Thinking outside the curve, part II: modeling fetal-infant mortality

Abstract

BackgroundGreater epidemiologic understanding of the relationships among fetal-infant mortality and its prognostic factors, including birthweight, could have vast public health implications. A key step toward that understanding is a realistic and tractable framework for analyzing birthweight distributions and fetal-infant mortality. The present paper is the second of a two-part series that introduces such a framework.MethodsWe propose estimating birthweight-specific mortality within each component of a normal mixture model representing a birthweight distribution, the number of components having been determined from the data rather than fixed a priori.ResultsWe address a number of methodological issues related to our proposal, including the construction of confidence intervals for mortality risk at any given birthweight within a component, for odds ratios comparing mortality within two different components from the same population, and for odds ratios comparing mortality within analogous components from two different populations. As an illustration we find that, for a population of white singleton infants, the odds of mortality at 3000 g are an estimated 4.15 times as large in component 2 of a 4-component normal mixture model as in component 4 (95% confidence interval, 2.04 to 8.43). We also outline an extension of our framework through which covariates could be probabilistically related to mixture components. This extension might allow the assertion of approximate correspondences between mixture components and identifiable subpopulations.ConclusionsThe framework developed in this paper does not require infants from compromised pregnancies to share a common birthweight-specific mortality curve, much less assume the existence of an interval of birthweights over which all infants have the same curve. Hence, the present framework can reveal heterogeneity in mortality that is undetectable via a contaminated normal model or a 2-component normal mixture model.

Characterizing Components in a Mixture Model for Birthweight Distribution

“…The rest of this article is organized as follows. Section 2 presents our analytic framework, which combines a modified version of Gage's [20] parametric mixtures of logistic regressions [20,21] with Bayes' Theorem and the Law of Total Probability. Section 3 illustrates the analytic framework through application to data publicly available from the Centers for Disease Control and Prevention on white singletons born in the United States between 1998 and 2002.…”

“…A practical implementation involving the expectation maximization algorithm and the optim function in the R statistical software package is described by Charnigo and colleagues [15]; the overall estimates are then acquired by averaging the samplespecific estimates. (These overall estimates are used in Steps 4 through 7 below whenever Equation (6) in [21] is invoked)…”

“…where P stands for probability, birthweight is continuous and ranges from (say) 500 to 5500 g, and component is categorical and ranges from 1 to k. Using any particular sample, this can be accomplished by applying a modified version of Gage's [20] parametric mixtures of logistic regressions (PMLR), as described by Charnigo and colleagues [21]. PMLR was originally designed as a tool to estimate birthweightspecific infant mortality within each component of a two-component normal mixture model but was subsequently modified to accommodate an arbitrary finite number of components.…”

“…Importantly, modified PMLR is not the same as performing an ordinary logistic regression with birthweight and component membership allowed to interact; indeed, performing such a logistic regression is impossible anyway because component membership is a latent variable. Moreover, the present application of modified PMLR is distinguished from that in [21] in that now, instead of infant mortality, we take high risk classification on the factor being related to component membership as our dichotomous outcome variable. Once sample-specific estimates of Equation 2are acquired, overall estimates and 95% confidence intervals may be obtained via formulas (6) and 7in [21],…”

“…To do so, we employ the Law of Total Probability, which says that Equation 4 4have been calculated, overall estimates and 95% confidence intervals may be obtained via formulas (6) and 7in [21].…”