A cautionary note on the use of the Grønnesby and Borgan goodness-of-fit test for the Cox proportional hazards model.

Grønnesby and Borgan (1996, Lifetime Data Analysis 2, 315-328) propose an omnibus goodness-of-fit test for the Cox proportional hazards model. The test is based on grouping the subjects by their estimated risk score and comparing the number of observed and a model based estimated number of expected events within each group. We show, using extensive simulations, that even for moderate sample sizes the choice of number of groups is critical for the test to attain the specified size. In light of these results we suggest a grouping strategy under which the test attains the correct size even for small samples. The power of the test statistic seems to be acceptable when compared to other goodness-of-fit tests.