Abstract: Tracking subjects with disease risks at multiple time points is an important objective for disease prevention and preventive medicine. Appropriate statistical tracking models are essential for identifying risk factors that remain persistent over time and the early detection of subjects with high disease risks. Because disease risks are often defined by multivariate response variables, we propose a class of bivariate risk-predictive probability models that quantify the likelihood of an individual's future disease risk. These models describe the relationships between bivariate risk outcomes at a later time point and covariates at an early time point using a class of conditional quantile-based joint distribution functions. We develop a simulation-based procedure under the stratified bivariate time-varying quantile regression framework to estimate the conditional joint distributions and risk-predictive probabilities. In addition, we use theoretical and simulation studies to show that the estimation procedure yields consistent estimates, and propose a statistical quantity that measures the relative risk to identify high-risk individuals. Finally, we apply the proposed models and procedures to data from the National Growth and Health Study to identify early adolescent girls who are more likely to be diagnosed with hypertension at late adolescence.

Key words and phrases: Bivariate longitudinal outcome, conditional joint distributions, nonparametric regression, quantile regression, time-varying coefficients.