Incorporating time-dependent covariates in the Cox proportional hazards model: The LVAR approach

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 need to be inferred from the observed values. In this dissertation, we consider an auto-correlated covariate process with random subject effect and measurement error and introduce the last value auto-regressed (LVAR) estimation method. We investigate the performance of this approach in different situations and compare it to several other established estimation approaches via a simulation study. The comparison shows this method results in a smaller mean square error over a large number of scenarios when considering the time-dependent covariate effect. A model selection procedure is also suggested to make LVAR approach more flexible. This approach is applied to a real problem involving Primary Biliary Cirrhosis data from the Mayo clinic. The application shows that LVAR results in stronger effects of log albumin and log prothromin time than several published methods.