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Survival models and health sequences

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Abstract

Survival studies often generate not only a survival time for each patient but also a sequence of health measurements at annual or semi-annual check-ups while the patient remains alive. Such a sequence of random length accompanied by a survival time is called a survival process. Robust health is ordinarily associated with longer survival, so the two parts of a survival process cannot be assumed independent. This paper is concerned with a general technique—reverse alignment—for constructing statistical models for survival processes, here termed revival models. A revival model is a regression model in the sense that it incorporates covariate and treatment effects into both the distribution of survival times and the joint distribution of health outcomes. The revival model also determines a conditional survival distribution given the observed history, which describes how the subsequent survival distribution is determined by the observed progression of health outcomes.

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Notes

  1. Missing from the latent-variable formulation in Henderson et al. (2000) and Xu and Zeger (2001) is an explicit recognition of the fact that health outcomes are observable only while patients live.

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Authors and Affiliations

  1. Department of Statistics, Harvard University, One Oxford Street, Cambridge, MA, 02138, USA

    Walter Dempsey

  2. Department of Statistics, University of Chicago, 5734 University Ave, Chicago, IL, 60637, USA

    Peter McCullagh

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  1. Walter Dempsey
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  2. Peter McCullagh
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Correspondence to Walter Dempsey.

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Dempsey, W., McCullagh, P. Survival models and health sequences. Lifetime Data Anal 24, 550–584 (2018). https://doi.org/10.1007/s10985-018-9424-9

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