Bayesian models for unmeasured confounder in the analysis of time-to-event data.

Observational studies that omit confounders are subject to bias. In this dissertation we consider the specific case of time-to-event data. We also provide both the Bayesian parametric and the semi-parametric “twin regression” approaches with distributional assumptions of an unmeasured confounding variable, and then we compare them with the naive model. This assumes we ignore the effect of the unmeasured confounder. To explore the ability of bias adjustment from different sources of information, we offer a Bayesian parametric regression with a normal unmeasured confounder. We also develop a Bayesian semi-parametric proportional hazards model accounting for unmeasured confoundings with binary and normal distributions. We can see that the approaches adequately decrease the bias, even with a small validation size. Furthermore, we offer a novel Bayesian bias adjustment model when only summary statistics are available in the external validation data. Finally, we discuss and obtain several sets of solutions for different sources of validation data, censoring rates and sample sizes through simulation studies.