Mortality Selection and Sample Selection: A Comment on Beckett

Abstract

Mortality Selection and Sample Selection: A Comment on Beckett* ANDREW NOYMER University of CaIifornia—BerkeIey Journal of Health and Social Behavior 2001, Vol 42 (Septmber): 326-327 In an interesting article, Megan Beckett (2000) examines the important question of converging health inequalities in later life. Many studies have shown that the differences in health across socioeconomic strata narrow at older ages. Using panel data from the National Health and Nutrition Examination Survey (NHANES), Beckett shows that the converging health inequality cannot be accounted for by mortality selection. The pre- sent comment reconsiders Beckett’s approach to the selection problem, which, while creative, is open to multiple interpretations. Consider the phenomenon that would cause converging health inequalities at later ages to be an “artifact,” as Beckett puts it, of mortality selection. At younger ages, persons with high- er socioeconomic status (SES) have lower lev- els of health problems than those with lower SES. At older ages, the prevalence of health problems in the two groups is closer to parity. If patterns in morbidity are mirrored in mortal- ity, then at older ages a lower SES cohort (higher morbidity and mortality) will be small- er compared to its starting size than a higher SES cohort (lower morbidity and mortality). Since the seminal work of Vaupel, Manton, and Stallard (1979) and Keyfitz and Littman (1979), many demographers have assumed that there are different rates of “frailty” within a population, which determine an individual’s deviation, at any age, from some baseline mor- tality risk. According to the frailty hypothesis, those who die at young ages tend to have high frailty, which skews the distribution of sur- vivors to be more robust. If this condition of nonrandom mortality risks is met, then the aged low SES cohort will be more robust than ‘Address correspondence to: Andrew Noymer, Departments of Sociology and Demography, University of Califomia-—Berkeley, 2232 Pied- mont Avenue, Berkeley, CA 94720; email: andrew@demog.berkeley.edu. when it started out. This reversal of fortune over the life course is called “cohort inversion” (Hobcraft, Menken, and Preston 1982). On the other hand, the low mortality, high SES cohort will have a much less-changed frailty distribu- tion, and will experience less cohort inversion. The greater cohort inversion of the low SES cohort could be enough to overcome the mor- tality disadvantage of being low SES. This problem must be analyzed cautiously, however, as the entire framework for understanding mortality selection effects rests on a counter- factual foundation. If we hold that convergence is a result of mortality selection, we imply that an intrinsic differential persists into older ages and that we would observe it were it not for the selection efiect. On the other hand, if we hold that the convergence is either intrinsic or the result of, for example, access to Medicare (Beckett 2000), we posit that even without selection we would see convergence. In both cases, there is the troubling verb “would.” In reality, we can only observe vital rates that do occur, not those that would occur if some con- dition is met. The general problem of sample selection is encountered frequently in the social sciences (cf. Stolzenberg and Relles 1997; Winship and Mare 1992), and as Beckett (2000) notes, dif- ferential mortality is just a special case of the more general problem. Although we cannot simply “control for” (i.e., condition on) selec- tion bias the same way we would a confound- ing variable, statistical techniques do exist that try to counteract the bias. However, mortality selection is a very special case of sample selec- tion, all the more so if the dependent variable in question is itself health-related. Because of cohort inversion, sample selection due to mor- tality has causal implications beyond nonran- dom missing data in panel followups. This is what makes Beckett’s approach problematic. Consider the statistical technique used by Beckett to set up the hypothetical of no mor- 326