Techniques for comparing efficacy and cost-effectiveness of cancer therapies, and improved inference tools

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Georgieva, Mina
Vidakovic, Brani
Haaland, Benjamin
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This thesis focuses on two separate topics, one lying at the intersection of health care and statistics, and the other one rising from classical statistical inference. Chapters 2 through 4 address the first topic. They explore and improve techniques for comparing both efficacy and cost-effectiveness of cancer therapies. Chapter 5 focuses on the second topic. It proposes a new estimator for the number of binomial experiments when the success probability is unknown. Chapter 2 of my thesis establishes an overall ranking of efficacy of possible interventions in patients with advanced or metastatic melanoma within a Bayesian setting. Currently, chemotherapy is established as the standard of care for melanoma, but is often associated with poor responses and short survival. However, recent groundbreaking discoveries in tumor biology and immune surveillance have yielded effective molecularly targeted therapies and immune agents. These new treatments have changed the therapeutic scenario to a completely new reality of high response rates, prolonged disease control, and the possibility of talking of a cure for some patients. These positive results have opened new avenues in the treatment of melanoma patients and, as expected, added layers of complexity to management of those patients. We perform a network meta-analysis in a hierarchical Bayesian random-effects model to assess the role of immunotherapies and targeted therapies. We also evaluate the impact of immunotherapy biomarkers within a hierarchical Bayesian setting with a view to support and improve the therapeutic decision-making process. Chapter 3 evaluates indirectly the effectiveness of two treatments for advanced castration-resistant prostate cancer (CRPC). Prostate cancer is the most commonly diagnosed cancer. It eventually progresses to CRPC. CRPC is one of the leading cause of cancer-related deaths among men in developed countries. Two novel androgen receptor pathway inhibitors, abiraterone acetate and enzalutamide, have recently become available. They have been developed with the aim of prolonging survival, minimizing complications, and maintaining or improving quality of life in patients with advanced or metastatic CRPC. However, these two treatment options have not been compared head to head against each other in a prospective randomized fashion. In order to choose the optimal treatment and the optimal sequencing of treatments, we perform two analyses. The first one is a comparative effectiveness study within a Bayesian hierarchical setting. The second one is a sequencing assessment of treatments in the context of exponential survival models, informed by Bayesian meta-analyses with between and within study variance components. Chapter 4 proposes an improved methodology for conducting both meta-analysis and secondary data analyses based on randomized controlled trials. One of the deficiencies inherent to traditional methodology is the lack of individual patient-level data which serves as a basic ingredient for secondary analyses. This shortcoming is handled by recovering the raw time-to-event data through the inverted Kaplan-Meier equations and simulations. The recovered survival distributions are then modeled within a Bayesian semi-parametric framework. We use a hierarchical Dirichlet Process to model discrete-time event probabilities across the time-line up to last follow-up, and a truncated Weibull model to model the tail of the distribution. This approach avoids assumption about the shape of the survival distributions up to the last follow-up time, allows incorporation of censored data, and accommodates study-to-study heterogeneity. The parametric nature of the Weibull model on the other hand is well suited to making inferences about the survival curve in the absence of data. Finally, patient-level disease trajectories are modeled using a Bayesian Markov model. We demonstrate this methodology using simulations and a study on advanced non-small cell lung cancer. Finally, Chapter 5 presents a new approach to the binomial n problem, which concerns the estimation of the number of binomial experiments when the success probability is unknown. Some real-life situations, where the problem arises, include the estimation of the number of unreported crimes as well as the number of undetected software errors. Due to its inherent instability, the problem remains fundamentally difficult. Furthermore, neither one of the two parameters of the binomial distribution are unbiasedly estimable when both are unknown. We present an efficient method of estimating the number of trials using a beta-binomial MLE approach. In the absence of replications, when inference about the parameter of interest is not possible, we present a Bayesian approach applied in the context of contingency tables.
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