A simple test for the absence of covariate dependence in duration models

This paper describes a simple extension of popular tests of equality of hazard rates in a two-sample or k-sample setup to a situation where the covariate under study is continuous. In other words, we test the null hypothesis that the hazard does not depend on the value of the covariate against the omnibus alternative, where the covariate is continuous. The tests developed are also useful in detecting trend in the underlying hazard rates (i.e., when the alternative hypothesis postulates that the hazard function is increasing or decreasing in the value of the covariate, for all durations) or changepoint trend alternatives (where the hazard function increases in covariate value over one range of the covariate space, and decreases over another). Asymptotic distributions of the test statistics are established using counting process techniques. Small sample properties of the tests are studied, and the use of the tests in empirical applications is illustrated.