Statistica Sinica 27 (2017), 1037-1057
Abstract: We consider the proportional hazards model with time-dependent covariates measured with error at informative observation times under shared random effects models. Although various approaches have been proposed to deal with measurement error for time-dependent covariates, very limited research has been done when the observation times are informative. We propose a new corrected score estimator that allows the observation times to depend on the survival time, the random effects, or other covariates. Compared to existing conditional score and corrected score approaches, it relaxes the requirement on non-informative observation times, may substantially improve the efficiency, and is much more robust to deviations from normality of the error. The performance of the estimator is evaluated via simulation studies and by application to data from an HIV clinical trial.
Key words and phrases: Conditional score, corrected score, informative observation times, joint modeling, measurement error.