Why not routinely use best linear unbiased predictors (BLUPS) as estimates of cholesterol, percent fat, and physical activity?

Stanek, E. J., Well, A. D., & Ockene, I.
Statistics in Medicine

Measures of biologic and behavioural variables on a patient often estimate longer term latent values, with the two connected by a simple response error model. For example, a subject's measured total cholesterol is an estimate (equal to the best linear unbiased estimate (BLUE)) of a subject's latent total cholesterol. With known (or estimated) variances, an alternative estimate is the best linear unbiased predictor (BLUP). We illustrate and discuss when the BLUE or BLUP will be a better estimate of a subject's latent value given a single measure on a subject, concluding that the BLUP estimator should be routinely used for total cholesterol and per cent kcal from fat, with a modified BLUP estimator used for large observed values of leisure time activity. Data from a large longitudinal study of seasonal variation in serum cholesterol forms the backdrop for the illustrations. Simulations which mimic the empirical and response error distributions are used to guide choice of an estimator. We use the simulations to describe criteria for estimator choice, to identify parameter ranges where BLUE or BLUP estimates are superior, and discuss key ideas that underlie the results.