Non-parametric estimators of hazard ratios for comparing two survival curves

We propose non-parametric estimators of the hazard ratio for comparing two survival curves using estimating equations defined in terms of group-specific cumulative hazard functions. We first describe the methods and their asymptotic properties in the case of a constant hazard ratio. We then extend the methods and the asymptotic results when the hazard ratio is time dependent and well approximated by a locally constant function. We propose a method to select the change points in the local hazard ratios. We extend the methods to stratified estimators and propose tests for heterogeneity of constant and time-dependent hazard ratios across strata. In a simulation study, we describe the finite sample properties of the proposed estimators and compare their performance with the Cox partial maximum likelihood estimator (MLE) in terms of efficiency and accuracy of coverage rates. An example is provided to illustrate an application of the proposed methods in practice.