Score based goodness -of -fit tests and the Cox proportional hazards mode

One of the most frequently used regression models for survival data was proposed by Sir David Cox in 1972, the proportional hazards (PH) model. Even though numerous goodness-of-fit tests have been proposed for the PH model, model assumptions are checked infrequently by researchers utilizing it (Andersen, 1991 and Concato et al. 1993). This might be due to the fact that most proposed test statistics require advanced programming skills or even simulations to calculate p-values.;In this research we provide results which make two overall goodness-of-fit test statistics that have been proposed for the PH model very accessible for applied researchers. One of these tests (called GB test) is developed by Gronnesby and Borgan (1996). We show (see also May and Hosmer, 1998) that the GB test statistic is equivalent to one derived by adding group indicator variables to the model and testing the hypothesis that the coefficients for the group indicator variables are zero via a score test. This test of adding group indicator variables to the model is also proposed by Parzen and Lipsitz (1999) who seem to have been unaware that their test statistic is equivalent to the Gronnesby and Borgan test statistic. The other test (called GBS test) is suggested by Parzen and Lipsitz (1999) as an extension to their (equivalently the GB) test statistic. For the GBS test we provide the details for calculation and implementation.;We show with a simulation study that the choice of the number of groups for the GB test is critical for the appropriateness of the approximating chi-square distribution. We propose a grouping strategy for which the approximating chi-square distribution seems appropriate. We show that for an adequate sample size and percent censoring both tests have reasonable power. Additionally, we present the details for a significant part of the proof of the asymptotic chi-square distribution of these test statistics.