A Nonlinear Model for Censored and Mis-Measured Time-Varying Covariates in Survival Models, with Applications in HIV/AIDS Studies

• Activity Number: 418 - From Survival Analysis to Survey Research
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Hongbin Zhang* and Lang Wu
• Companies: City University of New York, School of Public Health and University of British Columbia
• Keywords: Joint Model; Measurement Error; Nolinear covariate model; Censored covariate data

Abstract

In survival analysis, when time-dependent covariates are censored and mismeasured, a joint model is often considered. Typically, an empirical linear (mixed) model is assumed for the time-dependent covariates. Such an empirical linear covariate model may be inappropriate for the (unobserved) censored covariate values that may behave quite differently than the observed covariate process. In applications such as HIV/AIDS studies, a mechanistic nonlinear model can be derived for the covariate process based on the underlying data-generation mechanisms and nonlinear covariate model may provide better ``predictions" for the censored and mismeasured covariate values. We propose a joint Cox and nonlinear mixed effects model to model survival data with censored and mismeasured time-varying covariates. We use likelihood method for inference, implemented by the Monte Carlo EM algorithm. The models and methods are evaluated by simulations. An AIDS dataset is analyzed in details, where the time-dependent covariate is a viral load which may be censored due to a lower detection limit and measurement error. Some new insights are gained.