Binomial and Poisson regression with misclassified outcomes and binary covariates : a Bayesian approach.

Misclassification of an outcome and/or covariate is present in many regression applications due to the inability to have a "gold standard''. Therefore, fallible measurement methods are used when infallible tests are unavailable or too expensive. Ignoring misclassification results in biased regression estimates that can ultimately lead to an incorrect conclusion. In this dissertation we present a Bayesian approach to sample size determination for multilevel logistic regression models with misclassified outcomes to correct for the bias in the regression coefficients in order to obtain a more accurate sample size estimate. We explore a situation in which we only have one fallible test and also a situation in which we have two independent fallible tests. Further, we examine the influence of prior information on the posterior estimates of the coefficients for both of these situations. Secondly, we consider a multilevel generalized linear regression model for a Poisson response with a misclassified binary covariate. We again consider the situations in which one fallible test and two independent fallible tests are available to model the misclassified binary covariate. We conclude this section with a case study examining an India National health survey inspecting if being raised in a household with spousal abuse significantly impacts the number of children the child exposed has in their lifetime. Finally, the new FDA guidelines are requiring pharmaceutical companies to periodically monitor adverse events that are deemed ``anticipated'' throughout the life of a clinical trial. The event is only reported to the FDA before conclusion of the trial if it is determined that the rate of occurrence of the event is considerably higher than expected. We construct a two step Bayesian procedure to model the anticipated adverse events during a clinical trial that utilizes prior information to make a more informed decision. In the first step, for a blinded trial, the information remains blinded and is only unblinded (second step) when the overall rate of occurrence of the event is higher than a historical rate. In contrast to widely used methods, our proposed method controls for the Type I error rate and power.