On comparison of net survival curves

Relative survival analysis is a subfield of survival analysis where competing risks data are observed, but the causes of death are unknown. A first step in the analysis of such data is usually the estimation of a net survival curve, possibly followed by regression modelling. Recently, a log-rank type test for comparison of net survival curves has been introduced and the goal of this paper is to explore its properties and put this methodological advance into the context of the field.

We build on the association between the log-rank test and the univariate or stratified Cox model and show the analogy in the relative survival setting. We study the properties of the methods using both the theoretical arguments as well as simulations. We provide an R function to enable practical usage of the log-rank type test.

Both the log-rank type test and its model alternatives perform satisfactory under the null, even if the correlation between their p-values is rather low, implying that both approaches cannot be used simultaneously. The stratified version has a higher power in case of non-homogeneous hazards, but also carries a different interpretation.

The log-rank type test and its stratified version can be interpreted in the same way as the results of an analogous semi-parametric additive regression model despite the fact that no direct theoretical link can be established between the test statistics.