A global goodness-of-fit statistic for Cox regression models.

*(English)*Zbl 1059.62609Summary: A global goodness-of-fit test statistic for a Cox regression model, which has an approximate chi-squared distribution when the model has been correctly specified, is proposed. Our goodness-of-fit statistic is global and has power to detect if interactions or higher order powers of covariates in the model are needed. The proposed statistic is similar to the D. W. Hosmer and S. Lemeshow [Commun. Stat., Theory Methods A9, 1043-1069 (1980; Zbl 0447.62025)] goodness-of-fit statistic for binary data as well as D. Schoenfeld’s [Biometrika 67, 145–153 (1980; Zbl 0446.62039)] statistic for the Cox model. The methods are illustrated using data from a Mayo Clinic trial in primary billiary cirrhosis of the liver [T. R. Fleming and D. P. Harrington, Counting processes and survival analysis (1991; Zbl 0727.62096)] in which the outcome is the time until liver transplantation or death. The are 17 possible covariates. Two Cox proportional hazards models are fit to the data, and the proposed goodness-of-fit statistic is applied to the fitted models.