Robert H. Lyles
Department Biostatistics
Emory University
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 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 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 demonstrate prediction
methods yielding 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 considered. We evaluate the
techniques analytically and by simulation, and we illustrate them using
repeated measures data on fasting blood glucose from Type 2 diabetes
patients.
Key words: Classification, Constrained optimization, Prediction,
Squared-error loss
* Joint work with Amita K. Manatunga, Renée H. Moore, F. Dubois Bowman, and
Curtiss B. Cook
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