Hypothesis testing in Cox models when continuous covariates are dichotomized: bias analysis and bootstrap-based test

Hypothesis testing for the regression coefficient associated with a dichotomized continuous covariate in a Cox proportional hazards model has been considered in clinical research. Although most existing testing methods do not allow covariates, except for a dichotomized continuous covariate, they have generally been applied. Through an analytic bias analysis and a numerical study, we show that the current practice is not free from an inflated type I error and a loss of power. To overcome this limitation, we develop a bootstrap-based test that allows additional covariates and dichotomizes two-dimensional covariates into a binary variable. In addition, we develop an efficient algorithm to speed up the calculation of the proposed test statistic. Our numerical study demonstrates that the proposed bootstrap-based test maintains the type I error well at the nominal level and exhibits higher power than other methods, as well as that the proposed efficient algorithm reduces computational costs.