Correction of Retransformation Bias in Nonlinear Predictions on Longitudinal Data with Generalized Linear Mixed Models

Researchers often encounter discrete response data in longitudinal analysis. Generalized linear mixed models are generally applied to account for potential lack of independence inherent in longitudinally data. When parameter estimates are used to describe longitudinal processes, random effects, both between and within subjects, need to be retransformed in nonlinear predictions on the response data; otherwise, serious retransformation bias can arise to an unanticipated extent. This study attempts to go beyond existing work by developing a retransformation method deriving statistically robust longitudinal trajectory of nonlinear predictions. Variances of population-averaged nonlinear predictions are approximated by the delta method. The empirical illustration uses longitudinal data from the Asset and Health Dynamics among the Oldest Old study. Our analysis compares three sets of nonlinear predictions of death rate at six time points, from the retransformation method, the best linear unbiased predictor, and the fixed-effects approach, respectively. The results demonstrate that failure to retransform the random components in generalized linear mixed models results in severely biased nonlinear predictions, as well as much reduced standard error approximates.