Explicit Bayesian solution for incomplete pre-post test problems using inverse Bayes formulae

Abstract

Pre-Post test design is one of the commonly used designs in clinical trials where patients serve as their own control and the differentail effect of a treatment is assessed. The same scenario also arises in comparing pre-post test changes in either physiological variables or molecular or genetic targets. When missing data occurs due to either patients drop-out or some other unknown reasons, an important issue is how to best use the incomplete data to make inference. We develop an explicit Bayesian solution using noninformative priors on the parameters of interest assuming the data is missing at random. The explicit joint posterior is obtained via a noniterative sampling approach based on the inverse Bayes formulae (IBF) as opposed to the iterative sampling using Markov Chain Monte Carlo (MCMC) methods. Therefore, convergence diagnostics are no longer needed and analysis is greatly facilitated. We consider both the cases of a known and an unknown covariance matrix. The method is illustrated with an ongoing study of childhood sickle cell disease. Copyright © 2001 by Marcel Dekker, Inc.