Logistic regression with misclassified response and covariate measurement error: a Bayesian approach.

In a variety of regression applications, measurement problems are unavoidable because infallible measurement tools may be expensive or unavailable. When modeling the relationship between a response variable and covariates, we must account for the uncertainty that is inherently introduced when one or both of these variables are measured with error. In this dissertation, we explore the consequences of and remedies for imperfect measurements. We consider a Bayesian analysis for modeling a binary outcome that is subject to misclassification. We investigate the use of informative conditional means priors for the regression coefficients. Additionally, we incorporate random effects into the model to accommodate correlated responses. Markov chain Monte Carlo methods are utilized to perform the necessary computations. We use the deviance information criterion to aid in model selection. Next, we consider data where measurements are flawed for both the response and explanatory variables. Our interest is in the case of a misclassified dichotomous response and a continuous covariate that is unobservable, but where measurements are available on its surrogate. A logistic regression model is developed to incorporate the measurement error in the covariate as well as the misclassification in the response. The methods developed are illustrated through an example. Results from a simulation experiment are provided illustrating advantages of the approach. Finally, we expand this model to incorporate random effects, resulting in a generalized linear mixed model for a misclassified response and covariate measurement error. We demonstrate the use of this model using a simulated data set.