Update to Gage's "Birth-Weight-Specific Infant and Neonatal Mortality" (2002)

Abstract

Update to Gage's "Birth-Weight-Specific Infant and Neonatal Mortality" (2002) Timothy B. Gage Keywords Birth Weight, Infant Mortality, Gestational Age, pediatric paradox, maternal age Fryer et al. (1984), Gage and Therriault (1998), and Gage (2000) show that a two-component Gaussian mixture model describes the birth-weight distribution very well and gestational age distribution reasonably well. This finding led to the hypothesis that one of the subpopulations, the subpopulation that accounted for low-birth-weight and high-birth-weight infants (generally considered "compromised" births), might provide a useful alternative to the standard definition of low birth weight, that is, an infant weighing less than 2,500 grams. The standard definition of low birth weight had been widely criticized as arbitrary, and its applicability to populations with widely varying mean birth weights has been questioned (Gage and Therriault 1998). A mixture model fitted to the population at hand would immediately resolve this issue. The problem was how to incorporate this new approach into an analysis of infant mortality. This was the objective of my 2002 paper (Gage 2002a). The approach I proposed was to simultaneously fit two logistic regressions of infant mortality, one to each of the components. The regressions were weighted on the basis of the proportion of the total population accounted for by each subpopulation at each birth weight, so that summed, the two logistic regressions represented total birth-weight-specific infant mortality. In the 2002 paper the model was fitted in two stages. First, the mixture model was fitted to the birth-weight distribution using the maximum-likelihood method, and then the two logistics were fitted based on the mixture model results. Thus the full model did not necessarily represent a full maximum-likelihood result. Applications were carried out on the 1988 birth cohorts of New York state by sex and race. The results of this analysis showed that the mixture model divided the population into a subpopulation with a mean in the "normal" birth-weight range with a relatively small standard deviation and a second subpopulation with a significantly lower mean and larger standard deviation. Because of the large standard deviation, the second subpopulation accounted for the majority of births in both tails of the birth-weight distribution. The first subpopulation was considered a "normal" [End Page 773] fetal development subpopulation, whereas the second subpopulation was considered a "compromised" fetal development subpopulation, given its association with low and macrosomic births. The logistic regressions indicated that the birth-weight-specific infant mortality of both subpopulations was reverse J-shaped and surprisingly that the birth-weight-specific infant mortality of the "compromised" subpopulation was lower at every birth weight than the corresponding birth-weight-specific infant mortality of the "normal" subpopulation. On the other hand, the "compromised" subpopulation, as might be expected, had the higher overall infant mortality. This is due to Simpson's paradox and is a result of the different birth-weight distributions of the two subpopulations; that is, although birth-weight-specific mortality was lower among "compromised" births, more "compromised" births occurred at the lower (and higher) birth weights, where mortality was generally higher. The analysis also showed that the difference between the two logistic regressions was significant, indicating that the mixture model subdivided the birth cohort in a way that identified some hidden heterogeneity in the birth cohort. In particular, the birth-weight-specific infant mortality curve was not precisely reverse J-shaped (a second-degree polynomial; Fryer et al. 1984) but had a shoulder in the curve that occurred at about 2,000–3,000 grams. A second paper, Gage et al. (2004), extended this approach to a full likelihood method. In this case the mixture model was not fitted separately; instead, the mixture model and both regressions were all fitted simultaneously. This allowed infant mortality to inform the mixture submodel as well as the regression models. In addition, this method ensured that the statistical advantages of the maximum likelihood method applied to the resulting estimates. On the other hand, the results were basically identical with the two-stage fitting procedure. The 2004 paper left several issues unresolved: (1) the number of subpopulations, (2) the exact functional form of the subpopulations, and...