Graphing survival curve estimates for time-dependent covariates

Graphical representation of statistical results is often used to assist readers in the interpretation of the findings. This is especially true for survival analysis where there is an interest in explaining the patterns of survival over time for specific covariates. For fixed categorical covariates, such as a group membership indicator, Kaplan-Meier estimates (1958) can be used to display the curves. For time-dependent covariates this method may not be adequate. Simon and Makuch (1984) proposed a technique that evaluates the covariate status of the individuals remaining at risk at each event time. The method takes into account the change in an individual's covariate status over time. The survival computations are the same as the Kaplan-Meier method, in that the conditional survival estimates are the function of the ratio of the number of events to the number at risk at each event time. The difference between the two methods is that the individuals at risk within each level defined by the covariate is not fixed at time 0 in the Simon and Makuch method as it is with the Kaplan-Meier method. Examples of how the two methods can differ for time dependent covariates in Cox proportional hazards regression analysis are presented.