Improving point predictions of random effects for subjects at high risk.
The prediction of random effects corresponding to subject-specific characteristics (e.g. means or rates of change) can be very useful in medical and epidemiologic research. At times, one may be most interested in obtaining accurate and/or precise predictions for subjects whose characteristic places them in a tail of the distribution. While the typical posterior mean predictor dominates others in terms of overall mean squared error of prediction (MSEP), its tendency to 'overshrink' has motivated research into alternatives emphasizing other criteria. Here, we specifically target MSEP within a certain region (e.g. above a known cut-off for high risk or a specified percentile of the random effect distribution), and we consider minimizing this quantity with and without constraints on overall MSEP efficiency. We use the normal-theory random intercept model to derive prediction methods with potential to yield markedly better performance for subjects in the specified region, given a well-controlled and (if desired) modest concession of overall MSEP. Criteria geared toward classification as well as overall and regional prediction unbiasedness are also provided. We evaluate the proposed techniques and illustrate them using repeated measures data on fasting blood glucose from type 2 diabetes patients. A simulation study verifies that theoretical properties and relative performances of the proposed predictors are essentially maintained when calculating them in practice based on estimated mixed linear model parameters. Straightforward extensions to incorporate covariates and additional random effects are briefly outlined.