Comparing Kaplan-Meier curves with the probability of agreement

The probability of agreement has been used as an effective strategy for quantifying the similarity between the reliability of two populations. By contrast to hypothesis testing approaches based on P-values, the probability of agreement provides a more realistic assessment of similarity by emphasizing practically important differences. In this article, we propose the use of the probability of agreement to evaluate the similarity of two Kaplan-Meier curves, which estimate the survival functions in two populations. This article extends the probability of agreement paradigm to right censored data and explores three different methods of quantifying uncertainty in the probability of agreement estimate. The first approach provides a convenient assessment based on large-sample normal-theory (LSNT), while the other two approaches are nonparametric alternatives based on ordinary and fractional random-weight bootstrap (FRWB) techniques. All methods are illustrated with examples for which comparing the survival curves of related populations is of interest and the efficacy of the methods are also evaluated through simulation studies. Based on these simulations we recommend point estimation using the proposed LSNT calculation and confidence interval estimation via the FRWB approach. We also provide a Shiny app that facilitates an automated implementation of the methodology.