Improving Point Predictions of Random Effects for Subjects at High Risk: A Case Study

• Activity Number: 420
• Type: Contributed
• Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Robert H. Lyles*+ and Amita K. Manatunga and Renee H. Moore and F. DuBois Bowman
• Companies: Emory University and Emory University and Emory University and Emory University
• Keywords: Constrained optimization ; Prediction ; Shrinkage ; Squared-error loss

Abstract

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 predictions for subjects whose characteristic places them in a tail of the distribution. While it is known that the typical posterior mean predictor dominates others in terms of overall mean squared error of prediction (MSEP), its tendency to "overshink" has motivated research into alternatives geared toward other criteria. Here, we specifically target MSEP within a certain region (e.g., above a known cut-off for high risk), and we consider minimizing this quantity with and without placing constraints on overall MSEP efficiency. We use the normal-theory random intercept model to demonstrate a prediction method yielding markedly better performance for subjects in the specified region, given only a small and well-controlled concession of overall MSEP. The pros and cons of enforcing overall or regional prediction unbiasedness are also discussed. We evaluate the techniques analytically and by simulation, and we illustrate them with a biomedical example.