Bayesian nonparametrics for missing data in longitudinal clinical trials

Abstract

We discuss the problem of performing inference on a causal effect of interest, such as an intention-to-treat effect, in the context of longitudinal clinical trials with informatively missing data. Addressing this problem requires the modeling of infinite-dimensional nuisance parameters; modeling these nuisance parameters poorly can result in substantial bias in the original estimation problem. Additionally, the presence of informative (nonignorable) missingness results in effects of interest being unidentified in the absence of strong, unverifiable, assumptions.We argue that Bayesian nonparametric methods are natural in this setting because they (1) allow for flexible modeling and (2) allow for uncertainty in untestable assumptions to be taken into account through the use of informative priors elicited from subject matter experts. We further argue that a sensitivity analysis to assess the impact of unverifiable assumptions is essential. Flexible Bayesian approaches which incorporate the longitudinal structure of the data are presented in the context of categorical and continuous outcomes, and strategies for sensitivity analysis are discussed in both cases. The methods are illustrated on data from a clinical trial designed to assess the efficacy of treatments for acute Schizophrenia.