Semiparametric Modeling of Longitudinal Measurements and Time-to-Event Data-A Two-Stage Regression Calibration Approach

• Published in: Biometrics Vol. 64; no. 4; pp. 1238 - 1246
• Main Authors: Ye, Wen, Lin, Xihong, Taylor, Jeremy M.G
• Format: Journal Article
• Language: English
• Published: Malden, USA Blackwell Publishing Inc 01.12.2008; Blackwell Publishing Ltd
• Subjects: Biomarkers; biometry; Biometry - methods; Biostatistics; data collection; Humans; Joint modeling; Longitudinal data; Longitudinal Studies; Male; Proportional Hazards Models; Prostate-Specific Antigen; prostatic neoplasms; Prostatic Neoplasms - mortality; Prostatic Neoplasms - pathology; Recurrence; Regression Analysis; risk; Semiparametric mixed models; Smoothing splines; Statistical methods; statistical models; stochastic processes; Survival Analysis; Time
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/j.1541-0420.2007.00983.x

In this article we investigate regression calibration methods to jointly model longitudinal and survival data using a semiparametric longitudinal model and a proportional hazards model. In the longitudinal model, a biomarker is assumed to follow a semiparametric mixed model where covariate effects are modeled parametrically and subject-specific time profiles are modeled nonparametrially using a population smoothing spline and subject-specific random stochastic processes. The Cox model is assumed for survival data by including both the current measure and the rate of change of the underlying longitudinal trajectories as covariates, as motivated by a prostate cancer study application. We develop a two-stage semiparametric regression calibration (RC) method. Two variations of the RC method are considered, risk set regression calibration and a computationally simpler ordinary regression calibration. Simulation results show that the two-stage RC approach performs well in practice and effectively corrects the bias from the naive method. We apply the proposed methods to the analysis of a dataset for evaluating the effects of the longitudinal biomarker PSA on the recurrence of prostate cancer.