Renwen Luo (Beijing Normal-Hong Kong Baptist University ) – Modelling biomarker trajectory and variability in joint analysis of longitudinal and time-to-event data

The role of visit-to-visit variability of a biomarker in predicting related disease has been recognized in medical science. Existing measures of biological variability are criticized for being entangled with random variability resulted from measurement error or being unreliable due to limited measurements per individual. In this article, we propose two new measures to quantify the biological variability of a biomarker by evaluating the curvature of the biomarker trajectory behind longitudinal measurements. Given a mixed-effects model for longitudinal data with the mean function over time specified by cubic splines or a semiparametric multiplicative model, a Cox model is assumed for time-to-event data by incorporating the defined variability as well as the current level of the underlying longitudinal trajectory as covariates, which, together with the longitudinal model, constitutes the joint modeling framework in this talk. Estimation algorithm based on the EM algorithm or estimating equation is discussed. Simulation studies are conducted to reveal the advantage of the proposed method. To assess whether the variabiliy of the systolic blood pressure is predictive of cardiovascular events, the proposed method is applied to data from the Medical Research Council ( MRC ) Elderly Trial and the Atherosclerosis Risk in Communities ( ARIC ) study.