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The two‐way proportional hazards model

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  • Bradley Efron

Abstract

Summary. Survival analysis problems often involve dual timescales, most commonly calendar date and lifetime, the latter being the elapsed time since an initiating event such as a heart transplant. In our main example attention is focused on the hazard rate of ‘death’ as a function of calendar date. Three different estimates are discussed, one each from proportional hazards analyses on the lifetime and the calendar date scales, and one from a symmetric approach called here the ‘two‐way proportional hazards model’, a multiplicative hazards model going back to Lexis in the 1870s. The three are connected through a Poisson generalized linear model for the Lexis diagram. The two‐way model is shown to combine the information from the two ‘one‐way’ proportional hazards analyses efficiently, at the cost of more extensive parametric modelling.

Suggested Citation

  • Bradley Efron, 2002. "The two‐way proportional hazards model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 899-909, October.
  • Handle: RePEc:bla:jorssb:v:64:y:2002:i:4:p:899-909
    DOI: 10.1111/1467-9868.00368
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    Cited by:

    1. Carollo, Angela & Putter, Hein & Eilers, Paul H. C. & Gampe, Jutta, 2023. "Event history analysis with two time scales. An application to transitions out of cohabitation," SocArXiv 4ewv3, Center for Open Science.
    2. Kwun Chuen Gary Chan & Mei-Cheng Wang, 2017. "Semiparametric Modeling and Estimation of the Terminal Behavior of Recurrent Marker Processes Before Failure Events," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 351-362, January.
    3. Adithi Ramesh & C. B Senthil Kumar, 2017. "Structure and Intensity Based Approach in Credit Risk Models: A Literature Review," International Journal of Economics and Financial Issues, Econjournals, vol. 7(3), pages 609-612.
    4. Ming-Yueh Huang & Kwun Chuen Gary Chan, 2022. "Model selection among Dimension-Reduced generalized Cox models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(3), pages 492-511, July.
    5. Breeden, Joseph L., 2016. "Incorporating lifecycle and environment in loan-level forecasts and stress tests," European Journal of Operational Research, Elsevier, vol. 255(2), pages 649-658.
    6. Kwun Chuen Gary Chan, 2018. "Commentary: Alignment of time scales and joint models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 601-604, October.
    7. Kauermann, Goran & Khomski, Pavel, 2006. "Additive two-way hazards model with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1944-1956, December.
    8. J L Breeden & D Ingram, 2010. "Monte Carlo scenario generation for retail loan portfolios," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(3), pages 399-410, March.
    9. Joseph L Breeden & Lyn Thomas, 2016. "Solutions to specification errors in stress testing models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(6), pages 830-840, June.

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