Goodness-of-fit criteria for survival data

The definition of an appropriate measure for goodness-of-fit in case of survival data comparable to R^2 in linear regression is difficult due to censored observations. In this paper, a variety of answers based on different residuals and variance of survival curves are presented together with a newly introduced criterion. In univariate simulation studies, the presented criteria are examined with respect to their dependence on the value of the coefficient associated with the covariate; underlying covariate distribution and censoring percentage in the data. Investigation of the relations between the values of the different criteria indicates strong dependencies, although the absolute values show high discrepancies and the criteria building processes differ substantially