Time‐Varying Functional Regression for Predicting Remaining Lifetime Distributions from Longitudinal Trajectories

Summary A recurring objective in longitudinal studies on aging and longevity has been the investigation of the relationship between age‐at‐death and current values of a longitudinal covariate trajectory that quantifies reproductive or other behavioral activity. We propose a novel technique for predicting age‐at‐death distributions for situations where an entire covariate history is included in the predictor. The predictor trajectories up to current time are represented by time‐varying functional principal component scores, which are continuously updated as time progresses and are considered to be time‐varying predictor variables that are entered into a class of time‐varying functional regression models that we propose. We demonstrate for biodemographic data how these methods can be applied to obtain predictions for age‐at‐death and estimates of remaining lifetime distributions, including estimates of quantiles and of prediction intervals for remaining lifetime. Estimates and predictions are obtained for individual subjects, based on their observed behavioral trajectories, and include a dimension‐reduction step that is implemented by projecting on a single index. The proposed techniques are illustrated with data on longitudinal daily egg‐laying for female medflies, predicting remaining lifetime and age‐at‐death distributions from individual event histories observed up to current time.