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.