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Should We Choose Treatments by Comparing Hazard Functions?

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  • Appelbaum, Elie

Abstract

Hazard functions are widely used for comparing treatments, often through pointwise comparisons of their values over time. This note shows that such comparisons provide a sufficient but not necessary condition for treatment ranking. We demonstrate that the appropriate comparison criterion is based on cumulative hazard functions, i.e., the integrals of hazard functions over time. This perspective clarifies the interpretation of hazard-based comparisons and has implications for cases where hazard functions cross. The results suggest that commonly used comparison rules may be overly restrictive and may fail to identify clear treatment preferences.

Suggested Citation

  • Appelbaum, Elie, 2026. "Should We Choose Treatments by Comparing Hazard Functions?," MPRA Paper 129116, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:129116
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    File URL: https://mpra.ub.uni-muenchen.de/129116/1/MPRA_paper_129116.pdf
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    References listed on IDEAS

    as
    1. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    2. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    3. Appelbaum, Elie & Leshno, Moshe & Prisman, Eitan & Prisman, Eliezer, Z., 2025. "A Decision-Theoretic Method for Analyzing Crossing Survival Curves in Healthcare," MPRA Paper 124419, University Library of Munich, Germany.
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    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other
    • I10 - Health, Education, and Welfare - - Health - - - General

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