Empirical constrained Bayes predictors accounting for non-detects among repeated measures

When the prediction of subject-specific random effects is of interest, constrained Bayes predictors (CB) have been shown to reduce the shrinkage of the widely accepted Bayes predictor while still maintaining desirable properties, such as optimizing mean-square error subsequent to matching the first two moments of the random effects of interest. However, occupational exposure and other epidemiologic (e.g. HIV) studies often present a further challenge because data may fall below the measuring instrument's limit of detection. Although methodology exists in the literature to compute Bayes estimates in the presence of non-detects (Bayes(ND)), CB methodology has not been proposed in this setting. By combining methodologies for computing CBs and Bayes(ND), we introduce two novel CBs that accommodate an arbitrary number of observable and non-detectable measurements per subject. Based on application to real data sets (e.g. occupational exposure, HIV RNA) and simulation studies, these CB predictors are markedly superior to the Bayes predictor and to alternative predictors computed using ad hoc methods in terms of meeting the goal of matching the first two moments of the true random effects distribution.