Abstract: The rank-tracking probability (RTP) is a useful statistical index for measuring the "tracking ability" of longitudinal disease risk factors in biomedical studies. A flexible nonparametric method for estimating the RTP is the two-step unstructured kernel smoothing estimator, which can be applied when there are time-invariant and categorical covariates. We propose a dynamic copula-based smoothing method for estimating the RTP, and show that it is both theoretically and practically superior to the unstructured smoothing method. We derive the asymptotic mean squared errors of the copula-based kernel smoothing estimators, and use a simulation study to show that the proposed method has smaller empirical mean squared errors than those of the unstructured smoothing method. We apply the proposed estimation method to a longitudinal epidemiological study and show that it leads to clinically meaningful findings in biomedical applications.

Key words and phrases: Dynamic copula model, longitudinal study, rank-tracking probability, risk factor, two-step smoothing, unstructured smoothing.