Department of Anthropology, University at Albany, State University of New York, 1400 Washington Ave., Albany, NY 12222, USA

Department of Epidemiology and Biostatistics, University at Albany, State University of New York, 1400 Washington Ave., Albany, NY 12222, USA

Abstract

Background

It has been hypothesized that birth weight is not on the causal pathway to infant mortality, at least among "normal" births (i.e. those located in the central part of the birth weight distribution), and that US racial disparities (African American versus European American) may be underestimated. Here these hypotheses are tested by examining the role of birth weight on racial disparities in infant mortality.

Methods

A two-component Covariate Density Defined mixture of logistic regressions model is used to decompose racial disparities, 1) into disparities due to "normal" versus "compromised" components of the birth cohort, and 2) further decompose these components into indirect effects, which are associated with birth weight, versus direct effects, which are independent of birth weight.

Results

The results indicate that a direct effect is responsible for the racial disparity in mortality among "normal" births. No indirect effect of birth weight is observed despite significant disparities in birth weight. Among "compromised" births, an indirect effect is responsible for the disparity, which is consistent with disparities in birth weight. However, there is also a direct effect among "compromised" births that reduces the racial disparity in mortality. This direct effect is responsible for the "pediatric paradox" and maybe due to differential fetal loss. Model-based adjustment for this effect indicates that racial disparities corrected for fetal loss could be as high as 3 or 4 fold. This estimate is higher than the observed racial disparities in infant mortality (2.1 for both sexes).

Conclusions

The results support the hypothesis that birth weight is not on the causal pathway to infant mortality among "normal" births, although birth weight could play a role among "compromised" births. The overall size of the US racial disparities in infant mortality maybe considerably underestimated in the observed data possibly due to racial disparities in fetal loss.

Background

It has been argued that birth weight may not be on the "causal pathway" to infant mortality

The three plausible directed acyclic graphs are illustrated in Figure

Three directed acyclic graphs considered to be plausible models of the relationship of birth weight to infant mortality in response to a stressor (adapted from

**Three directed acyclic graphs considered to be plausible models of the relationship of birth weight to infant mortality in response to a stressor (adapted from ****)**. Model (a) assumes that the stressor has direct effects on birth weight and mortality, birth weight has direct effects on infant mortality, and an interaction of the stressor and birth weight are assumed to account for the reverse-J-shaped birth weight specific mortality curve. Model (b) also assumes that the stressor has direct effects on birth weight and mortality, birth weight has direct effects on infant mortality, and unobserved covariates U account for the reverse-J shape. Model (c) assumes that the stressor has direct effects on birth weight and mortality, the reverse-J shape is the result of unobserved covariates U, but birth weight does not have direct effects on mortality.

If birth weight is not on the "causal pathway", i.e. it does not mediate the effect of race on infant mortality (Figure

Wilcox and others

The objective of this paper is to quantitatively document the role that birth weight plays in racial disparities in infant mortality using the 2001 United States non-Hispanic African and European American birth cohorts controlling for sex. In particular, we statistically test the hypothesis that birth weight is on the "causal pathway" to infant mortality and decompose racial disparities in infant mortality into effects, which are independent of birth weight (direct effects of race) and effects, which are due to the racial disparities in birth weight (indirect effects of race mediated by birth weight). A secondary aim is to estimate the magnitude of the racial disparities in infant mortality while controlling for the "pediatric paradox". We do not propose that "race" is the cause of these disparities, but simply a proxy for a collection of stressors (e.g. socio-economic status, education, and genetic etc, some of which may be unobserved), which are the underlying causes of these differences.

Methods

Data Source

The data for this analysis are obtained from 2001 NCHS Birth Cohort Linked Birth/Infant Death data set. Race and ethnic origin are based on mother's reported race and ethnic origin. Approximately 6.4% and 8.7% of the non-Hispanic European and non-Hispanic African American births, respectively, are excluded from this analysis due to missing information or LMP gestational age <20 weeks or birth weight <500 grams. Summary statistics for the samples used are presented in Table

Descriptive statistics for the 2001 sample populations

**Birth Cohort**

**# Births**

**# Deaths**

**CDR**

**Birth Weight (grams)**

**Min**

**Mean**

**Median**

**Max**

Eur. Am. F.

1,023,583

3,558

3.48

500

3342

3365

6350

Eur. Am. M.

1,076,814

4,880

4.53

500

3461

3487

7858

Af. Am. F.

255,758

1,865

7.29

500

3092

3135

7002

Af. Am. M.

264,130

2,545

9.64

500

3200

3260

7220

Eur. = European; Af. = African; Am. = American; F. = females; M. = males

CDR = Crude death rate (death per 1000 births)

Statistical Model - CDDmlr

Covariate Density Defined mixture of logistic regressions (CDDmlr), while a generally applicable statistical procedure, was specifically designed to test the Wilcox-Russell hypothesis ^{nd }degree polynomial of birth weight) is the parsimonious model, that fits birth weight distributions

The model employed here is an extension of the two-subpopulation birth weight only CDDmlr model of infant mortality ^{nd }degree polynomials of birth weight or standardized birth weight, respectively) in the mortality submodel of the basic CDDmlr model

(i) the logit of minimum mortality (i.e. a vertical shift of the mortality curve by race, the direct effect of race);

(ii) the optimal standardized birth weight (i.e. a horizontal shift of the mortality curve by race, the indirect effect of race described by Wilcox-Russell

(iii) the particular shape of the reverse-J-shaped standardized birth weight specific mortality curve (i.e. a second possible indirect effect of race, not considered by Wilcox-Russell

This second indirect effect of race through birth weight (iii) occurs when a change in the variance of birth weight is not reflected in a compensatory change in the shape of the birth weight specific mortality curve. So that the standardized birth weight specific mortality curve changes by race. Finally, the mixing proportion may contribute to the overall observed racial disparities in infant mortality. This is an additional effect of race, which was not discussed in the Wilcox-Russell hypothesis

The likelihood function for the basic birth weight (_{2}(_{1}(

In the case of two truncated Gaussian subpopulations, the birth weight density submodel _{1}(

_{
s
}, 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
}(Eq. 3) transforms the 0 and 1 bounds on _{
s
}to minus and plus infinity, respectively. For _{i }
_{2}

where _{
s
}

The birth weight density submodel _{1}(

Overall, there are 11 parameters, five defining the birth weight distribution, and six defining the subpopulation-specific mortalities.

In this study, the basic CDDmlr model is extended in two ways. First, we have used European American births as the default and defined the African American "race" effect as an indicator variable (

This extended model includes 22 parameters, 11 representing the characteristics of European American births, and 11 representing the differences of African compared to European American birth outcomes, that is, the "race" effect. The 5 indicator variable terms in the density submodel (i.e. _{1}, _{i}
_{, 1}, and _{i, 1 }

Model Fitting

The birth weight density and mortality submodels are fitted simultaneously to individual level data using the method of maximum likelihood (ms() in the SPLUS statistical library ^{nd }degree polynomial of standardized birth weight specific mortality curves are fitted in linear form, and then transformed to non-linear form after fitting. This significantly reduces the computational resources necessary to fit the model. The resulting parameter estimates are presented in Table

Parameter estimates for the 2001 sample populations

**Birth Cohort**

**z = 0**

**z = 1**

**z = 0**

**z = 1**

**Eur. Am. F**.

**Af. Am. F**.

**Eur. Am. M**.

**Af. Am. M**.

_{
s, 0
}

-2.75

-2.62

_{
s, 1
}

0.46

0.35

_{
s, 0
}

2678

2739

_{
s, 1
}

-639

-706

_{
s, 0
}

1098

1098

_{
s, 1
}

205

238

_{
p, 0
}

3380

3509

_{
p, 1
}

-211

-221

_{
p, 0
}

455

474

_{
p, 1
}

0^{+}

-2^{+}

_{s, 0}

-7.12

-7.11

_{s, 0}

1.06

1.29

_{s, 0}

0.77

0.68

_{s, 1}

-1.73

-0.83^{+}

_{s, 1}

0.36^{+}

0.11^{+}

_{s, 1}

0.54

0.62

_{p, 0}

-6.85

-6.57

_{p, 0}

0.97

1.22

_{p, 0}

0.25

0.20

_{p, 1}

0.75

0.69

_{p, 1}

-0.15^{+}

-0.44

_{p, 1}

0.01^{+}

0.05^{+}

Eur. = European; Af. = African; Am. = American; F. = females; M. = males

^{+}: = not significantly different from zero based on the bias-adjusted 95% CI

Decomposition of the Racial Disparity

Decomposition of the racial disparity is carried out in two steps. First, the total absolute racial disparity in infant mortality is decomposed into deaths attributable to differences in the mixing proportion and rate effects for "normal" and "compromised" births using standard Kitagawa decomposition

The subpopulation specific disparities (rate effects) are further decomposed into direct (independent of birth weight) and indirect (potentially causal through birth weight) effects by factoring the subpopulation relative risks into direct and indirect multiplicative components. The probability of infant death for a European American birth with

And the overall infant mortality for the

For an African American birth with

And the overall infant mortality for the

The overall relative risk of infant death for African American births as compared to European American births in the

_{i}
_{,1 }is referred to as the direct factor of "race" in the _{i}

Results

Characteristics of Race Specific Birth Weight Distributions and Infant Mortality

The qualitative characteristics of the birth weight distributions and birth weight specific infant mortality are similar for both races (Table

Model-estimated birth weight distribution and mortality characteristics for the 2001 sample populations

**Birth Cohort**

**Eur. Am. F**.

**Af. Am. F**.

**Eur. Am. M**.

**Af. Am. M.**

**estimate**

**LCI UCI**

**estimate**

**LCI UCI**

**estimate**

**LCI UCI**

**estimate**

**LCI UCI**

"Normal" Subpopulation

Proportion (%)

94.0

(93.5; 94.3)

90.7

(90.5; 91.0)

93.2

(92.7; 93.6)

90.6

(90.5; 90.8)

Mean (g)

3380

(3378; 3382)

3169

(3168; 3170)

3509

(3507; 3512)

3288

(3287; 3289)

Standard Deviation (g)

455

(453; 457)

455

(454; 457)

474

(472; 476)

472

(471; 473)

LBW Rate (%)

2.8

(2.7; 2.9)

7.0

(6.9; 7.0)

1.8

(1.7; 1.9)

4.8

(4.7; 4.9)

Death Rate ^{#}

2.3

(2.1; 2.6)

4.4

(4.2; 4.5)

2.9

(2.7; 3.2)

5.2

(5.0; 5.4)

Percent of Total DR (%)

63.1

(58.2; 67.8)

54.7

(53.5; 56.1)

60.5

(55.6; 65.0)

49.0

(47.5; 50.5)

"Compromised" Subpopulation

Proportion (%)

6.0

(5.7; 6.5)

9.3

(9.0; 9.5)

6.8

(6.4; 7.3)

9.4

(9.2; 9.5)

Mean (g)

2678

(2630; 2730)

2039

(1995; 2072)

2739

(2684; 2785)

2034

(1995; 2072)

Standard Deviation (g)

1098

(1067; 1126)

1303

(1289; 1320)

1098

(1076; 1121)

1336

(1323; 1350)

LBW Rate (%)

42.3

(40.4; 43.8)

58.5

(57.7; 59.2)

40.4

(38.7; 42.4)

58.3

(57.5; 59.1)

Death Rate ^{#}

21.2

(18.3; 24.9)

35.5

(33.7; 37.1)

26.3

(23.0; 30.0)

52.4

(50.3; 55.0)

Percent of Total DR (%)

36.9

(32.2; 41.8)

45.2

(43.9; 46.5)

39.5

(35.0; 44.4)

51.0

(49.5; 52.5)

Total Population

LBW Rate (%)

5.2

(5.1; 5.3)

11.8

(11.7; 11.9)

4.5

(4.4; 4.6)

9.8

(9.8; 9.9)

Death Rate ^{#}

3.5

(3.2; 3.7)

7.3

(7.1; 7.4)

4.5

(4.3; 4.8)

9.6

(9.4; 9.9)

Eur. = European; Af. = African; Am. = American; F. = females; M. = males

LCI = lower 95% confidence interval; UCI = upper 95% confidence interval; LBW = low birth weight (i.e. <2500 grams); DR = death rate

^{#}: death per 1000 births

Model-estimated birth weight distributions and (standardized) birth weight specific infant mortality curves with bias-adjusted 95% confidence intervals for European American females (Eur. Am. F.) and African American females (Af. Am. F.)

**Model-estimated birth weight distributions and (standardized) birth weight specific infant mortality curves with bias-adjusted 95% confidence intervals for European American females (Eur. Am. F.) and African American females (Af. Am. F.)**. Panel (a) presents the subpopulation specific birth weight densities, while panel (b) shows the total birth weight densities. Panel (c) represents the standardized birth weight specific infant mortality of "normal" births, while panel (d) presents the standardized birth weight specific infant mortality of "compromised" births. Panel (e) shows the total birth weight specific infant mortality. Finally panel (f) compares the total birth weight specific infant mortality with and without (

Model-estimated birth weight distributions and (standardized) birth weight specific infant mortality curves with bias-adjusted 95% confidence intervals for European American males (Eur. Am. M.) and African American males (Af. Am. M.)

**Model-estimated birth weight distributions and (standardized) birth weight specific infant mortality curves with bias-adjusted 95% confidence intervals for European American males (Eur. Am. M.) and African American males (Af. Am. M.)**. Panel (a) presents the subpopulation specific birth weight densities, while panel (b) shows the total birth weight densities. Panel (c) represents the standardized birth weight specific infant mortality of "normal" births, while panel (d) presents the standardized birth weight specific infant mortality of "compromised" births. Panel (e) shows the total birth weight specific infant mortality. Finally panel (f) compares the total birth weight specific infant mortality with and without (

Racial Differences in Birth Weight Distributions

Race has substantial effects on the distribution of birth weight (Table

Racial Differences in Infant Mortality

There are substantial racial differences in infant mortality as well (Table

The estimated racial disparity can be decomposed into a mixing proportion effect and two rate effects (in particular, one for the "normal" subpopulation and the other for the "compromised" subpopulation) by applying Kitagawa decomposition analysis

Kitagawa decomposition of the observed racial disparities in infant mortality (death per 1000 births)

**Decomposition**

**Females**

**Males**

**estimate**

**LCI UCI**

**estimate**

**LCI UCI**

Mixing Proportion Effect

0.81

(0.67; 0.95)

0.90

(0.72; 1.08)

Rate Effect

"Compromised"

1.09

(0.79; 1.37)

2.11

(1.75; 2.48)

"Normal"

1.90

(1.67; 2.19)

2.08

(1.77; 2.39)

Total Disparity

3.81

(3.53; 4.07)

5.09

(4.81; 5.40)

LCI = lower 95% confidence interval; UCI = upper 95% confidence interval

Birth Weight and the Racial Disparity

A further decomposition of the subpopulation specific racial disparities into direct (independent of birth weight) and indirect (potentially causal through birth weight) effects based on relative risks is summarised in Table

Subpopulation specific racial effect (relative risk) of infant mortality # decomposed into direct and indirect multiplicative factors

**Racial Effect**

**Females**

**Males**

**estimate**

**LCI UCI**

**estimate**

**LCI UCI**

"Normal" Subpopulation

Relative Risk

1.89

(1.71; 2.14)

1.77

(1.63; 1.98)

Direct Factor

2.11

(1.87; 2.49)

2.00

(1.71; 2.68)

Indirect Factor

0.89

(0.78; 1.01)*

0.88

(0.71; 1.00)*

"Compromised" Subpopulation

Relative Risk

5.19

(4.29; 6.16)

5.12

(4.37; 6.08)

Direct Factor

0.18

(0.01; 0.69)

0.43

(0.11; 1.55)*

Indirect Factor

29.38

(13.83; 91.15)

11.80

(4.31; 33.46)

Total Birth Cohort

Relative Risk

3.10

(2.83; 3.41)

3.09

(2.89; 3.37)

^{#}: mortalities are calculated by the method of direct standardization using European American births as the reference (standard) population

LCI = lower 95% confidence interval; UCI = upper 95% confidence interval

*: relative risk or factor is not significantly different from 1 based on the bias-adjusted 95% CI

Among "normal" births, there is a significant direct effect of being African American that contributes to excess mortality in African American births (Table **reduce **African American mortality! The direction of this association is surprising given that mean birth weight of "normal" African American births is significantly smaller than that of European Americans (Table

Among "compromised" births, on the other hand, the indirect effect is significant and contributes to the excess African American infant mortalities (Table **reduces **infant mortality (Table

Overall, a direct effect on the "normal" subpopulation is responsible for the higher infant mortality of African American births in the normal birth weight range (Figures

Discussion

CDDmlr was designed to examine the Wilcox-Russell hypothesis

The analyses are based on the public use samples of the NCHS linked birth death files. These have very large sample sizes (Table

One technical difficulty in models of this kind is estimating unbiased direct and indirect effects. The qualitative analysis in Hernández-Diaz et al. ^{nd }degree polynomial of Z-scored birth weight standardized with respect to these Gaussians. This eliminates the main effects (associations) of race and birth weight and the logistic regressions can then estimate the direct effect of race on infant mortality versus potential interaction effects of race and birth weight on infant mortality. Direct and indirect effects can be estimated using procedures similar to direct standardization

One advantage of the decision theory approach is that the assumptions concerning the existence of counterfactuals are not necessary. However, like counterfactual methods, the same strong unmeasured covariate assumptions are required. In particular; a) no unmeasured covariates which affect the stressor (race in this case) and the racial disparities in infant mortality, b) no unmeasured confounding of race and birth weight, and c) no unmeasured confounding of birth weight and infant mortality. Assumption a is necessary to estimate total racial disparities, all three are needed to estimate "generated direct effects"

These assumptions may be less of a problem with race than with other variables such as smoking, which have more precise definitions. Race is typically considered to be socially constructed and defined as that collection of variables (some of which may be observable and some of which are currently unobservable) that are associated in some way with reported race. Given this view, all confounders of racial effects on birth weight or infant mortality, are integral parts of the definition of race. This is the assumption generally used when reporting total "racial disparities", such as those presented in Table

Based on the "pediatric paradox", Wilcox has argued that racial disparities may be underestimated due to unmeasured confounding

Model-based adjustment of this effect yields relative risks of 4.2 and 3.6 for African American female and male births, respectively. These are higher than the predicted total relative risks in Table

We assume that unmeasured confounding of birth weight and infant mortality (assumption c) is responsible for the reverse-J shape of the birth weight specific mortality curve ^{nd }degree polynomial, however, is a relatively flexible function, and is considered to provide an optimal fit to birth weight specific mortality in the homogeneous case

Moreover, the CDDmlr model corrects for some unmeasured confounding of birth weight and infant mortality, referred to as "normal" versus "compromised" births. It is unlikely that dividing birth cohorts into two Gaussian subpopulations will account for all of the unmeasured confounding between birth weight and infant mortality. Nevertheless, the two subpopulations display significantly different mortality patterns indicating that the CDDmlr model accounts for some otherwise unmeasured heterogeneity

The statistical results presented above (Tables

On the other hand, there is a substantial indirect effect, which disadvantages African American infant mortality among "compromised" births (Table

Overall, the findings suggest that interventions with respect to birth weight will not reduce racial disparities in mortality among "normal" births, but might reduce them among "compromised" births. Identification of the exact mechanisms and whether birth weight plays a "causal" role conditional on "compromised" birth will require additional analysis, i.e. control of potential confounding. The "compromised" subpopulation accounts for about 29-41% of the observed racial disparity for females and males respectively (Table

If our hypothesis concerning the selection effects of fetal loss on observed racial disparities is correct, then the total racial disparity is higher than observed, and the proportion of the disparity due to the "compromised" subpopulation is larger than observed. The confounding, represented by the mixing proportion, accounts for an additional 17-21% of the observed racial disparity for males and females, respectively (Table

Conclusions

Our results support the Wilcox-Russell

The true racial disparity in infant mortality between African and European American birth cohorts may be obscured by unobserved heterogeneity. This heterogeneity may be due to differential fetal loss, which appears to account for the "pediatric paradox". The true racial disparities may also be obscured by lack of consistently reporting births at below 500 grams in the NCHS linked birth death files.

Part of the racial disparity is due to mixing proportion effects, i.e. a larger number of "compromised" births among African Americans than European Americans. Reducing the disparity in the size of "compromised" births will somewhat reduce racial disparities. If all "compromised" births could be eliminated (i.e. eliminating all possible statistically significant birth weight dependent effects), the racial disparities would decrease slightly (1.9 and 1.8 for females and males, respectively) from the currently observed level (2.1 for both sexes). Therefore, the complete elimination of racial disparities in infant mortality requires the elimination of birth weight independent (i.e. direct) effects, as well as any birth weight dependent (i.e. indirect) effects.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

TBG planned the analysis and wrote the manuscript. FF and EKO carried out the analysis and helped revise the manuscript. AGD consulted on statistical matters and also helped revise the manuscript. All authors have read and approved this manuscript.

Acknowledgements

This project is supported by NIEHS R01 HD037405. We'd like to thank Dr. Howard Stratton for his many useful discussions and extensive comments on an early draft. We'd also like to thank Kiersten Fussell for her work in preparing the final draft.

Pre-publication history

The pre-publication history for this paper can be accessed here: