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 for the presence of an extra random effect in the exponential part of the hazard function. Assumptions about the distribution of the random effects are not made; only the correlation matrix must be specified. This can be done on the basis of an existing division of individuals into groups, such as families, or on the basis of the distance between observed covariates. The variance of the test statistic is derived using a counting process approach. Corrections for the estimation of parameters are available. The test is demonstrated in a simulated data set as well as in a real data set on ovarian cancer.

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doi.org/10.2307/2533676, hdl.handle.net/1765/31861
Erasmus MC: University Medical Center Rotterdam

Verweij, P., van Houwelingen, H., & Stijnen, T. (1998). A goodness-of-fit test for Cox's proportional hazards model based on martingale residuals. Biometrics, 54(4), 1517–1526. doi:10.2307/2533676