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Asymptotic efficiency of a proportional hazards model with cure

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  • Tsodikov, Alexander

Abstract

Nonparametric estimators of survivor function can be used in the presence of long-term survivors to estimate the probability of cure by the last point of a survivor curve. To explain the presence of long-term survivors the cumulative hazard is assumed bounded but otherwise unspecified to yield an improper survivor function. Within this formulation the PH model is asymptotically fully efficient as compared to a parametric model under certain conditions when estimating the ratio of cure rates. However, this is not the case if estimation of cure rates in absolute terms is of interest. The asymptotic relative efficiency tends to zero as the probability of cure decreases. It also decreases with increase of the coefficient of variation of covariates approaching the value computed under homogeneity. Partial likelihood is shown to be inefficient if the baseline hazard is completely known.

Suggested Citation

  • Tsodikov, Alexander, 1998. "Asymptotic efficiency of a proportional hazards model with cure," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 237-244, August.
  • Handle: RePEc:eee:stapro:v:39:y:1998:i:3:p:237-244
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    References listed on IDEAS

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    1. Li, Yi-Hwei & Klein, John P. & Moeschberger, M. L., 1996. "Effects of model misspecification in estimating covariate effects in survival analysis for small sample sizes," Computational Statistics & Data Analysis, Elsevier, vol. 22(2), pages 177-192, July.
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    Cited by:

    1. Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    2. Aurelie Bertrand & Catherine Legrand & Raymond J. Carroll & Christophe de Meester & Ingrid Van Keilegom, 2017. "Inference in a survival cure model with mismeasured covariates using a simulation-extrapolation approach," Biometrika, Biometrika Trust, vol. 104(1), pages 31-50.
    3. Muller, Ursula & Van Keilegom, Ingrid, 2016. "Goodness-of-t tests for the cure rate in a mixture cure model," LIDAM Discussion Papers ISBA 2016037, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Peng, Yingwei, 2003. "Estimating baseline distribution in proportional hazards cure models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 187-201, February.
    5. Portier, Francois & El Ghouch, Anouar & Van Keilegom, Ingrid, 2015. "Efficiency and Bootstrap in the Promotion Time Cure Model," LIDAM Discussion Papers ISBA 2015012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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