Bayesian methods for borrowing information in clinical drug development
von Burak Kürsad Günhan
Datum der mündl. Prüfung:2020-12-07
Betreuer:Prof. Dr. Tim Friede
Gutachter:Prof. Dr. Tim Friede
Gutachter:Prof. Dr. Thomas Kneib
EnglischClinical drug development is the process of investigating potential pharmaceutical therapies in clinical trials. The clinical investigation of drugs consists of four phases. The aim is bringing a candidate drug from early phase trials to a product approved for public use by the drug regulatory agencies. Clinical drug development is highly expensive and highly time consuming enterprise with very low probability of success. Thus, increasing the efficiency of clinical trials is critical, especially in the early phases of clinical drug development. One way to improve efficiency of the clinical trials is to utilize (or borrow) relevant information from external sources. Bayesian statistics is the mathematical procedure to update our prior distributions of the unknown parameters given the available data. The recursive nature of Bayesian statistics provides a promising framework for borrowing information. Another advantage of Bayesian statistics is to enable us to built more complicated models with the help of Markov chain Monte Carlo computation techniques. This helps to include, for instance, hierarchical structures in the model, when they are supported by the data. However, complicated models must be calibrated well, especially in the presence of sparse data, such as in early phase trials. The first aim of this dissertation is to investigate phase I trials involving multiple treatment schedules. A treatment schedule refers to a frequency of administration. There are two possible types of such trials: simultaneous and sequential investigations of multiple schedules. In a simultaneous design, doses and schedules are varied simultaneously in the same trial. In a sequential design, the information from a completed phase I design stage of a trial is used to inform a new phase I design stage with a different treatment schedule. To design and analyze both types of trials, I develop a Bayesian time-to-event pharmacokinetic (TITE-PK) model. The developed model uses PK principles to borrow information from different treatment schedules explicitly. Furthermore, TITE-PK makes use of an adapted escalation-with-overdose-control criterion to control the number of patients administered with overly toxic doses. For both types of investigations of multiple schedules, simulation results of TITE-PK yield desirable performance in terms of the common metrics such as the correct maximum tolerated dose declarations and the mean number of required patients in the trial. The second aim of this dissertation is to investigate phase II dose-finding trials involving multiple schedules, which is motivated by a phase II trial in atopic dermatitis. A common approach to estimate the dose-response function in such trials is pooling doses from different schedules after re-scaling them based on the frequency of administration. Recently, a partial pooling approach has been suggested, in which certain parameters are treated as schedule specific fixed-effects. As an alternative, I propose to use a Bayesian hierarchical model in which certain parameters are treated as random-effects, while others are assumed to be shared between schedules. Estimates of the dose-response function for each schedule are obtained by borrowing. In simulations, the proposed method yields better performance compared to complete pooling and partial pooling with fixed-effects in terms of the investigated metrics such as the mean absolute error and the mean coverage probability of interval estimates. I develop a publicly available R package, ModStan, to automate the implementation. The third aim of this dissertation is to study meta-analyses of few studies involving rare safety events. Meta-analysis is using statistical methods to combine multiple trials. Trials with no or very rare events, which can produce considerable bias in the estimation, are a major challenge. To overcome this, I suggest the use of a weakly informative prior (WIP) for the treatment effect parameter in a binomial-normal hierarchical model as a penalization technique. A WIP is constructed by assuming a normal prior with zero mean and an a priori interval for plausible values. Furthermore, the suggested WIP is verified empirically using the Cochrane Database of Systematic Reviews. The proposed method is assessed in simulations. It displays better or similar performance in terms of the accuracy of point estimates and the coverage probability of interval estimates compared to standard methods. The proposed method is illustrated by a meta-analysis dataset in pediatric transplantation. I implement the proposed method as a publicly available R package, MetaStan.
Keywords: Bayesian statistics, meta-analysis, phase I dose-escalation trials