A transformation model for two survival curves: An empirical process approach

Abstract

SUMMARY A new transformation model for two survival curves with possibly nonproportional hazards is presented. The model assumes the existence of an unknown transformation of the survival curves into Weibull distributions with different shape parameters. The partial likelihood approach fails in the model. A new method of estimation called the empirical process approach is proposed. This approach is based on the strong approximation of the Kaplan-Meier product-limit estimators and associated quantile functions. Asymptotic normality of the generalised least squares estimator derived from the approach is discussed. A readily defined Wald test is an alternative to the log-rank test. From the empirical process approach, a Pearson's x2 goodness-of-fit test of the transformation model assumption can also be derived, giving a new test for the proportionality of hazard functions. The model can be applied for K-sample problems as well.