Theoretical models of mortality selection have great utility in explaining otherwise puzzling phenomena. The most famous example may be the Black-White mortality crossover: at old ages, Blacks outlive Whites, presumably because few frail Blacks survive to old ages while some frail Whites do. Yet theoretical models of unidimensional heterogeneity, or frailty, do not speak to the most common empirical situation for mortality researchers: the case in which some important population heterogeneity is observed and some is not. I show that, when one dimension of heterogeneity is observed and another is unobserved, neither the observed nor the unobserved dimension need behave as classic frailty models predict. For example, in a multidimensional model, mortality selection can increase the proportion of survivors who are disadvantaged, or “frail,” and can lead Black survivors to be more frail than Whites, along some dimensions of disadvantage. Transferring theoretical results about unidimensional heterogeneity to settings with both observed and unobserved heterogeneity produces misleading inferences about mortality disparities. The unusually flexible behavior of individual dimensions of multidimensional heterogeneity creates previously unrecognized challenges for empirically testing selection models of disparities, such as models of mortality crossovers.
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This article benefitted from extensive discussion with Felix Elwert, along with helpful comments from James Montgomery, Alberto Palloni, Jenna Nobles, James Walker, Erik Olin Wright, Kirkwood Adams, Jenny Conrad, Michal Engelman, Josh Goldstein, Kathryn Grace, Sarah Grey, Jeffrey Grigg, Paul Hanselman, Anna Haskins, Vida Maralani, Jude Mikal, Phyllis Moen, Michelle Niemann, Sarah Thomas, and Rob Warren; valuable feedback and generous assistance from Andreas Wienke; and valuable feedback from five anonymous reviewers, two editorial teams, and the copyeditor. Funding for this research was provided by the Robert Wood Johnson Foundation Health and Society Scholars; an NICHD training grant (T32 HD07014); graduate fellowships from the National Science Foundation, the Ford Foundation, and the Institute for Research on Poverty at the University of Wisconsin–Madison; and core grants to the Minnesota Population Center (P2C HD041023) at the University of Minnesota, to the Center for Demography and Ecology at the University of Wisconsin–Madison (P2C HD047873), and to the Center for Demography of Health and Aging (P30 AG017266) at the University of Wisconsin–Madison.
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- Mortality crossovers
- Mortality disparities
- Mortality selection
- Survival models