Comparing the Predictive Powers of Survival Models Using Harrell's C or Somers’ D

Abstract

Medical researchers frequently make statements that one model predicts survival better than another, and they are frequently challenged to provide rigorous statistical justification for those statements. Stata provides the estat concordance command to calculate the rank parameters Harrell's C and Somers’ D as measures of the ordinal predictive power of a model. However, no confidence limits or p-values are provided to compare the predictive power of distinct models. The somersd package, downloadable from Statistical Software Components, can provide such confidence intervals, but they should not be taken seriously if they are calculated in the dataset in which the model was fit. Methods are demonstrated for fitting alternative models to a training set of data, and then measuring and comparing their predictive powers by using out-of-sample prediction and somersd in a test set to produce statistically sensible confidence intervals and p-values for the differences between the predictive powers of different models.