"Trajectories of Morbidity, Disability, and Mortality among the U.S. Elderly Population: Evidence from the 1984-1999 NLTCS," Eric Stallard, July 2007

North American Actuarial Journal, Jan 2008 by Cowell, Michael J

In the movie About Schmidt, the protagonist is an insurance company actuary deftly played by Jack Nicholson. Bemoaning his retirement, Schmidt returns one last time to finish clearing out his office, only to discover the culmination of his life's work, mortality tables recorded on reams of paper, already trashed by a much younger successor who has all the actuarial data he needs stored on so many gigabytes of computer memory.

Those of us who spent entire actuarial careers pricing contingencies of life, health, and disability by analyzing mortality and morbidity tables may lament the revelation that our methodologies have gone by the board. Professor Stallard's observation that "Full realization of the analytic potential" of data collected on longitudinally followed populations "will require new models and methods" lets us down somewhat more politely than Schmidt's treatment by his upstart replacement, but the implication is clear. Our attempts to coax predictors of longevity and wellness from family histories and lifestyle behaviors were rooted in methodologies and models dating to the first part of the nineteenth century, if not earlier. These ancient efforts seem destined to become supplanted by a prototype that from an analysis of 95 discretely quantifiable characteristics constructs separate life and health trajectories for each individual studied.

All this said, Professor Stallard is to be congratulated for this novel contribution to the literature, tantalizingly spurring the imagination of old-timers as to what we might have done with more powerful computing capacity. Not that many of us don't now realize, in retrospect, that we were creating crude precursors to "Grades of Membership" (GoMs) when subdividing insured populations, first by sex, then into "standard," "substandard," and "select" groupings on the basis of far fewer than 95 variables. Nor that we didn't appreciate the importance of heterogeneity, which the author emphasized in earlier work with Manton and Vaupel (1986). Quite to the contrary, some of us still bear battle scars from having defended the right to segment our data by sex at a time when political correctness run amok was insisting on "unisex" tables. Even a few actuarial colleagues, who should have known better than to temporarily abandon their science, were chiding us for appealing to biological rationale to explain the reasons that women outlive men. As mathematicians, we recognize the power of the law of large numbers. But, provided we have statistically credible samples, we also understand, if only intuitively, that the "purer," or more homogeneous, each of our subgroupings is with respect to the a priori risk of mortality or morbidity, the more tightly the actual numbers of deaths, illnesses, or disabilities will cluster around the mean values of our estimates. And the smaller the variance relative to the mean, the lower the risk premium, and the more efficient the pricing of insurance products, with benefits to the consumer and the market in general.

Professor Stallard refreshingly reinforces the importance of not only heterogeneity but also biology, confirming with references to other research that about half the variability in individual vitality-ability to resist the forces of aging-is genetically based. It is also instructive to explore the extent to which the remaining nongenetic half can be managed, but, except for the concluding comments, a more complete examination is beyond the scope of this discussion. Other claimants for the importance of biology to longevity have cited studies showing that those who live to advanced ages tend to cluster in families, and that children of centenarians are less susceptible in their own old age to such ailments as diabetes and heart disease than are their counterparts whose parents were not long-lived (Browner et al. 2004). This validation of the importance given in life and health insurance underwriting to family history is additionally helpful in the quest that Tenenbein and Vanderhoof, in their paper "New Mathematical Laws of Mortality," pursued to "reground actuarial science in the substructure of biology and gerontology" (1980, p. x).

In that seminal work the authors depended heavily on the law expounded in 1825 by Gompertz, namely, that the force of mortality μ^sub x^ = Bc^sup x^. This discussant has suggested elsewhere the mnemonic he finds useful: that the constant, B, captures part of the behavioral, that is, the nongenetic risk of mortality, while c largely transmits to this mathematical form the genetic information encoded in the human cell (Cowell 2008). Professor Stallard's principal criticism of Gompertz is that at advanced ages-he suggests a threshold of 80-90 years-increases in actual mortality are less than those predicted, though he also cites studies showing the opposite result. This leads to his question as to whether the delamination of actual mortality at advanced ages from that predicted by a Gompertz-type fit of rates from constants based on mortality at younger ages is an artifact of differential mortality selection, or evidence that Gompertz's formula should be considered a useful approximation rather than an immutable law of mortality. This discussant leans more to the former explanation.