Two time scales are commonly used in perinatology and these measure the duration of life in utero (gestational age, which is anchored to the first day of the last menstrual period) and the duration of life after birth (chronologic age, which is anchored to birth). The clinical problems caused by these dual overlapping scales are generally recognized, especially by clinicians in neonatology, who resort to a single scale for expressing age, namely, post-menstrual age or corrected gestational age. Such recognition is also reflected in the evolution of Bronchopulmonary Dysplasia, which was historically defined as a requirement for oxygen at more than 28 days after birth but now refers to a requirement for oxygen or ventilatory support at 36 weeks of post-menstrual age 47. An important aspect of the use of dual time scales that is not related to duration issues is the qualitative label that is assigned to death depending on whether death occurs before or after the second time scale becomes operational. Thus, a fetus who dies in utero at 38 weeks is a stillbirth but another who dies at 2 weeks of chronologic age after birth at 36 weeks is a neonatal death. Birth has a preeminent position in qualifying life events for reasons that appear to be more sociologic than biologic.

Gestational age is often treated as a determinant in perinatal epidemiologic studies. As a determinant, gestational age at birth (and birth weight, which is closely correlated with gestational age) serves as a powerful predictor of death and other adverse perinatal outcomes. However, from an epidemiologic perspective, gestational age is in fact follow up (survival) time and should be treated as such in causal models.

The incidence rate of any pregnancy related event at any gestation is defined as the number of new cases of the event that occur within that gestational week divided by the number of candidates at risk for the event at that gestation. Thus, the incidence of birth (Tables 1, 2) is calculated by dividing the number of births at any gestation by the number of fetuses at risk of birth at that gestation 155758. The concept is appropriately extended to all relevant perinatal phenomena including the incidence of labor induction, cesarean delivery 1559 and pregnancy complications (such as hyperemesis gravidarum 60 preeclampsia and chorioamnionitis 6162, Figure 3). In fact, documenting the incidence pattern of most pregnancy complications over the course of pregnancy has not been undertaken seriously. Although the exact time when a pregnancy complication occurs may sometimes be difficult to ascertain, this is not a sufficient reason for abandoning the study of the incidence patterns of pregnancy complications.

The incidence of growth restriction is a good example of an index whose estimation presents a challenge. Although routine obstetric practice includes screening for and diagnosis of growth restriction, the technology is insufficiently advanced to permit valid and complete ascertainment of all new cases at each gestation 636465. Given this limitation, an alternative index, namely, the incidence of revealed SGA (Tables 1, 2, Figure 1c, Figure 3) may be calculated by dividing the number of SGA births at any gestation by the number of fetuses at risk of SGA birth at that gestation 1516575859. The primary utility in estimating this proxy incidence rate is in order to approximate the incidence pattern of growth restriction with increasing gestational duration i.e., to estimate whether it increases, decreases or remains constant. The measure cannot provide the absolute rate of SGA at any gestation since the numerator of the index is dependant on birth (hence the term "revealed"). Improvements in technology will permit quantification of the absolute rate (incidence) of growth restriction at each gestation in the future.

The fetuses at risk approach for stillbirth is a survival analysis model with censoring of subjects (fetuses) at birth. This gestational age-specific stillbirth calculation provides estimates of the cumulative incidence of fetal death at each week of gestation and approximates the incidence density (hazard) of stillbirth. The extended fetuses at risk model integrates perinatal death and serious neonatal morbidity (e.g., severe respiratory distress syndrome, severe intraventricular hemorrhage, etc) into a single framework (Figure 4) since these events all have their origins in pregnancy, labour or birth 15166667. This is consistent with principles ingrained in routine obstetric practice and state-of-the-art clinical trials 6869 where the definitive obstetric outcome embraces perinatal mortality and serious neonatal morbidity. Similarly, with recent literature 707172 suggesting that cerebral palsy has a predominantly prenatal origin (i.e., critical neurologic injury occurs before birth), this outcome is also assigned to the point of birth, despite being diagnosed years later. Combining stillbirth, neonatal death and serious neonatal morbidity into a single composite outcome is consistent with traditions in obstetrics and is justified by the broadly overlapping multifactorial etiology that characterizes these distinct entities 15.

As mentioned, the extended fetuses at risk model most deviates from traditional models with respect to events that occur after birth and yet have a prenatal etiology. Under the traditional model of perinatal death, neonatal deaths occur among infants in the first month after birth and the unborn fetus is not a candidate for neonatal death. However from a broad biological, obstetric and ultimately epidemiologic point of view, a fetus at any gestation is at risk of stillbirth and neonatal death at that gestation. If one considers a woman at 28 weeks gestation with severe preeclampsia and fetal compromise, the risk of stillbirth is easy to conceptualize. The risk of neonatal death is substantial as well and can follow either premature labour or medically indicated delivery. The same risks apply in concept to a woman with a healthy pregnancy at 28 weeks gestation, despite the magnitude of the risks being considerably smaller 15. Thus, although neonatal deaths literally occur among infants, fetuses can be considered candidates for neonatal death as well. This is analogous to the calculation of age-specific rates of death from breast cancer. Such rates are calculated using all women in the population as the denominator (i.e., as candidates for death from breast cancer), although one could argue that death from breast cancer can only occur among women with breast cancer.

The extended fetuses at risk formulation of death provides 2 alternative models that treat time per epidemiologic principles (as survival time and on a single time scale). In the first model, namely, the comprehensive model of death, time is measured on the scale of post-menstrual (or post conceptional) age with fetuses/infants censored at death 15. Birth is ignored as a event (for truncating the original time scale) and no distinction is made between deaths that occur before and after birth. The epidemiologic risk set at any point in post-menstrual time is constituted by the fetuses/infants at risk of death at that point in time 15. When this framework is integrated into a proportional hazards model, birth may be introduced as a time-dependant covariate with time-varying effects 73. In the second model, namely, the obstetric model of death, time is measured on the scale of gestational age with fetuses censored at birth or death. All deaths that have their origins in prenatal or labour and delivery events are deemed relevant to obstetrics. Thus, as per traditions in obstetrics, stillbirths and neonatal deaths (and serious neonatal morbidity) are assigned to the point of birth. The epidemiologic risk set for such obstetric outcomes is constituted by the fetuses at risk for such events, namely, all unborn fetuses at the gestational age in question (Figure 4).

The fetuses at risk formulation brings coherence to the study of perinatal phenomena. It shows that the incidence of pregnancy complications such as preeclampsia and chorioamnionitis increases as gestational age advances 6162. Revealed SGA rates also increase with increasing gestational age (Figure 1c) and presage the rise in perinatal mortality rates 1516575859. Gestational age-specific perinatal mortality curves do not intersect in comparisons by smoking status, plurality (Figure 1c), race, parity, infant sex, etc 575859. Smokers have higher rates of revealed SGA and perinatal death than non-smokers at all gestational ages 58 and twins 57 have higher rates of revealed SGA and perinatal death than singletons at all gestational ages (Figure 1c). Similarly, the incidence of birth, labor induction and cesarean delivery show patterns that are congruent with patterns of revealed SGA and death 1557585967. The rising patterns of gestational age-specific revealed SGA and perinatal death also offer a preliminary justification for medically-indicated early delivery. Finally, the fetuses at risk approach provides insights into issues as diverse as the etiology of cerebral palsy 74 and the need for customized fetal growth standards 5975. Specifically, it shows that the rate of critical neurologic injury that causes cerebral palsy increases with advancing gestational age 74 and suggests that the pregnancy complications (which precede preterm birth) are the cause of cerebral palsy (and not preterm birth itself). With regards to fetal growth standards, the fetuses at risk formulation shows that perinatal mortality patterns are consistent with separate fetal growth standards for males and females but not with the available separate standards for blacks and whites in the United States 59.

The fetuses at risk formulation faces its most serious challenge from the traditional idea that perinatal mortality declines as gestational age increases. Indeed, this latter inference appears intuitive and is corroborated by the readily apparent relationship between birth weight and perinatal mortality. Despite the socially important prognostic purpose served by the traditional model of perinatal death, it is not appropriate as a causal model. The use of dual overlapping time scales for life in utero (gestational age) and after birth (chronologic age) and the truncation of the full biologic continuum (as in the calculation of neonatal mortality rates using live births at a particular gestational age as the denominator) is problematic on the level of first principles and also because it is responsible for numerous paradoxes and conundrums 15. The entire mortality experience of a cohort of fetuses (as documented on single time scale) is of interest, irrespective of whether death precedes or follows birth (see Figure 4).

As for explaining the rise in growth restriction and perinatal mortality rates with increasing gestation, one can speculate that the ability of the utero-placental system to support the fetus declines with increasing gestational age. Rising rates of growth restriction (as reflected in rising rates of revealed SGA) and perinatal death with increasing gestational duration reflect increases in the incidence of pregnancy complications such as preeclampsia and chorioamnionitis 6162 and also other stochastic processes that adversely affect vascular function within the utero-placental system.

The above-mentioned arguments suggest that the traditional and fetuses at risk models serve vastly different purposes. The distinction between descriptive versus causal models is particularly relevant in this context 76; traditional models which truncate the biologic continuum are better viewed as descriptive (noncausal) models which are ideal for setting prognosis at birth, while the fetuses at risk formulation represents a causal model that yields biologic insights and provides the basis for obstetric intervention 77.

The rate of labor induction and/or cesarean delivery increased with increasing gestational age (Figure 5a), being lowest among pregnancies with no medical risk factors and higher among pregnancies with complications. The incidence of birth showed a similar pattern. The incidence of revealed SGA rose with increasing gestational age and was highest among twins and lowest among uncomplicated pregnancies (Figure 5b). Rates of perinatal death also increased with increasing gestational age and patterns were generally consistent with clinical expectation and patterns of revealed SGA (Figure 5c).

The number needed to treat (NNT), an index widely used in therapeutics as part of risk-benefit equations, is insufficiently articulated in connection with medically indicated early delivery 79. This is in part because conventional models of perinatal mortality imply that early delivery is associated with an increased rate of perinatal death (Figure 1b). Nevertheless, the concept of the NNT remains as relevant and critical in the context of medically indicated early delivery as elsewhere in medicine. The NNT for medically indicated early delivery (given a specific indication) may be defined as the reciprocal of the difference between the rate of perinatal mortality or serious neonatal morbidity given no obstetric intervention and the rate of perinatal mortality or serious neonatal morbidity given medically indicated early delivery.

The clinical scenarios described below are characterized by varying background rates of perinatal mortality (which substantially modify the NNT). The first scenario involves an obstetric emergency (e.g., placental abruption with fetal bradycardia) where a rapid absolute increase in the (incidence density) rate of perinatal death is anticipated over a short time span (minutes). It is expected that an emergency cesarean delivery carried out within 15–30 minutes will prevent perinatal death in more than half the fetuses 80. This implies an NNT of approximately 2 or less. Similarly, in a second scenario involving a serious pregnancy complication and fetal compromise (e.g., severe preeclampsia with fetal growth restriction), an expected perinatal mortality reduction due to labor induction and/or cesarean delivery (as opposed to no intervention) of about 100 to 200 per 1,000 fetuses implies an NNT of 5 to 10. A third scenario involves routine delivery of twin pregnancy at 38 weeks gestation. If routine delivery at 38 weeks (relative to no obstetric intervention) reduces the rate of perinatal mortality by about 5 per 1,000 fetuses, this implies an NNT of 200. The final scenario involves routine delivery at 41 weeks gestation given an uncomplicated singleton pregnancy. If the difference between perinatal mortality given routine delivery at 41 weeks versus spontaneous delivery without obstetric intervention is approximately 1 per 1,000 fetuses at risk, this implies an NNT of 1,000. In other words, 1,000 routine early deliveries at 41 weeks gestation (through labor induction and/or cesarean delivery) would prevent one perinatal death.

Virtually all estimates used in the NNT calculations above are speculative even if they represent more or less reasonable approximations. In fact, most inputs into the NNT calculation cannot be estimated given current standards of care since the decision not to intervene is such situations (e.g., severe preeclampsia with fetal compromise) would constitute a breach of ethical standards.

The marginal NNT, which measures the effect of increases in medically indicated early delivery (beyond standard rates of medically indicated early delivery), is an alternative measure that is directly pertinent to obstetric practice. In this calculation, a temporal increase in medically indicated early delivery is set against the change in perinatal mortality in any particular domain.

Table 3 shows temporal changes in the incidence of obstetric intervention and perinatal death in the United States between 1995–96 and 1999–2000. The rate of labor induction and/or cesarean delivery among singleton pregnancies ≥ 28 weeks of gestation increased by 45.1 per 1,000 fetuses, from 339.4 per 1,000 fetuses in 1995–96 to 384.5 per 1,000 fetuses in 1999–2000 (P < 0.0001, Table 3). During the same period, the rate of perinatal death (excluding deaths due to congenital anomalies) decreased by 0.31 per 1,000 fetuses from 3.95 to 3.64 per 1,000 fetuses at ≥ 28 weeks of gestation (P < 0.0001). This yielded a marginal NNT rate of (45.1/0.31) or 145. Thus, 145 additional labor inductions/cesarean deliveries in 1999–2000 (relative to 1995–96) were responsible for preventing 1 perinatal death among singletons ≥ 28 weeks gestation. Marginal NNT estimates for specific subpopulations differed from those obtained for all singletons, being as low as 32 among twins ≥ 28 weeks and as high 927 among singletons ≥ 34 weeks with hypertension (Table 3).

Such marginal NNT calculations are analogous to calculations based on randomized trials which contrast routine induction of labor vs selective induction of labor at or beyond term 81 or those which contrast aggressive vs expectant management given severe preeclampsia before term gestation 82. A meta-analysis 81 of studies on the former issue showed that routine induction of labor reduced perinatal death rates several-fold (odds ratio of 0.20, 95% confidence interval 0.06 to 0.70). This implies an NNT of 1,250 for routine induction of labour at or beyond term gestation, assuming a perinatal mortality rate of 1.0 per 1,000 fetuses at risk following selective labor induction.

The proposed framework is based on two important assumptions. First, medically indicated early delivery is considered the final pathway for obstetric intervention. Thus, increases in labor induction and cesarean delivery are credited with preventing perinatal death even though such early delivery was facilitated by improved methods for assessing fetal well-being and supportive neonatal care. Early delivery is thus viewed as a therapeutic package which subsumes antenatal monitoring, diagnosis of fetal well-being, supportive neonatal care and other interventions that permit higher rates of early delivery to rescue compromised fetuses from a hostile intrauterine environment.

A second assumption is that temporal increases in labor induction and cesarean delivery rates and declines in perinatal mortality rates reflect true changes in obstetric practice (rather than changes in population characteristics). It is possible that changes in maternal characteristics (such as increases in older maternal age and pre-pregnancy obesity 8384) may have been partly responsible for changes in labor induction, cesarean delivery and perinatal mortality rates in the United States between 1995–96 and 1999–2000. Although such changes are unlikely to have affected the results substantially (since the study interval was only 4 years), regression adjustment can be used to address this issue where necessary.

Current limitations of the fetuses at risk approach include an inability to precisely document the incidence of fetal growth restriction. This is because diagnosis of growth faltering in utero, although much facilitated in recent decades through ultrasonographic means, remains inaccurate and essentially unavailable at the population level 636465. The alternative index of revealed SGA 15 is useful but limited by its relationship to birth rate patterns. Further developments in ultrasound technology are needed so that incidence rates can be estimated more accurately based on an identification of all new cases of growth restriction (in utero). Another approximation in the fetuses at risk approach relates to the timing of the pathologic process or event. Assigning events such as neonatal death and serious neonatal morbidity to the moment of birth often involves a systematic overestimation of the timing of the critical pathologic process or event 74. The systematic nature of the problem means that the incidence patterns of perinatal mortality and morbidity are not seriously affected, however.