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Asymptotic Relative Efficiency of Parametric and Nonparametric Survival Estimators

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  • Szilárd Nemes

    (BioPharma Early Biometrics and Statistical Innovation, Data Science & AI, BioPharmaceuticals R&D, AstraZeneca, 43183 Gothenburg, Sweden)

Abstract

The dominance of non- and semi-parametric methods in survival analysis is not without criticism. Several studies have highlighted the decrease in efficiency compared to parametric methods. We revisit the problem of Asymptotic Relative Efficiency ( A R E ) of the Kaplan–Meier survival estimator compared to parametric survival estimators. We begin by generalizing Miller’s approach and presenting a formula that enables the estimation (numerical or exact) of A R E for various survival distributions and types of censoring. We examine the effect of follow-up time and censoring on A R E . The article concludes with a discussion about the reasons behind the lower and time-dependent A R E of the Kaplan–Meier survival estimator.

Suggested Citation

  • Szilárd Nemes, 2023. "Asymptotic Relative Efficiency of Parametric and Nonparametric Survival Estimators," Stats, MDPI, vol. 6(4), pages 1-13, October.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:4:p:72-1159:d:1266772
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    References listed on IDEAS

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    1. Zheng, Gang & Gastwirth, Joseph L., 2001. "On the Fisher information in randomly censored data," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 421-426, May.
    2. Paul Meier & Theodore Karrison & Rick Chappell & Hui Xie, 2004. "The Price of Kaplan-Meier," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 890-896, January.
    3. Szilard Nemes & Andreas Gustavsson & Ziad Taib, 2020. "Variance Inflation Due to Censoring in Survival Probability Estimates," Statistica, Department of Statistics, University of Bologna, vol. 80(4), pages 395-412.
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