European Journal of Epidemiology

, Volume 33, Issue 6, pp 523–530 | Cite as

Two denominators for one numerator: the example of neonatal mortality

  • Quaker E. Harmon
  • Olga Basso
  • Clarice R. Weinberg
  • Allen J. Wilcox


Preterm delivery is one of the strongest predictors of neonatal mortality. A given exposure may increase neonatal mortality directly, or indirectly by increasing the risk of preterm birth. Efforts to assess these direct and indirect effects are complicated by the fact that neonatal mortality arises from two distinct denominators (i.e. two risk sets). One risk set comprises fetuses, susceptible to intrauterine pathologies (such as malformations or infection), which can result in neonatal death. The other risk set comprises live births, who (unlike fetuses) are susceptible to problems of immaturity and complications of delivery. In practice, fetal and neonatal sources of neonatal mortality cannot be separated—not only because of incomplete information, but because risks from both sources can act on the same newborn. We use simulations to assess the repercussions of this structural problem. We first construct a scenario in which fetal and neonatal factors contribute separately to neonatal mortality. We introduce an exposure that increases risk of preterm birth (and thus neonatal mortality) without affecting the two baseline sets of neonatal mortality risk. We then calculate the apparent gestational-age-specific mortality for exposed and unexposed newborns, using as the denominator either fetuses or live births at a given gestational age. If conditioning on gestational age successfully blocked the mediating effect of preterm delivery, then exposure would have no effect on gestational-age-specific risk. Instead, we find apparent exposure effects with either denominator. Except for prediction, neither denominator provides a meaningful way to define gestational-age-specific neonatal mortality.


Neonatal mortality Fetal pathology Preterm delivery Gestational-age paradox 



The authors gratefully acknowledge the comments on earlier drafts by Dr. Donna Baird, Dr. David Umbach, and anonymous reviewers.


This research has been supported in part by the Intramural Research Program of the National Institute of Environmental Health Sciences, National Institutes of Health.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Informed consent

Publicly available data with no identifying details were used. For this type of study formal consent is not required.

Supplementary material

10654_2018_373_MOESM1_ESM.docx (102 kb)
Supplementary material 1 (DOCX 102 kb)
10654_2018_373_MOESM2_ESM.xlsx (70 kb)
Supplementary material 2 (XLSX 70 kb)


  1. 1.
    Wang H, Liddell CA, Coates MM, Mooney MD, Levitz CE, Schumacher AE, et al. Global, regional, and national levels of neonatal, infant, and under-5 mortality during 1990-2013: a systematic analysis for the Global Burden of Disease Study 2013. Lancet. 2014;384(9947):957–79.CrossRefPubMedPubMedCentralGoogle Scholar
  2. 2.
    Linked Birth/Infant Death Records 2007–2013, as compiled from data provided by the 57 vital statistics jurisdictions through the Vital Statistics Cooperative Program, on CDC WONDER On-line Database [database on the Internet] 2015. Accessed 28 Aug 2015.
  3. 3.
    Wilcox AJ, Weinberg CR, Basso O. On the pitfalls of adjusting for gestational age at birth. Am J Epidemiol. 2011;174(9):1062–8.CrossRefPubMedPubMedCentralGoogle Scholar
  4. 4.
    Kramer MS, Zhang X, Platt RW. Analyzing risks of adverse pregnancy outcomes. Am J Epidemiol. 2014;179(3):361–7.CrossRefPubMedGoogle Scholar
  5. 5.
    Platt RW, Joseph KS, Ananth CV, Grondines J, Abrahamowicz M, Kramer MS. A proportional hazards model with time-dependent covariates and time-varying effects for analysis of fetal and infant death. Am J Epidemiol. 2004;160(3):199–206.CrossRefPubMedGoogle Scholar
  6. 6.
    VanderWeele TJ, Mumford SL, Schisterman EF. Conditioning on intermediates in perinatal epidemiology. Epidemiology. 2012;23(1):1–9.CrossRefPubMedPubMedCentralGoogle Scholar
  7. 7.
    Basso O. Implications of using a fetuses-at-risk approach when fetuses are not at risk. Paediatr Perinat Epidemiol. 2016;30(1):3–10.CrossRefPubMedGoogle Scholar
  8. 8.
    Joseph KS. Incidence-based measures of birth, growth restriction, and death can free perinatal epidemiology from erroneous concepts of risk. J Clin Epidemiol. 2004;57(9):889–97.CrossRefPubMedGoogle Scholar
  9. 9.
    Wilcox AJ, Weinberg CR, Basso O, Harmon QE. Re: “Analyzing risks of adverse pregnancy outcomes”. Am J Epidemiol. 2015;181(3):218.CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Ananth CV, Schisterman EF. Confounding, causality, and confusion: the role of intermediate variables in interpreting observational studies in obstetrics. Am J Obstet Gynecol. 2017;217(2):167–75.CrossRefPubMedPubMedCentralGoogle Scholar
  11. 11.
    Chen XK, Wen SW, Smith G, Yang Q, Walker M. Pregnancy-induced hypertension is associated with lower infant mortality in preterm singletons. BJOG. 2006;113(5):544–51.CrossRefPubMedGoogle Scholar
  12. 12.
    Papiernik E, Alexander GR, Paneth N. Racial differences in pregnancy duration and its implications for perinatal care. Med Hypotheses. 1990;33(3):181–6.CrossRefPubMedGoogle Scholar
  13. 13.
    Cheung YB, Yip P, Karlberg J. Mortality of twins and singletons by gestational age: a varying-coefficient approach. Am J Epidemiol. 2000;152(12):1107–16.CrossRefPubMedGoogle Scholar
  14. 14.
    Ananth CV, Smulian JC, Vintzileos AM. The effect of placenta previa on neonatal mortality: a population-based study in the United States, 1989 through 1997. Am J Obstet Gynecol. 2003;188(5):1299–304.CrossRefPubMedGoogle Scholar
  15. 15.
    Naeye RL. Causes of perinatal mortality in the US Collaborative Perinatal Project. JAMA-J Am Med Assoc. 1977;238(3):228–9.CrossRefGoogle Scholar
  16. 16.
    Silver RM, Varner MW, Reddy U, Goldenberg R, Pinar H, Conway D, et al. Work-up of stillbirth: a review of the evidence. Am J Obstet Gynecol. 2007;196(5):433–44.CrossRefPubMedPubMedCentralGoogle Scholar
  17. 17.
    Smith GCS. Quantifying the risk of different types of perinatal death in relation to gestational age: researchers at risk of causing confusion. Paediatr Perinat Epidemiol. 2016;30(1):18–9.CrossRefPubMedGoogle Scholar
  18. 18.
    The Stillbirth Collaborative Network Writing Group. Causes of death among stillbirths. JAMA J Am Med Assoc. 2011;306(22):2459–68.CrossRefGoogle Scholar
  19. 19.
    Wou K, Ouellet MP, Chen MF, Brown RN. Comparison of the aetiology of stillbirth over five decades in a single centre: a retrospective study. BMJ Open. 2014;4(6):e004635.CrossRefPubMedPubMedCentralGoogle Scholar
  20. 20.
    Hoyert DL, Gregory EC. Cause of fetal death: data from the fetal death report, 2014. Natl Vital Stat Rep. 2016;65(7):1–25.PubMedGoogle Scholar
  21. 21.
    Heron M, Hoyert DL, Murphy SL, Xu J, Kochanek KD, Tejada-Vera B. Deaths: final data for 2006. Natl Vital Stat Rep. 2009;57(14):1–134.PubMedGoogle Scholar
  22. 22.
    Birth Cohort Linked Birth-Infant Death Data Files [database on the Internet] 2006. Accessed 10 July 2015.
  23. 23.
    Fetal Death Data File [database on the Internet] 2006. Accessed 16 July 2015.
  24. 24.
    Basso O, Wilcox A. Mortality risk among preterm babies: immaturity versus underlying pathology. Epidemiology. 2010;21(4):521–7.CrossRefPubMedPubMedCentralGoogle Scholar
  25. 25.
    Talge NM, Mudd LM, Sikorskii A, Basso O. United States birth weight reference corrected for implausible gestational age estimates. Pediatrics. 2014;133(5):844–53.CrossRefPubMedGoogle Scholar
  26. 26.
    Yudkin PL, Wood L, Redman CW. Risk of unexplained stillbirth at different gestational ages. Lancet. 1987;1(8543):1192–4.PubMedCrossRefGoogle Scholar
  27. 27.
    Sibai BM, Caritis SN, Hauth JC, MacPherson C, VanDorsten JP, Klebanoff M, et al. Preterm delivery in women with pregestational diabetes mellitus or chronic hypertension relative to women with uncomplicated pregnancies. The National Institute of Child Health and Human Development Maternal–Fetal Medicine Units Network. Am J Obstet Gynecol. 2000;183(6):1520–4.CrossRefPubMedGoogle Scholar
  28. 28.
    Feig DS, Hwee J, Shah BR, Booth GL, Bierman AS, Lipscombe LL. Trends in incidence of diabetes in pregnancy and serious perinatal outcomes: a large, population-based study in Ontario, Canada, 1996–2010. Diabetes Care. 2014;37(6):1590–6.CrossRefPubMedGoogle Scholar
  29. 29.
    Knorr S, Stochholm K, Vlachova Z, Bytoft B, Clausen TD, Jensen RB, et al. multisystem morbidity and mortality in offspring of women with type 1 diabetes (the EPICOM study): a register-based prospective cohort study. Diabetes Care. 2015;38(5):821–6.CrossRefPubMedGoogle Scholar
  30. 30.
    Basso O, Wilcox AJ. Might rare factors account for most of the mortality of preterm babies? Epidemiology. 2011;22(3):320–7.CrossRefPubMedPubMedCentralGoogle Scholar
  31. 31.
    Platt RW. The fetuses-at-risk approach: an evolving paradigm. In: Louis GB, Platt RW, editors. Reproductive and perinatal epidemiology. Oxford: Oxford University Press; 2011.Google Scholar
  32. 32.
    Moster D, Lie RT, Markestad T. Long-term medical and social consequences of preterm birth. N Engl J Med. 2008;359(3):262–73.CrossRefPubMedGoogle Scholar
  33. 33.
    Lisonkova S, Paré E, Joseph K. Does advanced maternal age confer a survival advantage to infants born at early gestation? BMC Pregnancy Childbirth. 2013;13(1):87.CrossRefPubMedPubMedCentralGoogle Scholar
  34. 34.
    Ananth CV, VanderWeele TJ. Placental abruption and perinatal mortality with preterm delivery as a mediator: disentangling direct and indirect effects. Am J Epidemiol. 2011;174(1):99–108.CrossRefPubMedPubMedCentralGoogle Scholar
  35. 35.
    Auger N, Naimi AI, Fraser WD, Healy-Profitos J, Luo ZC, Nuyt AM, et al. Three alternative methods to resolve paradoxical associations of exposures before term. Eur J Epidemiol. 2016;31(10):1011–9.CrossRefPubMedGoogle Scholar
  36. 36.
    VanderWeele TJ. Commentary: resolutions of the birthweight paradox: competing explanations and analytical insights. Int J Epidemiol. 2014;43(5):1368–73.CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply [2018] 2018

Authors and Affiliations

  1. 1.National Institute of Environmental Health SciencesDurhamUSA
  2. 2.Department of Obstetrics and GynecologyMcGill UniversityMontrealCanada
  3. 3.Department of Epidemiology, Biostatistics and Occupational HealthMcGill UniversityMontrealCanada
  4. 4.Biostatistics and Computational Biology BranchNational Institute of Environmental Health SciencesDurhamUSA

Personalised recommendations