Joint modeling of longitudinal measurements and time -to -event data.

Abstract

Longitudinal studies in medical research often generate both repeated measurements of biomarkers and possibly censored survival data. Recently several joint models have been developed to deal with the challenges arising in this type of data. Commonly, in joint models, the longitudinal covariate is modeled by a linear mixed model. However, in some cases, the biomarker's time trajectory is not linear, such as the prostate-specific antigen (PSA) profile after radiation therapy for prostate cancer. We extend both the existing two-stage method and the joint likelihood based method to accommodate the non-linear longitudinal PSA trajectory semiparametrically with two types of regression splines. In Chapter 2, we propose two two-stage regression calibration approaches: risk set regression calibration and ordinary regression calibration. In both approaches, a semiparametric stochastic mixed model with smoothing splines is used to model the longitudinal data and a proportional hazards model is used to model the survival data. To improve the computation efficiency in joint modeling compared to an EM algorithm or the Bayesian approach, in Chapter 3 we propose an estimation procedure based on a penalized joint partial likelihood (PJL). The PJL is generated by a Laplace approximation of a joint likelihood and by using a partial likelihood instead of the full likelihood for the time-to-event data. In Chapter 4 we further propose a joint model using penalized cubic B-spline to accommodate the non-linear trajectory of longitudinal covariate measurements with estimation using the PJL method. Monte Carlo simulation and a case study of the association between the PSA profile and cancer recurrence in prostate cancer patients after radiation therapy demonstrate the effectiveness of these new approaches.