Nonparametric estimation of risk tracking indices for longitudinal studies

Tracking a subject's risk factors or health status over time is an important objective in long-term epidemiological studies with repeated measurements. An important issue of time-trend tracking is to define appropriate statistical indices to quantitatively measure the tracking abilities of the targeted risk factors or health status over time. We present a number of local and global statistical tracking indices based on the rank-tracking probabilities, which are derived from the conditional distribution functions, and propose a class of kernel-based nonparametric estimation methods. Confidence intervals for the estimators of the tracking indices are constructed through a resampling subject bootstrap procedure. We demonstrate the application of the tracking indices using the body mass index and systolic blood pressure data from the Coronary Artery Risk Development in Young Adults (CARDIA) study. Statistical properties of the estimation methods and bootstrap inference are investigated through a simulation study and an asymptotic development.