Analysis of the Cox Model with Longitudinal Covariates with Measurement Errors and Partly Interval Censored Failure Times, with Application to an AIDS Clinical Trial

Time-dependent covariates are often measured intermittently and with measurement errors. Motivated by the AIDS Clinical Trials Group (ACTG) 175 trial, this paper develops statistical inferences for the Cox model for partly interval censored failure times and longitudinal covariates with measurement errors. The conditional score methods developed for the Cox model with measurement errors and right censored data are no longer applicable to interval censored data. Assuming an additive measurement error model for a longitudinal covariate, we propose a nonparametric maximum likelihood estimation approach by deriving the measurement error induced hazard model that shows the attenuating effect of using the plug-in estimate for the true underlying longitudinal covariate. An EM algorithm is devised to facilitate maximum likelihood estimation that accounts for the partly interval censored failure times. The proposed methods can accommodate different numbers of replicates for different individuals and at different times. Simulation studies show that the proposed methods perform well with satisfactory finite-sample performances and that the naive methods ignoring measurement error or using the plug-in estimate can yield large biases. A hypothesis testing procedure for the measurement error model is proposed. The proposed methods are applied to the ACTG 175 trial to assess the associations of treatment arm and time-dependent CD4 cell count on the composite clinical endpoint of AIDS or death. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s12561-023-09372-y.