Bayesian approaches to medical studies under limited information

Medical studies aim to generate the best possible evidence to properly guide decision making. But often, there are limitations to the amount of information that can be gathered. An obvious and common limitation is the sample size, which particularly in rare diseases, such as in oncology and pediatrics, poses strong issues to the decision making process because the statistical inference is associated with large uncertainty. But even large sample sizes can be limited in information if essential parameters of the statistical model cannot be informed by the data. This thesis consists of three thesis projects, each of which approaches a specific problem in medical studies. In each project, the Bayesian approach is used for inference, which requires the specification of prior distributions to express the information available prior to seeing the data. The first project deals with the problem of dose-finding in pediatric oncological patients, which is an area where often only extremely small sample sizes are feasible. The Bayesian approach allows to express information from a preceding dose-finding trial in adults in an informative prior (“borrowing”). My coauthors and me demonstrate how this can be done in a formal statistical way and propose robust methods. In a simulation study, the proposed trial designs show acceptable operating characteristics even under extreme sample size restrictions. In the second thesis project, my coauthors and me develop two novel methods which predict the outcomes of patients in order to decide whether a single-arm phase II trials should be stopped for futility. Both methods avoid the risk of a long interruption at interim, as can happen with the standard approach, and do not require making strong assumptions about short-term endpoint, which is required by a recent approach. One method uses the Bayesian approach, the other is a likelihood-based approach. In a simulation study, we show the improved performance of the new methods over the existing approach in a number of relevant scenarios with slow patient recruitment. In the third thesis project, my coauthors and me demonstrate how a prevalence can be correctly estimated if the diagnostic accuracy in the study is imperfect and unknown. We show that a previous analysis in the field of depression was strongly biased and arrived at much too precise estimates. By expressing information about the diagnostic accuracy from another study in form of informative priors, we provide improved estimates. In this thesis, I present statistical solutions to three different medical applications with specific challenges for inference and decision making, which result from a strong limitation of information. For each, I show how Bayesian approaches can be used to improve inference and hence better guide decision making.