Semiparametric Modeling of Biomarker Trajectory and Variability With Correlated Measurement Errors

Renwen Luo, Chuoxin Ma, Jianxin Pan

Abstract: The prognostic significance of biomarker variability in predicting associated disease risk is well-established. However, prevailing methods that assess the relationship between biomarker variability and time to event often overlook within-subject correlation in longitudinal measurement errors, resulting in biased parameter estimates and erroneous statistical inference. Additionally, these methods typically assume that biomarker trajectory can be represented as a linear combination of spline basis functions with normally distributed random effects. This not only leads to significant computational demands due to the necessity of high-dimensional integration over the random effects but also limits the applicability because of the normality restriction imposed on the random effects. This paper addresses these limitations by incorporating correlated longitudinal measurement errors and proposing a novel semiparametric multiplicative random effects model. This model does not assume normality for the random effects and eliminates the need for integration with respect to them. The biomarker variability is incorporated as a covariate within a Cox model for time-to-event data, thus facilitating a joint modeling strategy. We demonstrate the asymptotic properties of the proposed estimators and validate their performance through simulation studies. The methodology is applied to assess the impact of systolic blood pressure variability on cardiovascular mortality using data from the Atherosclerosis Risk in Communities study.