Bayesian Approaches for Instrumental Variable Analysis with Censored Time-to-Event Outcome
The method of instrumental variable (IV) analysis has been widely used in economics, epidemiology, and other fields to estimate the causal effects of intermediate covariates on outcomes, in the presence of unobserved confounders and/or measurement errors in covariates. Consistent estimation of the effect has been developed when the outcome is continuous, while methods for binary outcome produce inconsistent estimation. In this dissertation, we examine two IV methods in the literature for binary outcome and show the bias in parameter estimate by a simulation study. The identifiability problem of IV analysis with binary outcome is discussed. Moreover, IV methods for time-to-event outcome with censored data remain underdeveloped. We propose two Bayesian approaches for IV analysis with censored time-to-event outcome by using a two-stage linear model: One is a parametric Bayesian model with normal and non-normal elliptically contoured error distributions, and the other is a semiparametric Bayesian model with Dirichlet process mixtures for the random errors, in order to relax the parametric assumptions and address heterogeneous clustering problems. Markov Chain Monte Carlo sampling methods are developed for both parametric and semiparametric Bayesian models to estimate the endogenous parameter. Performance of our methods is examined by simulation studies. Both methods largely reduce bias in estimation and greatly improve coverage probability of the endogenous parameter, compared to the regular method where the unobserved confounders and/or measurement errors are ignored. We illustrate our methods on the Women's Health Initiative Observational Study and the Atherosclerosis Risk in Communities Study.