Goodness-of-fit tests for the Cox model via bootstrap method

Abstract

Global goodness-of-fit tests for the Cox model, in which no partitions of the time and covariate spaces into cells are needed, are established. Test statistics are based upon the cumulative hazard process under the censored survival data. Although this process converges to a Gaussian process almost surely, a problem arises from the fact that the asymptotic covariance structure depends upon the underlying distribution which is unspecified. Therefore, a bootstrap method suggested by Efron (1981) is employed. It can be shown that the bootstrapped cumulative hazard process converges weakly to the same Gaussian process. As an illustration, the proposed tests are applied to analyze the Stanford heart transplant data. Finally, a discussion for dealing with discrete covariate is given. © 1995.