Altitude , birth weight , and infant mortality

Birth weight decreases with increasing altitude. However, some argue that there is no corresponding increase in infant mortality, implying that birth weight is not on the causal pathway to mortality. This research statistically examines the relationship between altitude, birth weight, and infant mortality using 1995-2002 linked birth/death files: European-American cohorts from high altitude Colorado and low altitude Iowa. Socioeconomic variation is controlled for by education. CDDmlr is used, which identifies “direct” and “indirect” effects of altitude on mortality in two latent birth categories interpreted as “normal” and “compromised” births. Mean birth weight declines in “normal” births 156-185 grams. The variance declines 484787 grams in “normal” births and 11,025-22,201 grams in “compromised” births. There is one significant increase in mortality in male, low socioeconomic, “normal” births. There are no indirect effects of birth weight on mortality indicating that birth weight distribution shifts are not involved in the change in mortality. INTRODUCTION Many studies have found that birth weight decreases with increasing altitude and further, that this decline is not associated with other low birth weight risk factors (for example, Jensen and Moore, 1997). However, the relationship between birth weight, altitude, and mortality is more complex. It is often assumed that infant mortality will increase if birth weights decrease and this assumption underlies the US national health policy of reducing infant mortality (USDOHHS, 2000). In contrast, other studies have found declining mean birth weight with no increase in mortality with increasing altitude, especially in high risk infants (Paranka et al, 2001). Wilcox (2001) observes that high altitude births have lower mortality at lower birth weights and higher mortality at higher birth weights compared to low altitude births. By standardizing the birth weight distributions and re-plotting the mortality curves, he then observes that the two mortality curves almost coincide. He concludes that for the case of altitude, the mortality curve shift corresponds to the birth weight distribution shift and therefore there is no change in overall mortality between high and low altitude births, implying that birth weight is not on the causal pathway to mortality. If birth weight is on the causal pathway to infant mortality, we would expect to see an uncoupling of birth weight and mortality, that is, we would see an additional horizontal shift in the mortality curve after standardizing the birth weight distribution and the overall mortality between the two groups would be different. This would represent an indirect effect of altitude on mortality that is mediated through birth weight. If an exogenous variable, like altitude, acts independently of birth weight, we expect to see a vertical shift of the mortality curve, which would be a direct effect of altitude on mortality. This research tests this hypothesis by statistically examining the relationship between altitude, birth weight, and infant mortality. DATA AND METHODS The data analyzed is from the US national 1995-2002 linked birth/infant death files: male and female European-American births. Socioeconomic variation associated with altitude is controlled for by maternal education level. The high altitude group is from Colorado (births geocoded from 5,000-10,000 feet) and the low altitude group is from Iowa (births from 472-1,640 feet). Descriptive statistics of the sample population can be found in Table 1. Table 1 about here These four birth cohorts are examined using Covariate Density Defined mixtures of logistic regressions (CDDmlr), which identifies “direct” (independent of birth weight) and “indirect” (through birth weight) effects of altitude on mortality in two latent birth categories. There are eight total cases to test the existence of direct and indirect mortality effects (sex X education X latent category). The model (f; Eq. 1) used in this analysis is an extension of Gage et al (2004) twosubpopulation CDDmlr model of infant mortality, which decomposes the birth weight distribution into two subpopulations by using standard mixtures of Gaussian distributions and simultaneously fits a separate birth weight specific mortality curve to each latent subpopulation. This model is extended by making the parameters functions of a dichotomous variable z which represents altitude (z = 0, low altitude; z = 1 , high altitude). Birth weight data is represented by x and mortality data is represented by y. The birth weight density submodel (f1; Eq. 2) has mixture parameters for each latent subpopulation represented by θ: mean birth weight, standard deviation of birth weight, and the proportion of births belonging to the secondary subpopulation (πs). The majority subpopulation is referred to as the primary subpopulation and the minority subpopulation is referred to as the secondary subpopulation which are interpreted as “normal” and “compromised” births and fetal development respectively. The mortality submodel (f2; Eq. 4) has parameters represented by β. The mortality is modeled as a quadratic logistic to allow for a reverse J-shaped birth weight specific mortality in each subpopulation. The mortality submodel is the product of the probability of death in the primary or secondary subpopulation and the conditional probability that an infant belongs to that subpopulation. The likelihood function for the CDDmlr model with altitude as an exogenous covariate of infant mortality ( ) is a product of the conditional mortality submodel y ) , ; x | y ( f 2 β θ and the birth weight (x) density submodel ) ; x ( f1 θ : ( ) ( ) ( ) θ β θ β θ ; x f , ; x | y f , ; y , x f 1 2 = (Eq. 1) )) , , , , ( ; z | x ( f p p s s s 1 σ μ σ μ π θ = )) z ( ), z ( ; x ( N )] z ( 1 [ )) z ( ), z ( ; x ( N ) z ( p p 500 s s s 500 s σ μ π σ μ π × − + × = (Eq. 2) ) z ( it log )) z ( ( it log ) z ( 1 0 s s α α η π × + = = (Eq. 3) ( ) ( ) ( ) ( ) [ ] ( ) p p p p s s s s s s c b a x y P x q c b a x y P x q x y f , , ; | ; 1 , , ; | ; , ; | 2 × − + × = θ θ β θ (Eq. 4) s π , the mixing proportion, is defined as the proportion of births belonging to the less numerous of the two subpopulations, that is, the secondary subpopulation (s) as opposed to the primary subpopulation (p). For i = p and s, ( ) 2 i i 500 , ; x N σ μ represents the Gaussian density, truncated at 500 grams, with mean i μ and variance . 2 i σ Births at low altitudes are the default and the altitude effect is defined as an indicator variable ( ) on each of the 11 parameters in the CDDmlr model. Birth weight is standardized according to the respective subpopulation density characteristics (i.e. mean and standard deviation) and then used in the corresponding logistic regression function. Therefore, z 1 0 i i z ) z ( γ μ i γ ×