title: Z-scores and the birthweight paradox.
abstract: Investigators have long puzzled over the observation that low-birthweight babies of smokers tend to fare better than low-birthweight babies of non-smokers. Similar observations have been made with regard to factors other than smoking status, including socio-economic status, race and parity. Use of standardised birthweights, or birthweight z-scores, has been proposed as an approach to resolve the crossing of the curves that is the hallmark of the so-called birthweight paradox. In this paper, we utilise directed acyclic graphs, analytical proofs and an extensive simulation study to consider the use of z-scores of birthweight and their effect on statistical analysis. We illustrate the causal questions implied by inclusion of birthweight in statistical models, and illustrate the utility of models that include birthweight or z-scores to address those questions. Both analytically and through a simulation study we show that neither birthweight nor z-score adjustment may be used for effect decomposition. The z-score approach yields an unbiased estimate of the total effect, even when collider-stratification would adversely impact estimates from birthweight-adjusted models; however, the total effect could have been estimated more directly with an unadjusted model. The use of z-scores does not add additional information beyond the use of unadjusted models. Thus, the ability of z-scores to successfully resolve the paradoxical crossing of mortality curves is due to an alteration in the causal parameter being estimated (total effect), rather than adjustment for confounding or effect decomposition or other factors.
authors.affiliation: Epidemiology Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD 20892, USA. schistee@mail.nih.gov
authors.forename: Enrique F
authors.initials: EF
authors.lastname: Schisterman
authors.forename: Brian W
authors.initials: BW
authors.lastname: Whitcomb
authors.forename: Sunni L
authors.initials: SL
authors.lastname: Mumford
authors.forename: Robert W
authors.initials: RW
authors.lastname: Platt
mesh_terms: D001724:Birth Weight; D015986:Confounding Factors, Epidemiologic; D005260:Female; D006801:Humans; D007226:Infant Mortality; D007230:Infant, Low Birth Weight; D007231:Infant, Newborn; D008297:Male; D008425:Maternal Behavior; D015233:Models, Statistical; D012307:Risk Factors; D012907:Smoking / Q000009:adverse effects* / Q000453:epidemiology; D012959:Socioeconomic Factors; D014481:United States / Q000453:epidemiology
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