1 Department of Pediatrics, Faculty of Medicine, McGill University, Montreal, Quebec, Canada.
2 Department of Epidemiology and Biostatistics, Faculty of Medicine, McGill University, Montreal, Quebec, Canada.
3 Perinatal Epidemiology Research Unit, Department of Obstetrics and Gynecology and Pediatrics, Faculty of Medicine, Dalhousie University, Halifax, Nova Scotia, Canada.
4 Section of Epidemiology and Biostatistics, Department of Obstetrics, Gynecology and Reproductive Sciences, Robert Wood Johnson Medical School, University of Medicine and Dentistry of New Jersey, New Brunswick, NJ.
Received for publication May 17, 2004; accepted for publication May 18, 2004.
We are delighted that our proposed alternative approach to analyzing fetal and infant mortality (1) has stirred up such vigorous and thoughtful discussion (2, 3). Our approach is based on alternative denominators (i.e., fetuses at risk), which, in our view, has a sound biologic and clinical underpinning. We explicitly model the risk of death for the fetus or infant at specific times postconception. This is a logical extension and operationalization of previous work (46), in which we proposed incidence-based measures of birth, growth restriction, and death (including a model of "obstetric mortality").
We like Wilcox and Weinbergs (2) suggestion that time since conception and time since birth should be included as separate time axes in the same survival model. The hazard due to livebirth is indeed highest in the first few minutes and hours of life and declines sharply thereafter, but it differs substantially depending on gestational age. While our model does not account for this sharp rise and fall in the hazard shortly after a live preterm birth, that is certainly worth considering in future refinements and extensions. Using time since birth as a continuous covariate with a declining hazard ratio as time increases is one potential approach. However, modeling this covariate would require careful attention to the assumptions of the underlying Cox model.
Wilcox and Weinberg suggest that perinatal epidemiologists have been "spoiled" by the easy availability of vital statistics data and that causal pathways should be examined much more closely. They bring up a specific example of a risk factor for which preterm delivery is on the causal path between the risk factor and mortality. However, our model requires no explicit adjustment for whether the child has been born. The effect of a factor that operates through preterm delivery is then estimated without bias. On the other hand, models that condition on gestational age (either explicitly or through birth weight) can address the causal effect of only those factors that operate independently of gestational age.
We agree with Klebanoff and Schoendorf (3) that removing the crossing of perinatal mortality curves is not the primary goal of statistical modeling of fetal and infant mortality. Rather, the goal is to provide a statistically sensible model that reflects the underlying biology. The fetuses-at-risk approach makes it clear that observed births at preterm gestational ages represent different proportions of the total number of conceptions for, for example, Blacks versus Whites. To understand the biology of the crossover, it is important first to understand how the source population (conceptions) develops into the observed population of births at specific gestational ages.
We thank Drs. Wilcox, Weinberg, Klebanoff, and Schoendorf for their careful and insightful comments, which have helped clarify and illustrate the complexity of appropriate measurement of risk of fetal and infant mortality. We hope that continuing discussion and research will lead to a better understanding of the determinants of birth and of death during fetal life and infancy.
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