Canadian Journal of Statistics

Using categorical markers as auxiliary variables in log‐rank tests and hazard ratio estimation

Journal Article


Markers, which are prognostic longitudinal variables, can be used to replace some of the information lost due to right censoring. They may also be used to remove or reduce bias due to informative censoring. In this paper, the authors propose novel methods for using markers to increase the efficiency of log‐rank tests and hazard ratio estimation, as well as parametric estimation. They propose a «plug‐in» methodology that consists of writing the test statistic or estimate of interest as a functional of Kaplan–Meier estimators. The latter are then replaced by an efficient estimator of the survival curve that incorporates information from markers. Using simulations, the authors show that the resulting estimators and tests can be up to 30% more efficient than the usual procedures, provided that the marker is highly prognostic and that the frequency of censoring is high.

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