Adjusting Survival Curves for Confounders: A Review and a New Method

When reporting results from survival analysis, investigators often present crude Kaplan-Meier survival curves and adjusted relative hazards from the Cox proportional hazards model. Occasionally, the investigators will also provide a graphical representation of adjusted survival curves based on regression estimates and the average covariate values in the study groups. In this paper, the authors review the limitations of this approach and examine alternative approaches to obtaining adjusted survival curves that have been proposed. Furthermore, a new method to obtain multivariate adjusted survival curves is described. This method is based on direct adjustment of the observed conditional probability of survival at the time of each event. When an unexposed group is used as a standard for adjusting an exposed group, the survival curve in the exposed group is adjusted to the covariate distribution among the unexposed at the time of the event. This method has the advantage over the average covariate method of allowing for the possibility that the adjusted survival curves differ in shape. The method can handle multiple fixed or time-dependent categorical covariates as well as left truncated data, and it allows for estimation of confidence intervals. The authors have written a macro in SAS language that produces the adjusted survival estimates and graphs. This macro is available on request and can be downloaded through the World Wide Web.