Effect of Categorizing a Continuous Covariate on the Comparison of Survival Time

Abstract The variance of the estimated hazard ratio between two groups when there is one categorized continuous gamma-distributed covariate is derived using exponential and Weibull regression models and asymptotic theory. Categorizing a continuous covariate increases the variance of the estimated hazard ratio and decreases the efficiency of the analysis. The efficiency of categorization is studied as a function of the strength of the relation between survival time and the covariate, the choice of cut points used in categorizing, and the number of categories. An application of the results to an advanced lung cancer clinical trial is given.