c is estimated by a panel xed-eects model. In the model specication (1), the 10-year window is represented by the last year of the window, the reference year t (2005, , 2015). MS ict =Year t + Class c + X 0 it + N ct + EM ict + EM ict N ct +" it (1) The market share of drug i realized during a 10-year window is denoted by MS ict . The time advantage/disadvantage, represented by the discrepancy in the market share between the early mover and the followers, is identied by the eect of being the early mover on the market share (hereafter, early mover eect). The early mover eect is captured by EM ict which is 1 if the drug i is the early mover of the market. Since the market share allocated to an individual drug tends to shrink as more drugs exist in the market, the number of the drugs in the market N ct is involved in the model. By the same logic, the early mover eect varied by N ct is represented by the interaction term between EM ict and N ct . The market share is adjusted by the individual drug characteristics, X it : time-on-the-market (i.e. the number of days after launch), TOM it ; a dummy for priority review, Priority i ; and a dummy for an orphan drug status, Orphan i . The year xed- eect, Year t , addresses secular trends in the market share. The class xed-eect, Class c , controls for time-invariant features of the therapeutic class. Standard errors are clustered at the drug level. The drug quality-adjusted market share of the early mover in the therapeutic class c's last 10 years (t 9 to t) is measured by the tted value with EM ict = 1: ct = E MS ict j EM ict = 1 As discussed previously, the estimated market share of early mover ct must control for the drug quality unveiled by clinical trials (hereafter, revealed drug quality). It is clear that the revealed drug quality is proportional to the \true" quality, but they are not equivalent. Therefore, a natural concern in the estimation of the reported model (1) is the endogeneity bias problem caused by an 31 omitted variable, namely using the revealed drug quality, not the \true" quality. The revealed drug quality may be related to the probability of being the early mover. A possible mechanism of the association is that a drug launched earlier is less likely to have been tested in quality clinical trials and a drug that is tested in quality clinical trials is more likely to be reported to be of good quality: Probability of being the early mover and the quality of clinical trials | Intuitively, good clinical trials require enough time to be completed; strict criteria for subject selection, a suciently long endpoint, a rigorous protocol, appropriate sta training, etc. Also, the more time clinical trials take, the less likely the drug is to be an early mover. Therefore, the probability of being the early mover is inversely proportional to the probability of being tested in quality clinical trials. The quality of clinical trials and the revealed drug quality | The appropriate drug form (such as strength or formulation) is developed during the sequence of clinical trials. 6 By allowing researchers to identify and compare safety and ecacy more accurately, 7 thereby helping nd a better drug form, quality clinical trials can improve the \true" quality of the drug, hence the re- vealed drug quality. Moreover, a well-designed study is likely to produce desirable results. Thus, a drug examined by quality clinical trials will more probably be reported to be of good quality than a drug examined by poor quality trials, although the drugs are not dierent in their \true" quality. The possible links described above indicate that the revealed drug quality can be negatively as- sociated with the probability of being the early mover. This suggests that the early mover eect presented by EM ict and EM ict N ct is biased downward; in turn, the quality-adjusted market share of early mover ct is undervalued. To deal with the potential endogeneity, the order of the patent ling date of each drug among all drugs in the relevant market and its interaction with N ct are used as instrumental variables. The dates are calculated based on the patent expiration dates provided by Orange Book patent and exclusivity date from the National Bureau of Economic Research. 8 The power of the instrumental variables is guaranteed in the sense that the earlier a patent is led, the more likely the drug is 6 https://en.wikipedia.org/wiki/Pharmaceutical formulation 7 American Cancer Society, Clinical Trials: What You Need to Know, https://www.cancer.org/treatment/ treatments-and-side-eects/clinical-trials/what-you-need-to-know/phases-of-clinical-trials.html. 8 The patent expiration dates of the NMEs that do not have records in Orange Book are predicted based on Pharmaproject (for Campral, Celexa, Monurol, and Proamantine) and relevant websites (https://en.wikipedia.org/ wiki/Trospium chloride for Sanctura and https://www.drugs.com/availability/generic-tindamax.html for Tindamax). 32 brought to the market early. Also, the instruments are not correlated with the revealed drug qual- ity (hence the idiosyncratic error in (1)). This is basically because the ling date happens ahead of clinical trials. Indeed, one might think that the technological progress in the initial discovery stage still harms the exogeneity of the instruments because a drug that is patented early is less likely to benet from technological progress. However, as discussed earlier, rms do not adjust their expectation of the market share distribution by the natural improvement of the drug quality made by the industry's technological progress. This implies that the exogeneity of the instruments is not threatened by technological progress. 2.5.2 Estimation of the eect of the drug quality-adjusted market share distribution on the R&D investment According to proposition 1, rms devote more eorts to R&D as higher market share is expected for the early mover. The suggested hypothesis is tested under the assumption of adaptive expectation discussed previously; rms adjust their expectations of the future market share distribution based on the quality-adjusted market share distribution realized over the previous 10 years. As in Blume- Kohout and Sood (2013), in every year t + 1 (2006, , 2016), the R&D investment is measured by the number of drugs in each development stage, Y ct+1 . Under the assumption of adaptive expectation, if proposition 1 is correct, the expectation of the higher quality-adjusted market share of the early mover induces pharmaceutical rms to initiate or conduct more (pre-)clinical tests with their molecule candidates, and thus more drugs will be observed in (pre-)clinical tests. The number of drugs in each drug development stage (preclinical testing and phase 1{3 clinical trials) is assumed to follow the Poisson distribution: f(Y ct+1 =y) = e ct+1 y ct+1 y! where y = 0; 1; 2;::: The rate parameter, ct+1 , is estimated by: ct+1 = E Y ct+1 = exp Year t + Class c + 1 N ct + 2 log(MktSize ct+ ) + 3 N ct log(MktSize ct+ ) + ct (2) 33 The positive coecient of the drug quality-adjusted market share of early mover lends validity to proposition 1. The models are controlled by the year xed-eect, Year t , the class xed-eect, Class c , the number of the drugs introduced over the previous 10 years, N ct , the log-transformed future market size, log(MktSize ct+ ), and its interaction with N ct . Prediction of the future market size is described in detailed below. Standard errors are clustered at the therapeutic class level. Following Acemoglu and Linn (2004) and Blume-Kohout and Sood (2013), I use demographic changes to predict the future market size of the therapeutic class c for the 10 years from the expected year of launch t +, MktSize c;t+ , as follows: MktSize c;t+ = X a X g MktSize c;a;g;t9 PopGroup a;g;t+ PopGroup a;g;t9 where is 4, 6, 8, and 10 if a rm makes a decision on the R&D investment in the phase 3, the phase 2, the phase 1 trials, and the preclinical testing stages att, respectively. The survey-weighted expenditure, adjusted by the 2018 US Consumer Price Index, in a therapeutic class c by a 5-year age-gender group (a;g) 9 for the last 10 years is denoted by MktSize c;a;g;t9 . For each age-gender group, the demographic change is represented by the ratio of PopGroup a;g;t+ to PopGroup a;g;t9 ; PopGroup a;g;t+ is the sum of the projected population of the age-gender group from t + to t + + 9 and PopGroup a;g;t9 is the sum of the population of the age-gender group from t 9 tot in the US. The projections of the age distribution and the gender ratio are provided by the United Nations Population Division World Population Prospects. 2.6 Empirical results The mean of the market shares of early movers and followers in 1996{2015 are documented for every N-drugs market in Table 2. In the markets where the number of drugs is equal to or less than 5 (N 5), the market share is, on average, higher for the early mover than a follower, and the dierence is statistically signicant at the 5% level. As shown in Table 3, the drugs that were under the priority review account for similar proportions among early movers and followers. The dierence in proportions of orphan status drugs among early movers and followers is also 9 For example, female aged between 1{5, male aged between 1{5, female aged between 6{10, male aged between 6{10, and so on. 34 insignicant. However, the days on the market of early movers is 50% higher than that of followers, on average. The results of the xed-eects models estimating (1) are reported in Table 4. The rst model (xed-eects, IV) addresses the endogeneity using the instruments discussed previously, but the second model (xed-eects) does not. The second model's tted value is therefore denoted as a drug quality-unadjusted market share. The quality-adjusted/unadjusted market shares of early movers are depicted in ch2Figure 2. 10 In an average 10-year window from 1996{2005 to 2006{2015, the quality-adjusted market share of early movers is higher than the quality-unadjusted market share; for example, the quality-adjusted versus quality-unadjusted market share of early movers is 81.4% versus 57.2% in the 2-drug market, 70.3% versus 51.8% in the 3-drug market, and 58.8% versus 42.9% in the 4-drug market. Compared to equal market share (N 1 ), the quality-adjusted and quality-unadjusted market shares of early movers are higher by 30.2% points and 10.6% points, on average. These results conrm that the downward bias of the early mover eect, made by the negative association between the revealed drug quality and the probability of being the early mover, is corrected in the xed-eects instrumental variables estimate. According to a one-sided test of a null ct > N 1 ct at the 1% signicance level, among 288 markets, early mover advantage (EMA) is present in 77 markets. There also exists EMA in 24.5% (43/151), 52.4% (33/63), and 4.4% (1/23) of the 2-, 3-, and 4-drug markets, respectively. In the same test at the 5% signicance level, it is shown that EMA exists in 170 markets in total; 57.6% (87/151), 93.7% (59/63), 91.3% (21/23), and 15.0% (3/20) of the markets with 2, 3, 4, and 5 drugs, respectively. There are no markets in which early mover disadvantage (EMdA) is present, even at the 5% signicance level. The results of the empirical models examining proposition 1 are reported in Table 5. The rst row of each column represents the development stage at which (2) is estimated. 11 In an average year from 2005 to 2015, an 1% point increase in the drug quality-adjusted market share of early movers causes 1.74%, 1.53%, and 2.02% more drugs to enter into phase 1, 2, and 3 trials (p<.01). 10 The markets with 10 or more NMEs (N 10; Antiviral, anti-HIV in 1996-2005, 1997-2006, 1998-2007, and 1999-2008) have negative predicted value of the early mover's market share, which is a limitation of a linear model. Since all the negative predictions are not signicant at the 5% level, they are set to zero. As explained previously, each of them accounts only for less than 1% in the total number of the markets. 11 Among the 288 markets, 1 is dropped in all of the preclinical testing and the phase 1{3 clinical trial models because of only 1 observation per therapeutic class. Additional 3 markets (cephalosporin, oral class) are dropped in the phase 1 and 2 clinical trial models because of all zero drugs on the development stages within the therapeutic class. 35 In preclinical testing, the eect of the early mover's market share is more modest and less precise (0.69% more drugs, p=.079). Conducting further analyses, I examine the robustness of the results obtained from the main model (2) (Table 6). Alternative model 1 | In order to see whether the implication is aected by how to measure future market size, I run a model omitting the log-transformed future market size and its interaction with the number of drugs. E Y ct+1 = exp Year t + Class c + 1 N ct + ct There are no meaningful changes in results compared to the main model. The marginal eects of the quality-adjusted market share of early movers are 0.67%, 1.79%, 1.36%, and 2.16% increases in the number of drugs in preclinical testing (p=.045) and phase 1{3 trials (p<.01), respectively. Alternative model 2 | Since rms' responses to the market share distribution might not be consistent over the dierent number of drugs in the market, the heterogeneous eect of the early mover's market share is addressed in the model as following: E Y ct+1 = exp Year t + Class c + 1 N ct + 2 log(MktSize ct+ ) + 3 N ct log(MktSize ct+ ) + 1 ct + 2 ct N ct The average eects of a 1% point additional quality-adjusted market share of early mover, weighted by the number ofN-drug markets, are 1.10% (p<.01), 0.82% (p=.011), and 2.12% (p<.01) in phase 1{3 trials. However, no eect is found in preclinical testing (0.08%, p=.829). In the phase 1 and phase 2 trial models, the eects of the early mover's market share are statistically signicant in the 2-drug to 7-drug markets, and the 2-drug to 4-drug markets at the 5% level respectively. In the phase 3 trial model, the eect is signicant in all N-drug markets. Alternative model 3 | I estimate a linear panel data model with xed eects using the same variables specied in (2) to see whether the main implication diers in dierent types of estimators: E Y ct+1 = Year t + Class c + 1 N ct + 2 log(MktSize ct+ ) + 3 N ct log(MktSize ct+ ) + ct 36 It is found that an additional 1% point market share of early movers induces 0.24 (p=.057), 0.37 (p<.01), and 0.20 (p<.01) more drug in ow into the phase 1{3 trials. At the mean of the number of drugs on each development stage (listed in Panel B of Table 3), the estimated eects correspond to 1.2%, 1.3%, and 2.2% increments of drugs in each development stage. Alternative model 4 | To examine how rms change their R&D decisions in response to the presence of EMA in the same model setting as (2), I replace the early mover's market share, ct , with an indicator variable for the presence of EMA, EMA ct . The variable is generated by the one-sided test of the null ct > N 1 ct at the 1% and 5% signicance levels; this variable is equal to 1 if the hypothesis is not rejected and 0 otherwise. E Y ct+1 = exp Year t + Class c + 1 N ct + 2 log(MktSize ct+ ) + 3 N ct log(MktSize ct+ ) +EMA ct (3) Overall, the results are qualitatively the same as those of the main model. In the markets where the presence of EMA is shown at the 1% signicance level (Alternative model 4-1), 15.39% more drugs enter into phase 2 trial (p<.01) than in the markets without EMA. No meaningful eects are found in phases 1 (3.74%, p=.726) and 3 (3.70%, p=.787). In contrast, in the markets where the existence of EMA is not rejected at the 5% signicance level (Alternative model 4-2), the number of drugs entering phase 1 and 3 trials is higher by 10.41% (p=.065) and 9.86% (p=.084), respectively, than in the markets where the hypothesis is rejected. Alternative model 5 | As the eect of the early mover's market share might be more distinctive in the markets where EMA is present, I restrict the sample to those with EMA and re-estimate (2). 12 In the 75 markets where EMA ct are 1 at the 1% signicance level (Alternative model 5- 1), 17.11% (p<.01), 7.71% (p=.068), and 22.86% (p=.084) more drugs enter into phase 1{3 trials, respectively, for 1% point higher quality-adjusted market share for early movers. The estimation with the 168 markets such that EMA ct = 1 at the 5% signicance level (Alternative model 5-2) results in 4.81% (p=.169), 4.36% (p<.01), and 5.04% (p=.338) increases of drugs entering phases 12 Among the 77 markets with EMA, 2 are dropped in all of the preclinical testing and the phase 1{3 clinical trial models because of only 1 observation per therapeutic class. 37 1{3, respectively. The alternative model 5-1 shows much stronger eects of the early mover's market share than the main model (2). Although statistically signicant only in the phase 2, the eects measured in the alternative model 5-2, which uses looser restrictions in identifying markets with EMA relative to the alternative model 5-1, are weaker than the eects in the alternative model 5-1, but still stronger than those in the main model. 2.7 Discussion The results of the empirical analysis indicate that in therapeutic classes where higher drug quality- adjusted market share is expected for early movers, pharmaceutical rms exert themselves more in R&D. This supports the hypothesis suggested by proposition 1 of the theory. The validity of the positive implication, in turn, justies an application of the normative implication demonstrated in proposition 2; in the market where EMA or the equal market share distribution is expected in the future, rms invest too much in R&D compared to the social optimum. Based on the drug quality-adjusted market share distribution, the market eciency of phar- maceutical R&D is discussed under the assumption that a rm expects EMA or EMdA in the relevant therapeutic class for 10 years post-launch, if EMA or EMdA actually existed in the class over the previous 10 years (adaptive expectation). However, it is reasonable not to consider the equal market share distribution as the sucient condition for overinvestment. Although analyz- ing a larger range of medical interventions (including non-NMEs and non-pharmaceuticals) over a dierent time period (1976{2001), Jena and Philipson (2008) estimates rms' appropriation level far less than 100% of the social benet (indeed, 37% of the social surplus, at most). As implied in Section 4 of the theory, if rms cannot fully appropriate the social benet of their innovations, the market share distribution necessarily leading to overinvestment must be more favorable to early movers than the equal market share distribution. It is noteworthy that one cannot directly conclude that a certain therapeutic class is over- or underinvested based only on the criterion suggested by the theory. This is because, in reality, there are an extensive range of factors that aect market competition and the market value of the prod- ucts, such as changes in bargaining power between pharmaceutical rms and third-party payers (Duggan and Scott Morton, 2010; Lakdawalla and Yin, 2015), and non-trivial o-label drug use (Bradford et al., 2018). Accordingly, the presence of EMA should be interpreted cautiously; it can 38 only raise the possibility of overinvestment, rather than leading the normative conclusion. After inclusion of the markets with one drug, the number of markets rises from 288 in 46 ther- apeutic classes (13 therapeutic groups) to 543 in 72 classes (14 groups), including 233 NMEs. A market with EMA is identied if EMA ct is 1 as in (3). I employ the 1% signicance level in the test of EMA. Table 7 and Figure 3 show the number of therapeutic classes in which at least one drug is introduced in each 10-year window (1996{2005, , 2006{2015) and in how many of them EMA is identied. Overall, there are an average of 49.4 (543/11) therapeutic classes per window that have at least one drug, and EMA is shown to exist in 7.0 (77/11) classes. Under the adaptive expectation assumption, proposition 2 implies that, in an average reference year between 2005 and 2015, pharmaceutical rms are likely to overinvest in clinical trials in 14.2% (77/543) of the thera- peutic classes. The same analysis is conducted for each therapeutic group (Table 7, Figure 3). In an average reference year, the therapeutic groups that have the highest proportion of therapeutic classes with the possibility of overinvestment are the biotechnology (54.5%) and the blood and clotting (40.0%) product groups. They are followed by the neurological (27.8%), the genitourinary (24.3%), the respiratory (14.0%), and the musculoskeletal (12.1%) product groups. On the other hand, the anti- cancer, the antiparasitic, the dermatological, the immunological, and the hormonal product groups do not have therapeutic classes that show a possibility of overinvestment. 2.8 Conclusions This paper analyzes how the oligopolistic structure of the pharmaceutical market aects rms' R&D decisions and the market eciency of the R&D investment, by applying the heterogeneous patent race framework (Kim, 2021). Using the new molecular entities (NMEs) developed from 1996{2015, it examines the positive implication on how pharmaceutical R&D decisions change according to the expectation of market share distribution. For this, it incorporates the sales revenue of a non-NME into that of its original NME(s) and calculates the sales revenue of individual NMEs for every 10-year window. Based on the sales revenue, it measures the 10-year market share of early movers, controlling for the drug quality, to identify pure time advantage/disadvantage; it is shown that early movers have a 30.2% point higher drug quality-adjusted market share than the equal market share, on average. It estimates that the number of NMEs entering into the clinical trial phases 1, 2, and 39 3, increases by 1.74%, 1.53%, and 2.02%, respectively, as the drug quality-adjusted market share of early movers increases by 1% point. These results lend validity to the positive implication of the theory. The measured market share distribution raises the possibility that, in 14.2% of therapeutic classes, rms invest excessively in clinical trials that begin in the reference period (2005{2015). In particular, such overinvestment decisions might be more prevalent in the biotechnology and the blood and clotting product groups than in other therapeutic groups. Responses of pharmaceutical R&D investment to changes in the intensive margin of the reward allocation carry important implications on the development of the COVID-19 vaccine. Although the FDA issued and expanded the Emergency Use Authorization for Remdesivir in treating COVID- 19, there has not yet been a vaccine launched. 13 The epidemic is highly contagious; the virus can be transmitted from an infected individual to 2.2 individuals on average (Li et al., 2020) and transmission can occur even from an asymptomatic individual (Hoehl et al., 2020; Rothe et al., 2020). As a result, there are considerable, immediate demands for vaccines in the global community (Corey et al., 2020). Related to R&D competition, this indicates that the rst rm completing vaccine development will take a substantial market share in the entire demand generated until the epidemic ends. Hence, given the market size, the theory and empirical evidences imply that much more investment is being directed to the COVID-19 vaccine relative to other drug classes. Industry-wise, too many resources might have been concentrated on this vaccine development. In this sense, the Accelerating COVID-19 Therapeutic Interventions and Vaccines (ACTIV), aiming \to develop a coordinated research strategy for prioritizing and speeding development of the most promising treatments and vaccines", 14 is helpful in improving market eciency without delay of vaccine introduction. This is because this program, led by the National Institutes of Health, encourages and facilitates collaboration among pharmaceutical rms, and thus can reduce resource use and enhance R&D productivity compared to when rms run R&D separately. 13 As of September 2020, there are 321 vaccine candidates and 6 of them are in the clinical trial phase 3 (Le et al., 2020). 14 National Institutes of Health (NIH), Accelerating COVID-19 Therapeutic Interventions and Vaccines (ACTIV), https://www.nih.gov/research-training/medical-research-initiatives/activ. 40 Table 2.1: NDA classication codes (1996-2015) Category NDA classication codes Number of NDA-approved drugs 1 NMEs Type 1 - New Molecular Entity 496 (26.5%) 519 (27.7%) Type 1/4 - NME + New Combination 23 (1.2%) Type 2 - New Active Ingredient 35 (1.9%) Type 3 - New Dosage Form 810 (43.3%) Type 4 - New Combination 212 (11.3%) Non-NMEs Type 5 - New Formulation/Manufacturer 270 (14.4%) 1,252 (72.3%) Type 2/3 - Type 2 + Type 3 4 (0.2%) Type 2/4 - Type 2 + Type 4 2 (0.1%) Type 3/4 - Type 3 + Type 4 19 (1.0%) Total 1,871 1 Proportions in parenthesis. 41 Table 2.2: Distribution of the markets and the average of the realized market shares by the number of NMEs (1996{2015) Number of NMEs Number of Number of Average of on the market markets 1) window-drugs the realized market shares P-value 2 early mover Follower 2 151 (52.4%) 302 59.9% 40.1% <0.01 3 63 (21.9%) 189 50.2% 24.9% <0.01 4 23 (8.0%) 92 36.3% 21.2% 0.012 5 20 (6.9%) 100 35.5% 16.1% <0.01 6 17 (5.9%) 102 18.9% 16.2% 0.640 7 3 (1.0%) 21 5.9% 15.7% 0.493 8 4 (1.4%) 32 14.0% 12.3% 0.843 9 3 (1.0%) 27 8.4% 11.5% 0.739 10 2 (0.7%) 20 15.1% 9.4% 0.292 11 1 (0.4%) 11 13.1% 8.7% N/A 13 1 (0.4%) 13 18.5% 6.8% N/A Total 288 909 49.4% 23.5% <0.01 1 Proportions in parentheses. 2 For comparison between early mover and followers of market share. Notes: A market is dened as as set of NMEs introduced into a therapeutic class for a 10-year window (1996{2005, , 2006{2015). It is equivalent to a window-class. An R&D decision is made in the last year of each of these windows (2005, , 2015). The year is referred to as a reference year and denoted by t. The windows for measuring the market share distribution and the reference years are listed in Table B.1. 42 Table 2.3: Descriptive statistics Panel A. Variables used in the estimation of the drug quality-adjusted market share distribution (1996{2015) All drugs Early mover Followers P-value 1 Number of drugs 909 288 621 N/A Proportion of drugs under priority review 25.4% 28.1% 24.2% 0.201 Proportion of drugs granted orphan status 5.0% 5.9% 4.5% 0.368 Time-on-the-market (days) 2,227 2,965 1,885 <0.01 1 For comparison between early mover and followers of the variable. Notes: The realized market share distributions are documented in Table 2. Panel B. Variables used in the estimation of the eect of the drug quality-adjusted market share distribution on the R&D investment Mean 1st quartile 3rd quartile Phase 3 trial 9.3 3 12 Number of drugs Phase 2 trial 28.1 8 40 on development stages 2 Phase 1 trial 18.9 6 27.5 Preclinical testing 59.8 12 82.5 for phase 3 trial $9.0B $1.2B $11.2B Future market size 3 for phase 2 trial $9.2B $1.2B $11.4B for phase 1 trial $9.4B $1.2B $11.6B for preclinical testing $9.6B $1.3B $11.9B 2 Counted in the next year of the reference year, i.e. t + 1. The reference year t runs from 2005 to 2015. Accordingly, the number of drugs is counted in 2006, , 2016. 3 Measured in t + 4 { t + 13 for phase3 trial, in t + 6 { t + 15 for phase2 trial, in t + 8 { t + 17 for phase1 trial, and in t + 10 { t + 19 for preclinical testing. The windows for measuring the future market size are listed in Table B.1. 43 Table 2.4: Estimation results of the drug quality-adjusted/unadjusted market share distribution Variable Fixed-eects, IV 1 Fixed-eects 2 EM 3 0.8185*** 0.2123** (0.0845) (0.2245) N 4 -0.0106 -0.0483*** (0.0121) (0.0193) EM N -0.0979** -0.0373** (0.0146) (0.0469) Priority 5 0.0241 0.0917* (0.0533) (0.0736) Orphan 6 -0.0382 -0.0824 (0.1129) (0.1397) log(TOM) 7 0.0226 0.1454*** (0.0762) (0.0173) Observations 909 Number of markets 204 Log likelihood -224.1 -72.18 1 Fixed eects instrumental variables estimation. The tted value represents the drug quality-adjusted market share. 2 Fixed eects estimation. The tted value represents the drug quality-unadjusted market share. 3 1 if the drug is the early mover of the market. 4 The number of the drugs in the market. 5 1 if the drug was under priority review. 6 1 if the drug is granted orphan drug status. 7 Log-transformed time-on-the-market. * signicant at 10%, ** signicant at 5%, *** signicant at 1% Notes: Standard errors are presented in parentheses, adjusted for clustering on the drug level. 44 Table 2.5: Estimation results of the eect of the drug quality-adjusted market share distribution on the R&D investment Variable Preclinical Phase 1 Phase 2 Phase 3 1 0.6888* 1.7407*** 1.5342*** 2.0190*** (0.3920) (0.5327) (0.2761) (0.3620) N 0.1578 0.3315** 0.0031 0.4581*** (0.1124) (0.1368) (0.0987) (0.0871) log(MktSize) 2 0.0459 0.0669 0.0070 0.0501 (0.0538) (0.0695) (0.0395) (0.0572) Nlog(MktSize) -0.0071 -0.0148 0.0162 -0.0262** (0.0131) (0.0140) (0.0111) (0.0102) Observations 287 284 284 287 Number of therapeutic classes 45 44 44 45 Log likelihood -775.0 -614.2 -642.7 -510.8 1 Drug quality-adjusted market share of early movers. 2 Log-transformed future market size. * signicant at 10%, ** signicant at 5%, *** signicant at 1% Notes: Standard errors are presented in parentheses, adjusted for clustering on the therapeutic class level. 45 Table 2.6: Robustness check Model Variable Preclinical Phase 1 Phase 2 Phase 3 Alternative model 1 1 0.6692** 1.7869*** 1.3649*** 2.1550*** (0.3340) (0.5570) (0.3382) (0.4613) Alternative model 2 2 0.3742 1.6605*** 1.3421*** 2.6534*** (0.4449) (0.5448) (0.3449) (0.3739) N -0.0952 -0.0201 -0.0543 0.1576* (0.0676) (0.0576) (0.0600) (0.0819) Alternative model 3 3 31.1363 23.6017* 36.7682*** 20.0960*** (25.6541) (12.0804) (12.3592) (7.1990) Alternative model 4-1 4 EMA 5 0.0474 0.0374 0.1539*** 0.0370 (0.0673) (0.1065) (0.0507) (0.1373) Alternative model 4-2 6 EMA 0.0061 0.1041* 0.0434 0.0986* (0.0323) (0.0564) (0.0415) (0.0570) Alternative model 5-1 7 4.5004 17.1057*** 7.7130* 22.8570* (4.5624) (3.6308) (4.2322) (13.2124) Alternative model 5-2 8 -0.1149 4.8122 4.3626*** 5.0366 (1.5577) (3.4956) (1.4884) (5.2606) Observations 287 284 284 287 Number of therapeutic classes 45 44 44 45 1 Count data model with xed-eects, excluding the log-transformed future market size and its inter- action with the number of drugs. 2 Count data model with xed-eects, including an interaction between the drug quality-adjusted mar- ket share and the number of drugs. 3 Linear panel data model with xed-eects. 4 Count data model with xed-eects, substituting the drug quality-adjusted market share with an in- dicator variable for a market where the null ct > N 1 ct is not rejected at the 1% signicance level. 5 1 if early mover advantage (EMA) is identied. 6 Count data model with xed-eects, substituting the drug quality-adjusted market share with an in- dicator variable for a market where the null ct > N 1 ct is not rejected at the 5% signicance level. 7 Count data model with xed-eects, restricting the sample to markets where the null ct > N 1 ct is not rejected at the 1% signicance level. 8 Count data model with xed-eects, restricting the sample to markets where the null ct > N 1 ct is not rejected at the 5% signicance level. * signicant at 10%, ** signicant at 5%, *** signicant at 1% Notes: Standard errors are presented in parentheses, adjusted for clustering on the therapeutic class level. 46 Table 2.7: Proportion of therapeutic classes where early mover advantage is identied, by therapeutic group Therapeutic group Number of therapeutic classes Number of therapeutic classes with at least one drug introduced, where EMA is identied 2 , (b)/(a) 3 in an average 10-year window (a) 1 in an average 10-year window (b) Alimentary/Metabolic 5.2 0.3 5.3% Anti-infective 7.5 0.5 6.1% Anticancer 1.6 0 0% Antiparasitic 1.0 0 0% Biotechnology 1.0 0.5 54.5% Blood and Clotting 1.4 0.5 40.0% Cardiovascular 5.6 0.5 8.1% Dermatological 1.6 0 0% Genitourinary 3.4 0.8 24.3% Hormonal 2.7 0 0% Immunological 0.4 0 0% Musculoskeletal 3.0 0.4 12.1% Neurological 10.5 2.9 27.8% Respiratory 4.5 0.6 14.0% Total 49.4 7.0 14.2% 1 The 10-year window runs from 1996{2005 to 2006{2015. 2 EMA is an abbreviation of early mover advantage. 3 The proportion of therapeutic classes where EMA is identied. 47 Figure 2.1: Time schedule of R&D decisions 48 Figure 2.2: Comparison of drug quality-unadjusted versus quality-adjusted market shares of early movers, by the number of drugs Notes: The box depicts the interquartile range. The bar in the middle of the box represents the median. The bars at the ends of the whiskers represent the upper and lower adjacent values. 49 Figure 2.3: The number of therapeutic classes where at least one drug is introduced and the number of therapeutic classes where early mover advantage (EMA) is identi- ed, by therapeutic group and 10-year window All therapeutic groups Notes: There are 46 therapeutic classes in 13 therapeutic groups in the sample. Alimentary/Metabolic product group Anti-infective product group 50 Anticancer product group Antiparasitic product group Biotechnology product group Blood and Clotting product group Cardiovascular product group Dermatological product group 51 Figure 2.4: Genitourinary product group Hormonal product group Immunological product group Musculoskeletal product group Neurological product group Respiratory product group 52 Chapter 3 Association between Verapamil Use and Serious Hypoglycemic Events among Per- sons with Type 1 Diabetes: A Retro- spective Cohort Analysis 1 3.1 Introduction Type 1 diabetes (T1D) is characterized by the loss of pancreatic cells, leading to impaired abil- ity to secrete insulin and various resultant macrovascular and microvascular complications (Eizirik and Darville, 2001; Steele et al., 2004). T1D presents a major economic burden to society and is associated with signicant morbidity and mortality, especially due to atherosclerotic cardiovascular disease (ASCVD) (Hex et al., 2012; Tao et al., 2010; Skrivarhaug et al., 2006; Secrest et al., 2010; Juutilainen et al., 2008; Orchard et al., 2015). Novel therapeutic agents have been explored for their potential to preserve function of pancreatic cells and reduce complications. One promising candidate for this role is verapamil, a non-dihydropyridine calcium channel blocker currently FDA approved and widely used for its antihypertensive properties (Lam and Cherney, 2018; Xu et al., 2012) Though the primary use of verapamil has been in treatment of hypertension and cardiomyopa- 1 Joint Work with Matthew Crane, Hasan Nadeem, Dana Goldman, Yusuke Tsugawa, and John Romley 53 thy, it is recognized for diverse metabolic eects, and recent literature has seen additional interest in the use of this agent in treatment of retinopathy and nephropathy (OPIE, 1984; Adeghate et al., 2010; Steuber et al., 2019; Tabur et al., 2015; Xu et al., 2019). The potential eect of verapamil on diabetes incidence was indicated as early as the SAMPLE study, but interest in this application has surged with the identication of its inhibitory action on thioredoxin-interacting protein (TXNIP), a proapoptotic gene implicated in the loss of pancreatic cells and progression of both type 1 and type 2 diabetes (Xu et al., 2012; Pepine et al., 2003; Cooper-DeHo et al., 2009; Minn et al., 2005). A recent clinical trial of 26 individuals newly diagnosed with T1D between the ages of 18 and 45 investigated this utility (NCT02372253) and conrmed preservation of cells, lending additional credibility to the use of verapamil in slowing diabetes progression (Ovalle et al., 2018). While lower incidence rates have been reported for adults than juveniles (Lin et al., 2014), the existing evidence on incidence in adulthood is limited (Bruno et al., 2016). Notably, a recent study in the United States did nd a larger number of new cases per year among non-elderly adults than juveniles (Rogers et al., 2017). In a European population, incidence rates among people in their seventies were seen to rebound to their childhood peak (Thunander et al., 2008). Some have argued that adult-onset diabetes has received inadequate scholarly attention (ster- gaard et al., 2016). There is reason to believe that the etiology of disease diers between adults and juveniles, for example, in the comparative susceptibility of beta cells to autoimmune destruction (Howson et al., 2011; Poudel et al., 2015). Older patients with T1D are known to have a higher risk of microvascular and macrovascular complications, as well as an increased rate of serious hy- poglycemic events, further justifying research interest in outcomes within this population (Sch utt et al., 2012; Chapman et al., 2013). Existing research has described potential benets of calcium-channel blockers in both type 1 and type 2 diabetes via the TXNIP pathway (Xu et al., 2012). Retrospective analysis using Taiwan?s National Health Insurance Research Database on these grounds found reduced risk of incident type 2 diabetes among verapamil users and improved protective function when compared to other calcium-channel blockers (Yin et al., 2017). To our knowledge, similar cohort analysis has not been conducted regarding the protective eect of verapamil on T1D progression. Previous studies regarding the preservation of pancreatic cells in verapamil users have also not employed the occurrence of hypoglycemic events as a measurement 54 device, despite an explicit connection with adverse outcomes such as retinopathy and nephropathy (Ovalle et al., 2018; Control and Group, 1993). This study seeks to describe the relationship between verapamil and T1D from a novel per- spective, examining whether the proposed protective eect extends to a reduction in serious hypo- glycemic events in a national sample of Medicare patients with newly diagnosed T1D. If a high- quality observational analysis were to nd such an eect, there would be a clearer rationale for scaling existing randomized evidence up to larger trials intended to identify potential improve- ments in clinical practice. 3.2 Materials and methods We performed retrospective cohort analysis using medical and pharmacy claims by examining a 20% random sample of Medicare beneciaries from 2006 through 2014. We used a validated algo- rithm to identify Medicare beneciaries with T1D (Hebert et al., 1999; Rector et al., 2004). 2 We excluded beneciaries who were younger than 65 years old at rst diagnosis, or who rst enrolled in Medicare due to disability or end stage renal disease, as reported in the Master Beneciary Summary File (MBSF). Because verapamil may also be prescribed for various cardiac-related conditions owing to its broad action as a calcium channel blocker (Schamroth et al., 1972; Rehnqvist et al., 1996), we limited our sample to a clinically homogeneous group of individuals diagnosed with hypertension (identied using a validated claims-based algorithm) as of the year of diabetes diagnosis (Rector et al., 2004; Black et al., 2007; Borzecki et al., 2004; Dutro et al., 2007; Elixhauser et al., 2014; Halpern et al., 2006; Quan et al., 2009; Quam et al., 1993). For this purpose and for comorbidity identication (described below), we used medical claims beginning in 2002. As with the trial noted previously (Yin et al., 2017), we considered patient outcomes during the second year after incident T1D diagnosis, in relation to verapamil use during the rst year after diagnosis. We therefore required continuous enrollment in Medicare Parts A and B during the two years after diagnosis as well as enrollment in a standalone prescription drug plan from Medicare Part D during the year after diagnosis. To ensure that diagnoses were incident, we further required 2 Centers for Medicare and Medicaid Services. Chronic conditions data warehouse: condition categories. Updated June 2018. Assessed October 4, 2018, www.ccwdata.org/chronic-conditions/index.htm. 55 continuous enrollment in Medicare Parts A and B in the six months prior to rst observed diagnosis (Kim et al., 2015; Sohn et al., 2015; Kreft et al., 2018). Verapamil lls in pharmacy claims were identied by National Drug Codes from First Data- bank46. Days supply in claims was used to measure 30-day-equivalent lls during the exposure window; we also assessed dosage. We dened and identied serious hypoglycemic events as an ad- mission to a short term acute care hospital or an emergency department (ED) visit with a diagnosis of hypoglycemia (ICD-9 codes 251.0, 251.1, and 251.2,), as reported in CMS Inpatient and Hospital Outpatient Files (Romley et al., 2015; Whitmer et al., 2009). The number of hospital admissions and ED visits during the outcome window was analyzed using multivariate Poisson regression. We took the natural logarithm of the number of verapamil lls (plus one) so that any relative (percentage) eect of use could diminish in magnitude with each additional ll49. We adjusted for age at diagnosis, gender, race / ethnicity, and the presence of 25 chronic comorbidities (all reported in the MBSF and measured using validated claims algorithms) at the time of diagnosis 3 . To address secular trends in verapamil use and patient outcomes, the regression included indicator variables for year of incident T1D diagnosis. We calculated standard errors that were robust to the violation of the Poisson assumption that the conditional variance is equal to the conditional mean (Wooldridge, 2010). Based on the regression results, we characterized the relationship between verapamil use and hypoglycemic events in terms of the rate of events per 1,000 person-years. In particular, we used the method of predictive margins to predict the rate of events that would have prevailed if all sample beneciaries had used various quantities of verapamil, with all else (such as demographics) held constant (Graubard and Korn, 1999). In additional analysis, we explored the association between use and outcomes across subpopula- tions, by sequentially interacting indicator variables for gender, young versus old (based on median age at diagnosis), and non-Hispanic white versus other race / ethnicity. Stata version 15.1 was used, and hypothesis tests were conducted with a probability of 0.025 in each tail, or a P-value of 0.05. In an observational analysis, unmeasured confounding is always a concern (Guyatt et al., 2011). 3 Chronic Conditions Data Warehouse: National CMS Medicare and Medicaid Research Database. User Docu- mentation. Accessed December 10, 2019, https://www2.ccwdata.org/web/guest/user-documentation. 56 To assess this concern, we analyzed the relationship between actual verapamil use and the pre- dicted likelihood of used based on the individual characteristics included in our primary analysis (e.g., comorbidities). Similar predicted likelihoods of use would be consistent with the hypothesis that measured and unmeasured determinants of utilization are comparable across actual use levels, and would oer some reassurance that confounding is not extensive in this context. To analyze this issue, we conducted an ordered logit regression on actual non-use, \low use" (below the median number of lls), and high use. We then plotted the distributions of predicted likelihoods of the use levels, in relation to actual use. This study was done without patient involvement. Patients were not invited to comment on the study design and were not consulted to develop patient relevant outcomes or interpret the results. Patients were not invited to contribute to the writing or editing of this document for readability or accuracy. 3.3 Results Over 2006-2014, we identied 74,545 individuals in our 20% random sample of Medicare beneciaries who had a diagnosis of T1D, and met all other inclusion / exclusion criteria for potential analysis. Of these individuals, 1,649 actually lled a verapamil prescription during the year after rst diagnosis. The number of individuals in each stage of sample selection is shown in Figure C.1. The predicted likelihood of use varied markedly between individuals who actually used verapamil and those who did not (as can be seen in Figure C.2). Table 1 compares non-users to low and high users. To minimize confounding, we limited our analysis to actual users, and so assessed the relationship between serious hypoglycemic events and the extent of use. As the gure shows, the predicted likelihood of use was reasonably comparable between low and high users (dened by the median number of 30-day-equivalent lls of 11). The characteristics of analysis sample individuals based on high versus low verapamil use are shown in Table 1. The two groups were similar in age at diagnosis (74.56 years (95% CI, 74.11 to 75.01) for low users versus 74.50 (95% CI, 74.00 to 75.00) for high users, P = 0.85 for a null hypothesis of equality), and also in gender and race / ethnicity. Measured comorbidity rates tended to be lower for high verapamil users; the dierences were statistically indistinguishable in most cases. The modal dosage was somewhat lower for low users than for high users (195.43 milligrams (95% CI, 191.74 to 199.12) versus 210.01 (95% CI, 206.34 57 to 213.68), P < 0.001); all lls in the sample were for oral administration (capsules or tablets). Without adjusting for patient characteristics, the regression of serious hypoglycemic events on the number of verapamil lls, reported in Table 2, implies that an additional ll was associated with 1.79 (95% CI, -3.59 to 0.01) fewer events per 1,000 person-years, averaging across the sample. Compared to the overall rate of 5.46 events per 1,000 person-years within the sample, the relative reduction is estimated to have been 32.9% (95% CI, -65.8 to 0.1). However, this association fails to achieve statistical signicance (P = 0.051). After adjusting for patient characteristics, the association was smaller in magnitude, with a relative reduction of 25.6% (95% CI, -47.4 to -3.8), but became signicant (P = 0.022). Quantifying the relative reduction at the individual level, the average reduction was 11.0% (95% CI, -20.4 to -1.6), because larger (absolute) reductions were concentrated among individuals at relatively high risk of hypoglycemic events. Figure 1 shows the predicted relationship between various quantities of verapamil lls and adverse outcomes in absolute terms. At the 25th percentile of verapamil use (7 lls), the rate is predicted to decrease with an additional verapamil ll from 4.83 (95% CI, 1.41 to 8.26) per 1,000 person-years to 4.47 (95% CI, 1.15 to 7.79), a 7.5% reduction in relative terms. At the median level of use (11 lls), the estimated rate would decrease with an additional verapamil ll from 3.71 (95% CI, 0.60 to 6.82) per 1,000 person-years to 3.53 (95% CI, 0.46 to 6.59), a smaller (5.0%) relative reduction. Predicted changes in hypoglycemic events with an extra verapamil ll are shown for various groups in Figure 2. The average change for the sample as a whole was -1.79 events per 1,000 person-years in the unadjusted analysis (as previously noted) and -1.40 (95% CI, -2.59 to -0.21) in the adjusted analysis. Distinguishing between young and old beneciaries (based on a median sample age of 74.5 years), the average predicted changes are statistically insignicant in both cases. Distinguishing between male and female, the average change is estimated to be positive for males (2.37 (95% CI, -3.02 to 7.76) per 1,000 person-years) and negative for females (-2.16 (95% CI, -3.40 to -0.93) per 1,000 person-years). The latter negative change for females is signicant; the change for males, however, is insignicant. Finally, the change for non-whites is negative and large in magnitude (-4.65 (95% CI, -6.87 to -2.43) per 1,000 person-years), and statistically signicant. 58 3.4 Conclusions We examined the association between verapamil use and serious hypoglycemic events, as measured by hospital admissions or ED visits for hypoglycemia, in a nationally representative sample of older Medicare beneciaries with newly diagnosed T1D. After adjusting for patient characteristics, we found that an additional 30-day-equivalent ll of verapamil beyond the median quantity during the 12-month exposure period was associated with a 5.0% reduction in the number of acute hospital admissions and ED visits during the 12-month follow-up period. This association was concentrated among female and non-white beneciaries. Existing evidence on the eects of verapamil in relation to the condition of diabetes provide signicant context to our ndings. Ovalle and colleagues explored the impact of verapamil on pancreatic cell function in a trial of 26 adults with newly diagnosed T1D and found preclinical and clinical evidence of cell preservation by downregulation of a key apoptotic pathway leading to suggested therapeutic applications (Ovalle et al., 2018). The chief proposed mechanism by which verapamil may reduce progression of T1D is the well described pathway thioredoxin-interacting protfoundein (TXNIP) (Lam and Cherney, 2018; Pepine et al., 2003; Minn et al., 2005). The importance of pancreatic cell preservation and residual insulin secretion after onset of T1D is described by the Diabetes Control and Complications Trial, nding improved glycemic control and decreased risk of complications, including hypoglycemia (Control et al., 1998). Retrospective cohort analysis on the association of verapamil and reduced incidence of type 2 diabetes in elderly patients has been performed by Yin and colleagues (Yin et al., 2017). In addition, Khodneva and colleagues found lower fasting blood glucose levels among people with diabetes who also used vera- pamil (Khodneva et al., 2016). Our analysis has elaborated on these ndings by showing a negative association between verapamil use after diagnosis of T1D and the subsequent occurrence of serious hypoglycemic events. Our study has limitations. First, some of the patients in our analyzed cohort could have ex- perienced onset of T1D before their Medicare enrollment, which would not be evidenced within the available data. The eect of this measurement error would be an underrepresentation of newly diagnosed cases in the analysis sample. To mitigate this concern, a 6-month washout period was employed in normal practice with similar retrospective analyses (Kim et al., 2015; Sohn et al., 2015; 59 Kreft et al., 2018). Second, verapamil use was measured using prescriptions lled in Medicare drug claims. This practice is common in retrospective cohort analyses but may have introduced the mea- surement error, resulting in attenuation bias in favor of a null nding of no association. Third, the association demonstrated here was not necessarily causal in nature. While \high" and \low" users of verapamil (based on median number of lls) were similar in demographics, high users had higher rates of some comorbidities, raising the possibility of unmeasured confounding. Fourth, while our ndings reinforce recent evidence from a small trial (26 individuals), our analysis sample was still limited in size (1,649 patients). Finally, these results may be specic to an older population and may not generalize to younger individuals. Despite these limitations, this study lls an important gap that is common in clinical research. In particular, this study uses a high-quality observational database to complement a small ran- domized trial. The ndings suggest that the use of verapamil by adults with new onset T1D may help to prevent serious adverse outcomes, consistent with a clinically plausible pathway through which disease progression could be slowed. This evidence is not suciently strong to drive clinical practice, and could be strengthened in various ways. In terms of observational analysis, we believe it would be worthwhile to identify and exploit physician-level variation in verapamil prescribing, and also to investigate individuals newly diagnosed with hypertension who do and do not use ver- apamil, in both cases with the objective of further mitigating the potential for confounding. Based on this kind of analysis and evidence, a larger clinical trial may prove to be warranted. 60 Table 3.1: Characteristics of study population 1) Characteristics Full sample Low 2) verapamil High users P value 3) (n=1,649) users (n=925) (n=724) Mean age 4) , years (SD) 74.5 (6.9) 74.6 (7.0) 74.5 (6.9) 0.85 Female, n(%) 1183 (71.7) 651 (70.4) 532 (73.5) 0.165 Non-Hispanic white , n(%) 1276 (77.4) 708 (76.5) 568 (78.5) 0.36 Comorbidities, n(%) Acquired Hypothyroidism 205 (12.4) 134 (14.5) 71 (9.8) 0.004 Acute Myocardial Infarction 21 (1.3) 17 (1.8) 4 (0.6) 0.021 Alzheimer's Disease 110 (6.7) 66 (7.1) 44 (6.1) 0.39 ADRD or Senile Dementia 240 (14.6) 145 (15.7) 95 (13.1) 0.145 Anemia 707 (42.9) 423 (45.7) 284 (39.2) 0.008 Asthma 191 (11.6) 124 (13.4) 67 (9.3) 0.009 Atrial Fibrillation 253 (15.3) 151 (16.3) 102 (14.1) 0.21 Benign Prostatic Hyperplasia 89 (5.4) 61 (6.6) 28 (3.9) 0.015 Breast Cancer 81 (4.9) 47 (5.1) 34 (4.7) 0.72 Cataract 423 (25.7) 238 (25.7) 185 (25.6) 0.94 Chronic Kidney Disease 498 (30.2) 315 (34.1) 183 (25.3) <0.001 COPD 373 (22.6) 248 (26.8) 125 (17.3) <0.001 Colorectal Cancer 22 (1.3) 15 (1.6) 7 (1.0) 0.25 Depression 320 (19.4) 196 (21.2) 124 (17.1) 0.039 Endometrial Cancer 5 (0.3) 4 (0.4) 1 (0.1) 0.28 Glaucoma 248 (15) 134 (14.5) 114 (15.7) 0.48 Heart Failure 546 (33.1) 349 (37.7) 197 (27.2) <0.001 Hip/Pelvic Fracture 28 (1.7) 21 (2.3) 7 (1.0) 0.042 Hyperlipidemia 1209 (73.3) 669 (72.3) 540 (74.6) 0.30 Ischemic Heart Disease 809 (49.1) 508 (54.9) 301 (41.6) <0.001 Lung Cancer 17 (1.0) 7 (0.8) 10 (1.4) 0.21 Osteoporosis 138 (8.4) 91 (9.8) 47 (6.5) 0.015 Prostate Cancer 53 (3.2) 35 (3.8) 18 (2.5) 0.138 Rheumatoid Arthritis / Osteoarthritis 698 (42.3) 400 (43.2) 298 (41.2) 0.40 Stroke / Transient Ischemic Attack 125 (7.6) 90 (9.7) 35 (4.8) <0.001 Mean dosage, milligrams (SD) 201.8 (1.4) 195.4 (1.9) 210.1 (1.9) <0.001 COPD = chronic obstructive pulmonary disease ADRD = Alzheimer?s Disease, Related Disorders 1 Values are numbers (percentages) unless stated otherwise. 2 \Low" corresponds to median number of 30-day-equivalent lls (11) or fewer. 3 For comparison between low- and high users of verapamil. 4 Age at diagnosis. 61 Table 3.2: Poisson regression results Variable Unadjusted Adjusted Constant -3.860*** -6.238** (0.731) (2.809) Fills -0.754* -0.585** (0.386) (0.255) Age -0.00759 (0.0502) Female 0.483 (1.322) Non-Hispanic White -0.121 (0.743) Observations 1,649 1,649 Pseudo R-squared 0.042 0.452 Estimation results of the comorbidities: See Table C.1. 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Yin, Ti, Shu-Chen Kuo, Yea-Yuan Chang, Yung-Tai Chen, and Kai-Wei Katherine Wang, \Verapamil use is associated with reduction of newly diagnosed diabetes mellitus," The Journal of Clinical Endocrinology & Metabolism, 2017, 102 (7), 2604{2610. Zeira, Joseph, \Innovations, patent races and endogenous growth," Journal of Economic Growth, 2011, 16 (2), 135{156. 75 Appendix A Appendix to Chapter 1 A.1 Proof of Proposition 1 Dene the left-hand side of (8) by G(xj ). Suppose that G(xj ) G(xj 0 ) holds for 0 and 6= 0 . Then, there must be at least one N such that w oligo N (xj ) w oligo N (xj 0 ) by quasi-concavity of E N for all N. To see this, pick an arbitrary N. Then, there must be at least one n equal to or less than N 1 such that the derivative of w oligo N (xj) with respect to n is non-positive: @w oligo N @ n = 1 n ( (n + 1)f(N 1)h +Rg f(Nn 1)h +Rg(Nh +R) n X k=0 1 (Nk)h +R ) 1 Nh n Y k=0 (Nk)h (Nk)h +R ! v 0 h 0 0 To make this hold, the term in the brace must be non-positive. (n + 1)f(N 1)h +Rg f(Nn 1)h +Rg(Nh +R) n X k=0 1 (Nk)h +R = n X k=0 ( 1 (Nn 1)h +R 1 h Nh +R ! 1 (Nk)h +R ) 0 However, this indicates that: n X k=1 n + 1k (Nk)h +R 0 holds. This contradicts to N 1n. Accordingly, the following holds: @G(xj) @ N > 0;8N where 1NM 1 Therefore, by quasi-concavity of E N for all N, the implicit function theorem indicates that: x ()>x ( 0 ) 76 holds for 0 and 6= 0 . 77 A.2 Proof of Proposition 2 Suppose not, i.e. if x x e , then 2M A [f g. Because of x x e and quasi-concavity of E N for all N, combining the left-hand sides of (8) and (13) at x e , we get: M X N=2 P N w oligo N (x e ) 0 This indicates that there is at least one N where 2NM inducing w oligo N 0. From (10), we know that such N must have at least one of n where 1 n N 1 satisfying n < (n + 1) 1 . This contradicts to 2M A [f g. 78 A.3 Proof of Proposition 3 Let x (;) and x e () denote the industry equilibrium and the socially optimal level given a pair (;). Also, P M N=2 P N w oligo N (x;;) means the expected marginal revenue in the oligopoly market for the given (;). Note that, for any 2 [0;r), P M N=2 P N w oligo N (x e ( ); ; )> 0 holds by proposition 2. Since P M N=2 P N w oligo N (x;;) is continuous on , there always exists ( )2f( 2 ( ); ; M ( ))j N ( ) 0;8N; and6= 0 for at least oneNg such that, for any ( ) ( ), M X N=2 P N w oligo N (x e ( );( ); ) 0 holds by proposition 1. For each , dene a set of such( ) byM D M D . Note thatM D cannot be a null set because every has at least one ( ) satisfying this equation. From (10), we know that P M N=2 P N w oligo N (x e ();;) diverges to negative innity in an extreme case where!r. However, since P M N=1 P N n w mono N +w oligo N o (x e ();;) is non-negative systemat- ically, there must be at least one high enough to make P M N=1 P N n w mono N +w oligo N o (x e ();;) = 0. Accordingly, since P M N=1 P N w mono N (x e ();;) is always positive by (9), M X N=2 P N w oligo N (x e ();( );)< 0 holds for a set of large enough, a subset of a's interval [ ;r). Then, since P M N=2 P N w oligo N (x;;) is continuous in (x;) where 2 [0;r), the intermediate value theorem guarantees the existence of ( )2 [ ;r) such that M X N=2 P N w oligo N (x e ( ( ));( ); ( )) = 0 79 is satised, and thus x (( ); ( )) =x e ( ( )) holds. Also, there is at least one sub-interval of a 's interval ( ( );r), denoted byP D , such that x (( );)<x e () holds: M X N=2 P N w oligo N (x e ();( );)< 0 for all 2P D . For each , for any2M D \ M D c , proposition 1 indicates that x (;)<x e () holds for, at least, all 2P D due to 0 and 6= 0 where 0 2M D . Therefore, for all 2 S M D , there is at least one such that x (;) = x e () holds and at least one 's interval in [min ( );r) such that x (;) < x e () holds. Also, for all 2M D \ S M D c , there is at least one's interval in [min ( );r) such thatx (;)<x e () holds, but no such that makes x (;) =x e (). 80 Appendix B Appendix to Chapter 2 Table B.1: Time windows for measuring the market share distribution and the future market size Windows for measuring Reference year 1 Windows for measuring future market size market share distribution Phase 3 Phase 2 Phase 1 Preclinical 1996{2005 2005 2009{2018 2011{2020 2013{2022 2015{2024 1997{2006 2006 2010{2019 2012{2022 2014{2023 2016{2025 1998{2007 2007 2011{2020 2013{2023 2015{2024 2017{2026 1999{2008 2008 2012{2021 2014{2024 2016{2025 2018{2027 2000{2009 2009 2013{2022 2015{2024 2017{2026 2019{2028 2001{2010 2010 2014{2023 2016{2025 2018{2027 2020{2029 2002{2011 2011 2015{2024 2017{2026 2019{2028 2021{2030 2003{2012 2012 2016{2025 2018{2027 2020{2029 2022{2031 2004{2013 2013 2017{2026 2019{2028 2021{2030 2023{2032 2005{2014 2014 2018{2027 2020{2029 2022{2031 2024{2033 2006{2015 2015 2019{2028 2021{2030 2023{2032 2025{2034 1 Year when R&D decisions are made. 81 Table B.2: List of therapeutic classes and groups in the study sample Therapeutic group Therapeutic class Number of Number of Number of drugs window-drugs window-classes 1 Alimentary/Metabolic Anorectic/Antiobesity 2 6 3 Antidiabetic 13 68 11 Antiemetic 2 4 2 Antiulcer 2 8 4 GI in ammatory/bowel disorders 2 10 5 Laxative 2 6 3 Stomatological 2 4 2 Anti-infective Antibacterial, other 2 16 8 Antibiotic, other 3 12 5 Antifungal 4 17 8 Antiviral, anti-HIV 19 95 11 Antiviral, other 11 44 11 Cephalosporin, oral 2 6 3 Quinolone antibacterial 5 21 8 Anticancer Anticancer, hormonal 3 5 2 Anticancer, other 2 2 1 Antiparasitic Protozoacide 2 12 6 Biotechnology Recombinant hormone 4 14 6 Blood and Clotting Antithrombotic, anticoagulant 4 14 6 Antithrombotic, other 2 6 3 Cardiovascular Antihypertensive, renin system 9 36 11 Hypolipaemic/Antiatherosclerotic 8 38 10 Dermatological Antipruritic/in amm, allergic 2 4 2 Genitourinary Female contraceptive 3 20 7 Male sexual dysfunction 3 19 8 Prostate disorders 3 16 7 Urological 10 57 11 Hormonal Hormone 2 4 2 Insulin 2 20 10 Musculoskeletal Antiarthritic, other 2 8 4 Osteoporosis treatment 4 13 5 Neurological Analgesic, NSAID 3 14 5 Antidepressant 5 25 11 Antiepileptic 8 41 11 Antimigraine 6 29 7 Antiparkinsonian 5 13 4 Antipsychotic 8 42 11 Cognition enhancer 4 18 6 Dependence treatment 2 16 8 Hypnotic/Sedative 3 24 10 Psychostimulant 3 16 7 Respiratory Antiallergic, non-asthma 4 13 6 Antiasthma 8 26 6 COPD treatment 2 6 3 Ophthalmological, antiglaucoma 5 15 5 Ophthalmological, other 2 6 3 Total 204 909 288 1 Referred to as markets. 82 Appendix C Appendix to Chapter 3 Figure C.1: CONSORT diagram 83 Figure C.2: Empirical cumulative density functions of the predicted probability of being a non-user, a low user, or a high user 84 Table C.1: Poisson regression results of comorbidities Variable Unadjusted Adjusted Acquired Hypothyroidism -17.225*** (0.667) Acute Myocardial Infarction -18.102*** (1.563) Alzheimer?s Disease 2.441*** (0.814) ADRD or Senile Dementia 0.068 (0.828) Anemia 1.741 (1.193) Asthma -14.229*** (0.925) Atrial Fibrillation 1.669 (1.041) Benign Prostatic Hyperplasia -13.699*** (2.087) Cataract 0.087 (0.978) Chronic Kidney Disease 1.528 (0.971) COPD -0.095 (1.020) Heart Failure -1.170 (1.093) Glaucoma -0.953 (0.800) Hip/Pelvic Fracture 0.669 (1.703) Ischemic Heart Disease -2.125*** (0.561) Depression -0.503 (1.001) Osteoporosis -0.007 (1.706) Rheumatoid Arthritis / Osteoarthritis 2.067* (1.136) Stroke / Transient Ischemic Attack 1.898*** (0.648) Breast Cancer -14.926*** (0.919) Colorectal Cancer -17.205*** (2.424) Prostate Cancer -20.423*** (1.930) Lung Cancer -16.738*** (1.696) Endometrial Cancer -20.267*** (1.832) COPD = chronic obstructive pulmonary disease. ADRD = Alzheimer?s Disease, Related Disorders. * signicant at 10%, ** signicant at 5%, *** signicant at 1%. 85
Abstract (if available)
Abstract
This dissertation comprises three essays in pharmaceutical and health economics. The first paper studies the structure of research and development (R&D) competition in an industry where hetero-geneous technologies with the same innovative contribution are patented and launched on the same market. In such industries, R&D competition does not end up with winner-takes-all as is implicitly assumed in the conventional theory of innovation investment. This paper suggests an alternative framework to incorporate such a market structure into R&D competition: the heterogeneous patent race. In this framework, the industry equilibrium of R&D increases as the higher market share is predicted for the early mover, i.e. the winner of the competition. Contrary to the conventional theory that necessarily results in overinvestment, R&D can be over- or underinvested depending on whether early mover advantage or disadvantage is expected. ❧ The second paper explores pharmaceutical R&D competition applying the heterogeneous patent race model. An empirical study of pharmaceutical expenditures and pipelines in 1996–2016 shows that the R&D effort, measured by the number of drugs in clinical trials, increases by 1.5%–2.0% in response to a 1% point increase in the expected market share of early movers. The estimated market share distribution suggests that in 14.2% of the therapeutic classes, too many resources were invested in clinical trials beginning between 2005 and 2015. ❧ The last paper performs a retrospective cohort study of fee-for-service Medicare beneficiaries with type 1 diabetes to determine whether the use of verapamil by persons with type 1 diabetes is associated with a lower risk of serious hypoglycemic events. It shows that an additional 30-day-equivalent fill of verapamil beyond the median quantity during the 12-month exposure period was associated with a 5.0% reduction in the number of acute hospital admissions and emergency department visits during the 12-month follow-up period. This evidence is consistent with the findings from a small trial of the effect of verapamil on pancreatic β cell survival in newly diagnosed adults.
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Kim, Jaehong
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Essays in pharmaceutical and health economics
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Health Economics
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2021-08
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