Complications in Clinical Trials: Bayesian Models for Repeated Measures and Simulators for Nonadherence

Ahmad Hakeem Bin Abdul Wahab, Purdue University

Abstract

Clinical trials are the gold standard for inferring the causal eects of treatments or interventions. This thesis is concerned with the development of methodologies for two problems in modern clinical trials. First is analyzing binary repeated measures in clinical trials using models that reflect the complicated autocorrelation patterns in the data, so as to obtain high power when inferring treatment eects. Second is simulating realistic outcomes and subject nonadherence in Phase III pharmaceutical clinical trials under the Tripartite Framework. Bayesian Models for Binary Repeated Data: The Bayesian General Logistic Autoregressive Model and the Polya-Gamma Logistic Autoregressive Model. Autoregressive processes in generalized linear mixed eects regression models are convenient for the analysis of clinical trials that have a moderate to large number of binary repeated measurements, collected across a fixed set of structured time points, for each subject. However, much of the existing literature and methods for autoregressive processes on repeated binary measurements permit only one order and only one autoregressive process in the model. This limits the flexibility of the resulting generalized linear mixed eects regression model to fully capture the dynamics in the data, which can result in decreased power for testing treatment eects. Nested autoregressive structures enable more holistic modeling of clinical trials that can lead to increased power for testing eects. We introduce the Bayesian General Logistic Autoregressive Model (BGLAM) for the analysis of repeated binary measures in clinical trials. This model extends previous Bayesian models for binary repeated measures by accommodating flexible and nested autoregressive processes with non-informative priors. We describe methods for selecting the order of the autoregressive process in BGLAM based on the Deviance Information Criterion (DIC) and marginal loglikelihood, and develop an importance sampling-weighted posterior predictive p-value to test for treatment eects in BGLAM. The frequentist properties of BGLAM compared to existing likelihood- and non-likelihood-based statistical models are evaluated by means of extensive simulation studies involving dierent data generation mechanisms. We apply our model for data collected from a clinical trial on the eects of Service Dogs for reducing PTSD symptoms of United States Veterans. Ultimately, on the basis of simulation studies and the real-life case study, we conclude that BGLAM provides a more eective and comprehensive approach for testing treatment eects in clinical trials with repeated binary measures and complex autoregressive patterns. Two features of BGLAM that can limit its practical application are the computational eort involved in executing it and the inability to integrate added heterogeneity across time in its autoregressive processes. We develop the Polya-Gamma Logistic Autoregressive Model (PGLAM) for addressing these limiting features. This new model enables the integration of additional layers of variability through random eects and heterogeneity across time in nested autoregressive processes. Furthermore, PGLAM is computationally more ecient than BGLAM because it eliminates the need to use the complex types of samplers for truncated latent variables that is involved in the Markov Chain Monte Carlo algorithm for BGLAM. We exhibit via additional, extensive simulation studies that the new features introduced by PGLAM do not adversely aect its frequentist properties in a significant manner.

Degree

Ph.D.

Advisors

Sabbaghi, Purdue University.

Subject Area

Animal sciences|Pharmaceutical sciences

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