Rank Tests and a One-Sample Logrank Test for Comparing Observed Survival Data to a Standard Population

For Cox's proportional hazards model, test procedures are described for the comparison of randomly right-censored observed and expected (standard population) survival data. It is observed that the class of linear rank tests proposed by Prentice (1978, Biometrika 65, 167-179) may be employed to test regression hypotheses in this one-sample setting. In order to compare globally the observed and expected survival data the one-sample limit of Mantel's logrank test is formally derived. The statistic derived is identical to one proposed from a diflerent viewpoint by Breslow (1975, Intemational Statistical Review 43, 45-58). Throughout it is assumed that the standard population survival function is a continuous function of time and that the survival or censoring time for each study-sample individual is exact and is not grouped into categories.