Incorporating time-dependent covariates in survival analysis using the LVAR method

In survival analysis, use of the Cox proportional hazards model requires knowledge of all covariates under consideration at every failure time. Since failure times rarely coincide with observation times, time-dependent covariates (covariates that vary over time) need to be inferred from the observed values. In this paper, we introduce the last value auto-regressed (LVAR) estimation method and compare it to several other established estimation approaches via a simulation study. The comparison shows that under several time-dependent covariate processes this method results in a smaller mean square error when considering the time-dependent covariate effect.