American Journal of Epidemiology Advance Access originally published online on August 24, 2006
American Journal of Epidemiology 2006 164(11):1121-1123; doi:10.1093/aje/kwj276
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Invited Commentary: The Perils of Birth Weight—A Lesson from Directed Acyclic Graphs
From the Epidemiology Branch, National Institute of Environmental Health Sciences, Durham, NC
Correspondence to Dr. Allen J. Wilcox, Epidemiology Branch, MD A3-05, National Institute of Environmental Health Sciences, P.O. Box 12233, Durham, NC 27709 (e-mail: wilcox{at}niehs.nih.gov).
Received for publication February 24, 2006. Accepted for publication March 15, 2006.
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The strong association of birth weight with infant mortality is complicated by a paradoxical finding: Small babies in high-risk populations usually have lower risk than small babies in low-risk populations. In this issue of the Journal, Hernández-Díaz et al. (Am J Epidemiol 2006;164:1115–20) address this "birth weight paradox" using directed acyclic graphs (DAGs). They conclude that the paradox is the result of bias created by adjustment for a factor (birth weight) that is affected by the exposure of interest and at the same time shares causes with the outcome (mortality). While this bias has been discussed before, the DAGs presented by Hernández-Díaz et al. provide more firmly grounded criticism. The DAGs demonstrate (as do many other examples) that seemingly reasonable adjustments can distort epidemiologic results. In this commentary, the birth weight paradox is shown to be an illustration of Simpson's Paradox. It is possible for a factor to be protective within every stratum of a variable and yet be damaging overall. Questions remain as to the causal role of birth weight.
birth weight; confounding factors (epidemiology); infant, low birth weight; infant mortality; smoking
Abbreviations: DAG, directed acyclic graph
In this issue of the Journal, Hernández-Díaz et al. (1) use directed acyclic graphs (DAGs) to tackle the contentious problem of birth weight analysis. DAGs provide a rigorous tool of visual logic, dissecting causal pathways to uncover bias. The pathways being dissected here are those leading to infant mortality. Does adjustment for birth weight in the analysis of infant mortality produce bias? Hernández-Díaz et al. show that it does.
On the face of it, the relation of birth weight to mortality appears simple and direct. Newborn mortality is higher by at least 100-fold among babies with the lowest birth weights. This is true even when the sample is restricted to full-term births. The remarkable strength of this association has led birth weight to be regarded as key to infant mortality. Adjustments for birth weight are common.
But there is a fly in this ointment. Small babies from a low-risk group (e.g., mothers who don't smoke) often have higher mortality than small babies from a high-risk group (smokers). This "birth weight paradox" is found in comparisons of Whites and African Americans, persons of high and low socioeconomic status, singletons and twins, and others (2).
Earlier authors (2, 3) have regarded the birth weight paradox as a reason for caution in the analysis of infant mortality. For example, the paradox argues against standardizing mortality by absolute birth weight (3). Standardization assumes homogeneous mortality effects across strata (4), an assumption which birth weight clearly does not satisfy. Indeed, given the reversal of risk among weight-specific categories, any analysis based on stratification into categories of absolute birth weight must be suspect. These concerns have so far failed to dissuade most researchers from their usual practices.
DAGs may help to change this.
What does the logic of DAGs contribute to this controversy? With smoking as their exposure of interest, Hernández-Díaz et al. (1) show that the birth weight paradox can be explained by the presence of other unmeasured factors that reduce birth weight and increase mortality. While the authors are cautious in their interpretation, their analysis leaves little doubt that routine birth weight adjustment in the analysis of infant mortality will distort the results.
Do DAGs tell us anything more? Hernández-Díaz et al. provide two possible DAGs for the observed relations among smoking, birth weight, and mortality (see their figure 3, parts 3.6 and 3.7) (1). One DAG lacks any causal connection between birth weight and mortality. The other has only a partial connection, through the unmeasured confounder. From the standpoint of DAGs, no causal arrow from birth weight to mortality seems to be necessary in order to capture the empirical relations among these variables. In light of these analyses, it is reasonable to ask whether low birth weight is in itself a cause of mortality (5).
This question of causality is not merely academic: The policies of the World Health Organization and other health agencies encourage interventions designed to increase birth weight—for example, through improvement of maternal nutrition. Such interventions are frustratingly ineffective at best; some have even been dangerous (6). In the quest to improve infant health, might interventions focused on birth weight ultimately be futile?
Returning to more academic questions, it is curious that the birth weight paradox is seen specifically among small babies. Hernández-Díaz et al. do not explore this, but the answer seems to lie in the particular shape of the weight-specific mortality curve (see their figure 2). If the mortality curve were instead straight (i.e., with a simple log-linear decline over the whole birth weight distribution), the birth weight paradox would be present at every weight. Such an example is shown here in figure 1. Population B has smaller infants than population A and lower mortality at each given birth weight. However, overall infant mortality is higher for population B (see table 1 for data).
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A naïve interpretation of this figure might be that the exposure improves weight-specific mortality, with this benefit being cancelled out by lower birth weights. (Indeed, the birth weight paradox has generated just such discussions (7).) Alternatively, we can see the figure as an illustration of Simpson's Paradox (8), in which a factor associated with risk within subsets of a population has the opposite association for the population as a whole. The bias illustrated in figure 1 is due to stratification of a variable (birth weight) that is affected by the exposure of interest and shares unmeasured causes with the outcome (mortality) (9).
Conversion of birth weight to "z" scores (with units based on standard deviations of the normal distribution) has been used to assess weight-specific mortality (2). Such a scale preserves the rank order of birth weights but not their absolute values. The use of relative birth weight resolves the typical birth weight paradox (2) (at least crudely) and would remove Simpson's Paradox in the example. Still, it is not obvious what z-score adjustment represents in the language of DAGs. This might be an interesting question for Hernández-Díaz et al. to explore.
It is the mantra of observational studies that we can never rule out unobserved confounding. Perhaps we need a second mantra: Never adjust for covariates just because they are handy. Epidemiologists cannot depend on adjustments (or stratifications of any sort) to bring results closer to the truth. Indeed, as Hernández-Díaz et al. remind us, baseless adjustments are easily worse than no adjustment at all. If low birth weight brings peril, such peril may be not to the babies but to the analysts.
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ACKNOWLEDGMENTS |
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This work was supported by the Intramural Research Program of the NIH, National Institute of Environmental Health Sciences.
Conflict of interest: none declared.
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References |
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TOPABSTRACTReferences |
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- Hernández-Díaz S, Schisterman EF, Hernan MA. (2006) The birth weight "paradox" uncovered? Am J Epidemiol 164:1115–20.
[Abstract/Free Full Text] - Wilcox AJ. (2001) On the importance—and the unimportance—of birth weight. Int J Epidemiol 30:1233–41.
[Abstract/Free Full Text] - Wilcox AJ and Russell IT. (1983) Perinatal mortality: standardizing for birthweight is biased. Am J Epidemiol 118:857–64.
[Abstract/Free Full Text] - Fleiss JL. (1973) Statistical methods for rates and proportions. 1st ed (John Wiley and Sons, Inc, New York, NY).
- Basso O, Wilcox AJ, Weinberg CR. (2006) Birth weight and mortality: causality or confounding? Am J Epidemiol 164:303–11.
[Abstract/Free Full Text] - Rush D, Stein Z, Susser M. (1980) A randomized controlled trial of prenatal nutritional supplementation in New York City. Pediatrics 65:683–97.
[Abstract/Free Full Text] - Collins JW and David RJ. (1990) Differential survival rates among low-birth-weight black and white infants in a tertiary care hospital. Epidemiology 1:16–20.[Medline]
- Simpson EH. (1951) The interpretation of interaction in contingency tables. J R Stat Soc B 2:238–41.
- Weinberg CR. (2005) Invited commentary: Barker meets Simpson. Am J Epidemiol 161:33–5.
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Related articles in Am. J. Epidemiol.:
- The Birth Weight "Paradox" Uncovered?
- Sonia Hernández-Díaz, Enrique F. Schisterman, and Miguel A. Hernán
Am. J. Epidemiol. 2006 164: 1115-1120.[Abstract] [FREE Full Text]
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  S. Hernandez-Diaz, E. F. Schisterman, and M. A. Hernan Hernandez-Diaz et al. Respond to "The Perils of Birth Weight" Am. J. Epidemiol., December 1, 2006; 164(11): 1124 - 1125. [Full Text] [PDF]
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