Prediction of random effects when data are subject to a detection limit

When the prediction of subject-specific random effects is of interest, constrained Bayes predictors have been shown to reduce the shrinkage of the Bayes predictor while maintaining favorable properties such as minimal bias, reasonable mean square error of prediction, and matching the first two moments of the distribution of the random effects of interest. However, occupational exposure and HIV epidemiologic studies present a unique challenge in obtaining predictions of subject-specific random effects because the data are often subject to a limit of detection.; This dissertation work combines general methods found in the literature for computing constrained Bayes estimates with methods for computing Bayes estimates in the presence of non-detects. The resulting constrained Bayes predictors allow us to provide subject-specific estimates of mean occupational dust exposure for a group of animal feed mill workers and estimated predictions of intercepts and slopes of HIV RNA levels pertaining to individuals in a HIV cohort study. We also present results from simulation studies that compare the constrained Bayes predictors with the Bayes predictor and with ad hoc predictors found in the literature describing longitudinal studies with non-detectable values. In addition, we develop a constrained Bayes predictor that enables us to predict the HIV RNA levels of infants at the time each infant reached Class A HIV Status, as defined by the Centers for Disease Control and Prevention. We also use simulation studies to evaluate the performance of this proposed constrained Bayes predictor.; Finally, we provide an evaluation of predictors as a diagnostic tool for classifying subjects in the presence of non-detects. We begin with a proof showing that in the random intercept only model with no censoring, the Bayes predictor is optimal for minimizing the overall misclassification probability. Through analogous arguments and simulation studies, we show this result also holds in the presence of non-detects. We show that the constrained Bayes predictor offers an appealing compromise in terms of sensitivity and specificity when classifying individuals' true mean exposure relative to a threshold.