Multiple mortality optima due to heterogeneity in the birth cohort: A continuous model of birth weight by gestational age‐specific infant mortality

Abstract

Birth weight and gestational age are both important predictors of infant survival. Covariate Density Defined mixture of logistic regressions (CDDmlr), a method that accounts for unobserved heterogeneity, has been applied to birth outcomes using birth weight alone. This paper investigates a CDDmlr model of birth outcomes that includes birth weight and gestational age. Applications to four birth cohorts, composed of all non-Hispanic singleton African/European American female/male live births in New York State from 1985-1988, are presented. Multiple birth weight by gestational age optimal (minimal) mortalities are observed in the birth weight by gestational age-specific mortality surface. Multiple optima have not been mentioned in the published literature, but they do appear in some published plots of birth weight by gestational age mortality. It is possible that misreporting of gestational age contributes to this phenomenon, but it cannot completely explain the locations of the local optima. The global optimum is associated with a "normal" fetal development subpopulation, while the local optima are due to a subpopulation that accounts for most low birth weight, intrauterine growth retarded, pre-term, post-term, and small for gestational age births, as well as, births with misestimated gestational ages. These two subpopulations have significantly different birth weight by gestational age-specific mortality surfaces. Consequently, the presence of multiple optima can be attributed to heterogeneity in the birth cohort. Comparisons of CDDmlr based on birth weight by gestational age and birth weight alone might statistically identify births with "erroneous" gestational age.

Thinking outside the curve, part I: modeling birthweight distribution

“…Since gestational age is sometimes considered in tandem with birthweight [19,20], we now comment on its relation to the methodology in this two-part series.…”

Joint Bayesian analysis of birthweight and censored gestational age using finite mixture models

“…The unique shape of the joint birthweight and gestational age distribution (see Figure 2) can be flexibly modeled using finite-mixture models [23, 24] as discussed in [2, 4, 5]. We use the s -component mixture model specified by normal distributions $${(b_i,g_i)}^{\prime }~\sum _{k=1}^s{\pi }_{k}N(g_i\mid {\mu }_{g,k}+z_i^{\prime }{\beta }_{g,k},{\sigma }_{g,k}^2)N(b_i\mid {\mu }_{b,k}+z_i^{\prime }{\beta }_{b,k}+(g_i-({\mu }_{g,k}+z_i^{\prime }{\beta }_{g,k})){\beta }_{\ast k},{\sigma }_{b\mid g,k}^2);$$ i.e.…”

“…[2, 4, 5] who use direct maximum likelihood (ML) estimation, we employ the data augmented form for finite mixture models and introduce latent indicators v i ~ MN (π 1 ,⋯,π s ), ${\sum }_{k=1}^s{v}_{i,k}=1$, denoting the component to which ( g i , b i )′ belongs. The resulting model is marginally equivalent to the original specification: $${(g_i,b_i)}^{\prime }~\sum _{k=1}^{s}N(M_k,S_k)I_{[v_{i,k}=1]}.$$ Under this specification, ML estimation of model parameters proceeds through the Expectation-Maximization (EM) algorithm, whereas full Bayesian posterior inference proceeds by specifying priors and utilizing Markov chain Monte Carlo (MCMC) methodology.…”

“…Section 1.2 describes our motivating application data, the NCDBR. Section 2 reintroduces the finite mixture of bivariate regressions model specification for the joint variable birthweight and gestational age [2, 4, 5] and extends the model to allow for the common interval censored form of gestational age. In Section 3, the consequences of analyses using intermediate variables (e.g.…”

“…Models for the joint birthweight and gestational age variable have subsequently been incorporated as sub-models in analyses of further adverse birth outcomes (e.g. fetal death), as in [4, 5]. These models introduce a logistic regression conditional birthweight and gestational age to model a trivariate outcome.…”