Browsing by Author "Missov, TI"

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    Mortality implications of mortality plateaus
    (SIAM Review, 2015-01-01) Missov, TI; Vaupel, JW
    This article aims to describe in a unified framework all plateau-generating random effects models in terms of (i) plausible distributions for the hazard (baseline mortality) and the random effect (unobserved heterogeneity, frailty) as well as (ii) the impact of frailty on the baseline hazard. Mortality plateaus result from multiplicative (proportional) and additive hazards, but not from accelerated failure time models. Frailty can have any distribution with regularly-varying-at-0 density and the distribution of frailty among survivors to each subsequent age converges to a gamma distribution. In a multiplicative setting the baseline cumulative hazard can be represented as the inverse of the negative logarithm of any completely monotone function. If the plateau is reached, the only meaningful solution at the plateau is provided by the gamma-Gompertz model.
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    Unobserved population heterogeneity: A review of formal relationships
    (Demographic Research, 2014-01-01) Vaupel, JW; Missov, TI
    © 2014 James W. Vaupel & Trifon I. Missov.Background: Survival models accounting for unobserved heterogeneity (frailty models) play an important role in mortality research, yet there is no article that concisely summarizes useful relationships. Objective: We present a list of important mathematical relationships that govern populations in which individuals differ from each other in unobserved ways. For some relationships we present proofs that, albeit formal, tend to be simple and intuitive. Methods: We organize the article in a progression, starting with general relationships and then turning to models with stronger and stronger assumptions. Results: We start with the general case, in which we do not assume any structure of the underlying baseline hazard, the frailty distribution, or their link to one another. Then we sequentially assume, first, a relative-risk model; second, a gamma distribution for frailty; and, finally, a Gompertz and Gompertz-Makeham specification for baseline mortality. Comments: The article might serve as a handy overall reference to frailty models, especially for mortality research.