METHOD OF SIEVES TO JOINTLY MODEL SURVIVAL AND LONGITUDINAL DATA

In biomedical studies, longitudinal covariates are often used to monitor the progress of a disease as well as survival time. However, a sparse covariate history, possibly in combination with measurement error, adds complications to the survival analysis. Moreover, marginal analysis of the longitudinal covariates may incur biases due to informative dropout of the longitudinal processes when death is the endpoint for survival time. Joint modeling of survival and longitudinal data can gain information from both components, and has proved as an effective way to model their relationship. A common approach is the semiparametric joint likelihood approach of Wulfsohn and Tsiatis (1997). However, it suffers from computational instability due to the large number of parameters involved in the likelihood and difficulties with standard error estimation. In this article, we propose the method of sieves and establish asymptotic consistency and the rate of convergence of the resulting sieve maximum-likelihood estimate (SMLE), including the estimate for the baseline hazard function. Results from numerical studies support this approach. The proposed SMLE is applied to a liver cirrhosis study for further illustration.