A decision-theoretic method for analyzing crossing survival curves in healthcare

The problem of crossing Kaplan–Meier curves has not been solved in the medical research literature to date. This paper integrates survival curve comparisons into decision theory, providing a theoretical framework and a solution to the problem of crossing Kaplan–Meier curves. The application of decision theory allows us to apply stochastic dominance concepts and risk preference attributes to compare treatments even when standard Kaplan–Meier curves cross. The paper shows that as additional risk preference attributes are adopted, Kaplan–Meier curves can be ranked under weaker restrictions, namely with higher orders of stochastic dominance. Consequently, even Kaplan–Meier curves that cross may be ranked. The method we present allows us to extract all possible information from survival functions; hence, superior treatments that cannot be identified using standard Kaplan–Meier curves may become identifiable. Our methodology is applied to two examples of published empirical medical studies. We show that treatments deemed non-comparable because their Kaplan–Meier curves intersect can be compared using our method.