In applications such as human immunodeficiency virus–acquired immune deficiency syndrome studies, a mechanistic non‐linear model can be derived for the covariate process on the basis of the underlying data generation mechanisms and such a non‐linear covariate model may provide better ‘predictions’ for the censored and mis-measured covariate values. This study proposed a joint Cox and non‐linear mixed effect model to model survival data with censored and mis-measured time varying covariates. The study used likelihood methods for inference, implemented by the Monte Carlo EM algorithm. The models and methods are evaluated by simulations. An acquired immune deficiency syndrome data set is analyzed in detail, where the time‐dependent covariate is a viral load which may be censored because of a lower detection limit and may also be measured with errors. The results based on linear and non‐linear covariate models are compared and new insights are gained.
Citation: Zhang H, Wu L. A non‐linear model for censored and mismeasured time varying covariates in survival models, with applications in human immunodeficiency virus and acquired immune deficiency syndrome studies. J R Stat Soc C. 2018 Apr 29. doi:10.1111/rssc.12279. Link to Article>>