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Accelerated Failure Time Models with Log-concave Errors

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  • Ruixuan Liu
  • Zhengfei Yu

Abstract

We study accelerated failure time (AFT) models in which the survivor function of the additive error term is log-concave. The log-concavity assumption covers large families of commonly-used distributions and also represents the aging or wear-out phenomenon of the baseline duration. For right-censored failure time data, we construct semi-parametric maximum likelihood estimates of the finite dimensional parameter and establish the large sample properties. The shape restriction is incorporated via a nonparametric maximum likelihood estimator (NPMLE) of the hazard function. Our approach guarantees the uniqueness of a global solution for the estimating equations and delivers semiparametric efficient estimates. Simulation studies and empirical applications demonstrate the usefulness of our method.

Suggested Citation

  • Ruixuan Liu & Zhengfei Yu, 2019. "Accelerated Failure Time Models with Log-concave Errors," Tsukuba Economics Working Papers 2019-003, Faculty of Humanities and Social Sciences, University of Tsukuba.
  • Handle: RePEc:tsu:tewpjp:2019-003
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    References listed on IDEAS

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    1. Tripathi, Gautam, 2000. "Local Semiparametric Efficiency Bounds Under Shape Restrictions," Econometric Theory, Cambridge University Press, vol. 16(5), pages 729-739, October.
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    3. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    4. Meinhofer, Angélica & Witman, Allison E., 2018. "The role of health insurance on treatment for opioid use disorders: Evidence from the Affordable Care Act Medicaid expansion," Journal of Health Economics, Elsevier, vol. 60(C), pages 177-197.
    5. Zaric, G.S. & Barnett, P.G. & Brandeau, M.L., 2000. "HIV transmission and the cost-effectiveness of methadone maintenance," American Journal of Public Health, American Public Health Association, vol. 90(7), pages 1100-1111.
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