A goodness-of-fit test for Cox's proportional hazards model based on martingale residuals

A goodness-of-fit test for Cox's proportional hazards model is proposed on the basis of martingale residuals. The test is derived as the score test fo r the presence of an extra random effect in the exponential part of the haz ard function. Assumptions about the distribution of the random effects are not made; only the correlation matrix must be specified. This can be done o n the basis of an existing division of individuals into groups, such as fam ilies, or on the basis of the distance between observed covariates. The var iance of the test statistic is derived using a counting process approach. C orrections for the estimation of parameters are available. The test is demo nstrated in a simulated data set as well as in a real data set on ovarian c ancer.