Computational methods for Bayesian covariance structure modeling and multi-armed bandit-based design of clinical trials

Randomized controlled trials are often called the gold standard for comparison of a novel treatment to the current standard of care. However, a productivity crisis in the pharmaceutical industry has led people to reconsider the current standards, leading to the uptake of alternative designs and analysis methods. Potential solutions to the productivity crisis include combining multiple outcomes, Bayesian approaches, and adaptive designs. This thesis provides methodological contributions in these directions and considers Bayesian covariance structure modeling and multi-armed bandit-based response-adaptive clinical trials.

The first part of the thesis considers the development of Bayesian covariance structure models (BCSMs) and efficient inference methods for multi-way nested interval-censored survival data and balanced multi-way nested and crossed continuous data. The results show that BCSMs lead to a novel way of analyzing the data, and a more efficient and reliable analysis than commonly used multilevel random intercept models. The thesis furthermore compares methods for combining multiple outcomes, with special attention to patient-reported outcomes and patient-centric trials.

The second part of the thesis focuses on multi-armed bandit-based response-adaptive clinical trial designs. Multi-armed bandit algorithms target a certain objective (e.g., maximizing the sum of rewards) by sequentially sampling rewards from one of several distributions, trading off learning and earning. An often-mentioned application is clinical trials. However, partially due to problems with statistical inference, the implementation of multi-armed bandit-based clinical trials mostly limits itself to specific, suboptimal, designs. First, a general sampling-based approximation method to compute the Gittins index policy (having the potential to show very high expected treatment outcomes) for general models is introduced and evaluated, which is shown to yield a good approximation in standard and novel bandit settings. Second, a constrained Markov decision process approach is introduced to, e.g., construct response-adaptive procedures that maximize expected outcomes while controlling the Bayesian average power and type I error. Three applications, focusing on testing, estimation, and prior robustness, show the generality of this approach. Third, we develop and analyze exact tests for binary outcomes collected under a general response-adaptive design, where, contrary to known results for the fixed balanced design, a conditional exact test often yields highest power.