Stillbirths and Neonatal Mortality in the Context of the Global Burden of Disease

This section first introduces the nomenclature used throughout the chapter. It then provides estimates of deaths and death rates that highlight stillbirths and neonatal deaths and discusses deaths by cause at different ages.

Numbers of Deaths and Death Rates

In 2001, approximately 10.6 million children born alive died before their fifth birthday (8.2 percent of births). Of these deaths, 3.9 million occurred during the neonatal period, that is, under the age of 28 days. Another 3.3 million stillborn children remained outside the vital registration systems of most countries (WHO 2005a). When stillbirths are included among deaths, about half of all deaths of children under five occur under the age of 28 days.

Table 6.1 provides estimates of the numbers of stillbirths in 2001, with numbers broken down by World Bank income categories. The stillbirth numbers in the table come from rates estimated by the World Health Organization (WHO) (WHO 2005a) applied to the birth numbers reported in the table. The table shows that in 2001, the high-income countries (those with a gross national income per capita of more than US $9,076 in 2002) had 11.37 million live births and the low-and middle-income countries had 118.51 million live births.

Table 6.1

Population Totals and Numbers of Births, 2001 thousands.

Table 6.2 provides an age breakdown of deaths among children under five, again with a breakdown by World Bank income category. Early neonatal deaths account for 75 percent of all neonatal deaths. The eight-day period encompassing intrapartum stillbirths and early neonatal deaths accounts for almost 30 percent of the 13.9 million deaths occurring under the age of five. Thus, as shown in figure 6.1 for the low- and middle-income countries, roughly a quarter of the deaths under age five occur in each of the following categories: stillbirths, neonatal deaths, postneonatal infant deaths, and child deaths.

Table 6.2

Age Distribution of Deaths under Age 5, 2001 thousands.

Figure 6.1

Age Distribution of Deaths of Children under Five in Low-and Middle-Income Countries, 2001

Three recent studies provide extensive literature reviews and model-based estimates of the number of stillbirths and neonatal deaths that extend the WHO estimates used here (WHO 2005a). Lawn, Shibuya, and Stein (2005, tables A–J) focus on intrapartum stillbirths and intrapartum-related neonatal deaths. Stanton and others (forthcoming) provide estimates of the number of stillbirths for 190 countries and Hill (forthcoming) provides estimates for neonatal deaths. The midpoints of their fairly wide confidence intervals accord with the numbers we use.

Table 6.3 shows death rates, expressed per 1,000 live births, that correspond to the death totals in table 6.2. Column (c), for example, shows an under one or infant mortality rate (₁q₀) for low- and middle-income countries of 64 per 1,000. Column (d) shows the effect of including stillbirths to give the complete under one mortality rate (_1.25q_−.25), which is markedly higher at 89 per 1,000 live births. By including stillbirths and providing relatively fine-grained age breakdowns, table 6.3 provides a more comprehensive set of estimates of mortality rates under age five than has hitherto been available. The wide confidence interval that needs to be attached to the estimates (Stanton and others forthcoming) indicates both the need for caution when using these numbers and the importance of further research. Nevertheless, the estimates in table 6.3 are reasonable given currently available information.

Table 6.3

Estimated Death Rates under Age 5, by Country Income Level, 2001 Probability of dying in the x years following age y (_xq_y), expressed per thousand live births.

Deaths by Cause

Estimates of the total number of deaths in different age groups provide a starting point for breaking those totals down into deaths by cause. This task inevitably involves some degree of arbitrariness because of problems with classifying multiple causes of death or underlying versus proximal causes. That said, available data from vital registration, sentinel surveillance, and verbal autopsy can provide reasonable approximations for most causes. Chapter 3 provides background on how this was done and generates the death by cause estimates used throughout this book.

We use the estimates from chapter 3 for deaths by cause in the newborn through age four age group and aggregate chapter 3 data on age groups over age five into a single category of deaths for those age five and older. In their preparatory work for chapter 3, its authors estimated cause-specific breakdowns of deaths under age five both for infant deaths and for deaths from age one through age four, that is, deaths occurring at one year of age or older but under age five, and we have used their data in this chapter. Table 6.4 presents this information on deaths by cause aggregated, as previously indicated, into 35 groups of conditions rather than the 136 used in chapter 3.

Table 6.4

Deaths by Age and Cause, 2001 (thousands).

The aggregate numbers for neonatal deaths and for stillbirths come from WHO (2005a) as reported in table 6.2 (see also WHO 2005b, pp. 170–71). Table 6.4 breaks down neonatal deaths into six causes: diarrheal diseases, tetanus, respiratory infections, low birthweight (essentially preterm birth), birth asphyxia and birth trauma, and congenital anomalies. ² The estimates by cause were generated for WHO's Child Health Epidemiology Reference Group (CHERG) (see Bryce and others 2005 for a comprehensive presentation of data sources and methods of estimation). WHO (2005b, annex table 4) provides a summary of the numbers.

For the most part, the neonatal death categories used by CHERG align with the categories used by the GBD assessment in chapter 3; however, note the following exceptions:

• CHERG includes a pneumonia and sepsis category, which accounts for 26 percent of neonatal deaths globally and 27 percent in low- and middle-income countries. The GBD categories include respiratory infections (category I.B in our tables), which account for 1.945 million deaths worldwide in the age group 0–4. We allocate all the CHERG-estimated deaths from the combined category sepsis and pneumonia to the neonatal age group's respiratory infections category in order to remain as consistent as possible with the GBD framework in chapter 3. A number of studies have estimated the percentage of the broad category sepsis and pneumonia that is pneumonia with a wide range of findings (see, for example, Bhutta and others 2004 and Bhutta, Ali, and Wajid 2004). Even with blood cultures and chest x-rays, one cannot say for sure if a newborn has sepsis or pneumonia or both, and in any case, the treatment is the same, so one programmatic category is currently appropriate (Lawn, Cousens, and Wilczynska forthcoming).
• CHERG's percentage of neonatal deaths due to tetanus (7 percent) exceeds the GBD estimate for all infant deaths from tetanus but is very close to WHO and GAVI estimates for the year 2000 of 220,000. In keeping with this chapter's spirit of staying as close as possible to GBD estimates from chapter 3, we remain within the GBD envelope for the under-five age group and, as a first approximation, allocate all under one tetanus deaths to the neonatal period. However, while remaining within the under five GBD envelope for tetanus, we have modified, in this case only, the (unpublished) GBD age breakdown between ages 0–1 and 1–4 to allocate 90 percent of under five tetanus deaths to under age one (see table 6.4, note a). The difference between the CHERG and WHO with the GBD estimates for tetanus deaths is substantial and is clearly a priority area for further work.
• The GBD work uses the category low birthweight, which is an outcome of either preterm birth or intrauterine growth retardation. Preterm birth is a major cause of neonatal death. Again in the spirit of remaining within the GBD framework, we allocate preterm births to the low birthweight GBD category. This should not cause confusion as long as it is understood that, for neonatal deaths, low birthweight refers almost entirely to preterm birth. The quantitative importance of preterm birth suggests that this is another category that could be presented separately in the next GBD effort.

We are not aware of any effort to aggregate data on causes of stillbirths that parallels the CHERG effort for neonatal deaths, hence the GBD calculations in this chapter do not attempt to allocate stillbirths by cause. However, even though this chapter does not attempt a review of the CHERG type of the causes of stillbirth, we can advance a few tentative hypotheses. First, an important cause of stillbirth is intrapartum complications. A recent systematic analysis of intrapartum stillbirths gives estimates for 192 countries based on 73 study populations (52 countries, n = 46,779 [73 populations]) suggesting that 1.02 million intrapartum stillbirths (uncertainty 0.66–1.48 million) occur annually, accounting for 26 percent of global stillbirths. Second, congenital anomalies constitute an important cause of antepartum stillbirth. Third, sexually transmitted diseases and other infections cause antepartum stillbirth, but systematic global estimates are currently limited.

Our categorization of neonatal deaths within the GBD framework has been deliberately conservative in that where interpretation was in any way uncertain, we assigned deaths to the not allocated category. We expect future efforts to be able to substantially reduce the not allocated component for both stillbirths and neonatal deaths, but doing so will require both improved empirical information and modification of the current GBD framework to include classifications important for deaths near the time of birth. Until such improvements are possible, table 6.4 provides a plausible extension of the GBD cause of death framework to include causes of infant and neonatal deaths.

The Burden of Disease Resulting from Events Near the Time of Birth

This section explains the use of DALYs as a measure of the disease burden and identifies a number of problems associated with the traditional DALY formulation when dealing with events around the time of birth. It proposes a generalized formulation (which annex 6A describes more fully). The chapter then calculates the disease burden using two approaches to explore the sensitivity of GBD estimates to alternative formulations as follows:

• the current DALY formulation extended so as to value the DALY loss from a stillbirth the same as the DALY loss from a death at age 0,
• a generalized DALY formulation allowing the acquisition of life potential (ALP) to be gradual rather than instantaneous.

Defining and Redefining DALYs

The DALY family of indicators measures the disease burden from the age of onset of a condition by summing an indicator of YLL due to the condition and an indicator of disability-adjusted YLD resulting from the condition. While, in principle, the disability weights used in this adjustment could arise from any of the procedures typically used to construct quality- adjusted life years, obtaining disability weights for a large number of causes using any procedure other than the judgments of selected reference groups is currently impractical. Chapter 3 describes the methods currently used.

DALYs generate a measure of the disease burden resulting from premature mortality by integrating a discounted, age-weighted, disability-adjusted stream of life years from the age of death (see equation 6A.2 in annex 6A). The formulation within the family of DALYs previously used to empirically assess the global burden of disease specifies a constant discount rate of 3 percent per year and an age-weighting function that gives low weight to early childhood and older ages and greater weight to middle ages. This volume reports global burden of disease estimates generated using uniform age weights. Chapter 5 provides an extensive exploration of the uncertainty and sensitivity inherent in disease burden assessment, including the results of differing assumptions about age weighting and discount rates.

To be clear about the particular form of DALY being used, the following terminology is employed throughout this volume. DALYs(r,K) are DALYs constructed using a discount rate of r percent per year and an amount of age weighting indexed by a parameter K. Two versions of the DALY are discussed at some length in chapter 5, both using a discount rate of 3 percent per year. DALYs(3,1) are DALYs generated with a discount rate of 3 percent per year and with full age weighting, that is, K = 1. DALYs(3,0) are DALYs generated with a discount rate of 3 percent per year and with no age weighting, that is, K = 0. This volume's results concerning the burden of disease (chapter 3) and of risk (chapter 4) are based on DALYs(3,0). Annex 6B contains tables summarizing alternative calculations of the global burden of disease, and table 6B.4 presents the chapter 3 GBD results based on DALYs(3,0), using this chapter's aggregation of causes, for age groups under five and over five as an aggregate.

This chapter extends the DALY family by modeling a concept of ALP. The intuition behind the ALP concept is that an infant (or fetus) only gradually acquires the full life potential reflected in a stream of life years beginning at birth, that is, ALP can be gradual. The ethical understanding of the concept is based on two judgments: (a) an individual life acquires value only as it acquires self-awareness, and (b) an individual life acquires additional value as it develops bonds with others. (See the discussion in Steinbock 1992, who argues that what we label as life potential is probably acquired some time in the second trimester of pregnancy. Her position is, implicitly, that whenever it occurs, ALP is instantaneous.) To some extent, the age-weighting function of the current DALY formulation attempts to capture these judgments, and in this chapter, gradual acquisition of ALP is modeled as an alternative to age weighting. ³ Mathematically, however, ALP and age weighting are independent and can be introduced simultaneously.

Our objective in this chapter is not to provide a detailed philosophical, economic, or medical rationale for gradual ALP, but to generate and apply a straightforward mechanism that allows for it. Annex 6A describes this mechanism, which essentially consists of multiplying the DALYs conventionally generated by a factor that is less than one for younger ages. This factor is zero for an age of −13 weeks (or −0.25 years), rises to a factor value of f ⁰ at birth, then rises to 1 at time T. Figure 6.2 graphs both the ALP function used later in this chapter and the special case of ALP that jumps from 0 to 1 at age 0 (instantaneous ALP). The ALP implicit in traditional DALYs is instantaneous.

Figure 6.2

ALP, Traditional DALYs, and DALYs (3,0,.54)

Annex 6A introduces a parameter, A, that indicates the speed of ALP (see equations 6A.3 through 6A.5 for a precise definition of A). A is constructed so that for the fastest possible speed of ALP, namely, instantaneous ALP, A = 1. A is bounded below by 0. This chapter extends the notation DALYs(r,K) used elsewhere in the book in two ways. First, it explicitly indicates the level of A by extending the DALY nomenclature to DALYs(r,K,A). Thus using this nomenclature, DALYs(3,0) become DALYs(3,0,1), because the standard DALY is the special case with instantaneous ALP. Second, when stillbirths are included in the range of events to be measured in the global burden of disease, this is explicitly noted in the DALY nomenclature as DALYs_SB(r,K,A). Notation around YLL is similarly extended.

Explicit modeling of ALP allows not only the reflection of the ethical judgments just indicated, but also permits three instrumentally useful improvements to the current family of DALYs:

• The DALY loss from a death seconds before birth is, in the current formulation, 0; it jumps to more than 30 years at birth. The ALP formulation allows, but does not require, this discontinuity to be avoided. See column (a) of table 6.5 for values at different ages of the ALP function associated with traditional DALYs and columns (c), (d), and (e) for values of three ALP functions defined in annex 6A.
• The ALP formulation allows, but does not require, a positive DALY loss associated with stillbirths.
• The ratio of the DALY loss from a death at age 20, say, to that at birth is close to 1 for any reasonable set of parameter values in the current DALY formulation. Many people's ethical judgments would give this ratio a value substantially greater than 1. The ALP formulation allows, but does not require, these judgments. Figure 6.3 shows how this ratio varies as a function of the age-weighting parameter (K) for values of r equal to 3 percent and 10 percent. The ratio rises only to 1.7 with full age weighting and an implausibly high discount rate of 10 percent.

Table 6.5

Values of Selected ALP Functions.

Figure 6.3

Ratio of DALYs Lost at Age 20 to Age 0 as a Function of Age Weighting

Alternative Calculations of the Burden of Disease

As previously indicated, annex table 6B.4 (based on annex tables 6B.1 to 6B.3) presents the chapter 3 GBD estimates in terms of DALYs(3,0)—or DALYs(3,0,1)—for the under and over five age groups. The DALY(3,0) is the sum of the YLL(3,0,1) and YLD. Annex tables 6B.1, 6B.2, and 6B.3 report deaths by cause, YLL(3,0,1) by cause, and YLD by cause from chapter 3. The numbers in table 6B.4 are the sum of the corresponding numbers in tables 6B.2 and 6B.3.

We generate two alternative assessments of the global burden of disease. Both incorporate stillbirths and the second permits gradual ALP. The YLD numbers that we use come from annex table 6B.3. The YLL differ from YLL(3,0,1) for ages under age five, but are the same for over age five.

Our first alternative is probably the simplest way to incorporate stillbirths. It does so by having an instantaneous ALP function, as with traditional DALYs, but by having that function jump from 0 to 1 at age −13 weeks (−0.25 years) instead of at age 0. Stillbirths are then given the same DALY loss as a death at birth in generating YLL. Column (b) of table 6.5 shows values for this ALP function, which is uniformly 1. We label the YLL generated from this ALP function and a 3 percent discount rate the YLL_SB(3,0,1). We label the DALYs based on this YLL as DALYs_SB(3,0,1). Table 6.6 shows values of YLL_SB(3,0,1) compared with YLL(3,1) and YLL(3,0) for different ages. Annex table 6B.5 shows values for YLL_SB(3,0,1) and annex table 6B.6 shows the resulting burden of disease estimates in terms of DALYs_SB(3,0,1).

Table 6.6

Discounted YLL at Different Ages of Death for Several DALY Formulations.

Our second alternative burden of disease assessment is based on gradual ALP. Equation 6A.1 in annex 6A provides our general ALP function and the text describes the meaning of its four parameters. One of the parameters, f⁰, is the value of the function at age 0. The intuitive interpretation of f⁰ is that it is approximately the ratio of the YLL loss associated with a death at age 0 to that from a death at age 20. Another parameter is T, the age at which the function becomes 1. Annex 6A characterizes three alternative gradual ALPs: f₁, f₂, and f₃. Figure 6.4 shows YLL at different ages for these functions and for YLL(3,0) and YLL(3,1). Table 6.5 shows values for the functions at different ages in columns (c), (d), and (e). We use f₂ (with A = .54) to construct the disease burden estimates reported in this chapter and label the resulting YLL and DALYs as YLL_SB(3,0,.54) and DALYs_SB(3,0,.54). Table 6.6 shows YLL_SB(3,0,.54), which are, as intended, markedly lower than YLL_SB(3,0,1) for very young ages. That is, YLL_SB(3,0,.54) gives less weight to deaths near the time of birth or to deaths immediately after birth than YLL_SB(3,0,1).

Figure 6.4

YLL for Deaths at Different Ages

Only a limited number of empirical studies have attempted to assess directly the views of individuals concerning deaths at different ages. In an important early study, Crawford, Salter, and Jang (1989) relate grief from a death to the concept of reproductive potential in population biology. They conclude that for several diverse human groups the relationship shows grief to be closely related to prehistoric reproductive value. Cropper, Aydede, and Portney (1994) and Johannesson and Johansson (1997) survey members of populations of high-income countries for trade-offs between deaths in middle and older ages. All three of these studies find that people judge deaths at older middle age as much less important than deaths at younger middle age, but provide no information concerning the trade-off for deaths near the time of birth.

An Institute of Medicine (1985) review of vaccine development priorities uses infant mortality equivalence in cost-effectiveness calculations. The committee members preparing the report collectively judged that the loss from a death at age 20 should be about two times that from an infant death, well above the numbers shown in figure 6.3 for any standard DALY. However, some preliminary trade-off studies by one of the authors of this chapter suggest a value closer to three or four times. What is clear is that no defensible estimate (or even range) is currently available, and hence the numbers we report should be viewed only as perhaps reasonable but only suggestive and as indicating the sensitivity of global burden of disease results from younger ages to better estimates of this parameter.

Annex tables 6B.7 and 6B.8 show YLL_SB(3,0,.54) and DALYs_SB(3,0,.54). While table 6B.7 only shows the total of DALYs for ages under five, the calculations underlying those totals reflect the age distribution of deaths under age five shown in table 6.4 and the YLL_SB(3,0,.54) for deaths at different ages as shown in table 6.6.

Annex tables 6B.1, 6B.6, and 6B.8 provide three alternative assessments of the global burden of disease based on deaths by cause, on DALYs(3,0), DALYs_SB(3,0,1), and DALYs_SB(3,0,.54). Table 6.4 provides estimates of deaths by cause that include stillbirths (table 6.4, column [k]). We thus have five alternative indicators of the importance of disease at different ages and from different causes. Table 6.7 provides a summary for low- and middle-income countries of the distribution of the disease burden at different ages as assessed by these different measures. DALYs_SB(3,0,1) and DALYs_SB(3,0,.54) both point to the significance of stillbirths relative to DALYs(3,0), which exclude them altogether, but the gradual ALP approach of DALYs_SB(3,0,.54) gives much less importance to stillbirths than DALYs_SB(3,0,1) and substantially less importance to the under five burden than DALYs(3,0).

Table 6.7

Disease Burden at Different Ages Using Different Measures, Low- and Middle-Income Countries, 2001.

Table 6.8 provides a similar summary of how the assessed burden across groups varies with the measure used. DALYs_SB(3,0,.54) give more weight to Group II (noncommunicable diseases) and Group III (injuries) causes than do DALYs(3,0), while DALYs_SB(3,0,1) give less weight to these groups than DALYs(3,0). For example, DALYs_SB(3,0,.54) give about a 10 percent greater weight to cardiovascular disease than does the DALY (3,0), that is, 14.2 percent versus 12.9 percent.

Table 6.8

Disease Burden from Selected Groups of Causes Using Different Measures, Low- and Middle-Income Countries, 2001.

Conclusions

Previous assessments of the global burden of disease have not included stillbirths or sufficiently emphasized the important causes of neonatal death. This was understandable given the intended focus of these studies. In addition, the inclusion of stillbirths would have highlighted issues about how to weight deaths at different ages that would have been difficult to incorporate into the DALY metrics being used to assess the global burden of disease.

Data on the numbers of stillbirths and neonatal deaths have improved, and a recent major effort by CHERG now provides a much better picture than before of the causes of neonatal death. (Annex C describes the CHERG effort and compares its results with estimates that result from fitting the CHERG estimates into the overall death envelope of chapter 3.) This chapter proposes an approach that incorporates modeling ALP, which allows flexibility in assessing how to weight stillbirths and other early deaths in constructing aggregate measures of the disease burden. This chapter combines new information and new methods into a reassessment of the global burden of disease that is based closely on, but goes beyond, what is reported in chapter 3.

We draw the following conclusions from this exercise:

• The numbers of stillbirths and of neonatal deaths are large. This underscores the importance of implementing tools and policies for addressing them. A number of recent publications point to directions for policy (for example, Darmstadt and others 2005; Institute of Medicine 2003; Lawn and others 2006; Martines and others 2005; Stoll and Measham 2001; Tinker and others 2005; WHO 2005b; Zupan 2005).
• The inclusion of stillbirths within the standard GBD framework is now feasible, and future assessments of the global burden of disease could consider doing so.
• The GBD cause structure would need relatively minor modifications to incorporate deaths at early ages. Birth asphyxia and preterm births could be separate subcategories and sepsis and pneumonia could also be included as a separate category. Rather than reporting a single burden estimate for the under five age group, the more fine-grained age breakdown of table 6.4 could be used.
• The databases on numbers and causes of stillbirths and neonatal deaths require major investments so they can be improved. Undertaking a CHERG type of review of the existing literature to gain a better understanding of the causes of stillbirths is also a priority.
• The selection of a generally appropriate ALP function requires more data on preferences or trade-offs concerning deaths at different ages.

Annex 6a: Flexible Functional Forms for the Acquisition of Life Potential

This annex provides a technical discussion of issues raised by incorporating late fetal deaths (stillbirths) into the global burden of disease, as measured within the disability-adjusted life year (DALY) framework. One approach is simply to take the DALY loss at birth and discount back to the time of the stillbirth, indicating that there are no life years to lose before birth, but that there are still all the postpartum life years. Essentially this is the standard DALY, but with an age-weighting function equal to 0 before birth. This is feasible, but has several potential drawbacks, in particular, any reasonable discount rate (for example, 3 percent) would thence count all late fetal losses almost the same as a loss at birth. This approach yields the DALYs_SB(3,0,1) measure as described in the main text, and table 6B.6 presents global burden of disease estimates using DALYs_SB(3,0,1) because these are the simplest extension of DALYs(3,0).

However, as with traditional DALYs, DALYs_SB(3,0,1) assume instantaneous acquisition of life potential (ALP), as illustrated in figure 6.2 and discussed in the main text. Whether or not one wishes to include stillbirths in the global burden of disease, this discontinuity (at some given age) is troublesome. The purpose of this annex is to provide a flexible, yet tractable, explicit function that allows for gradual ALP.

One natural approach is to weight the YLL from outside the integral instead of from the inside (as with age weighting), that is, to create a multiplier function (the ALP function), which takes on values between 0 and 1 as a function of age, and use it to ratchet down the YLL function, potentially starting before birth. For convenience and with some regard to the known physiological underpinnings, we take this starting point in time to be the beginning of the third trimester of pregnancy. Roughly speaking, the rate of natural fetal loss becomes noticeable after the beginning of some level of consciousness during the second half of the second trimester. One could force this function to equal 1 at birth, recovering the standard DALYs from that point onward, and this will be a special case of our formulation. However, we have no definitive reason to think that ALP is necessarily complete at birth. Indeed, quite a bit of evidence suggests that in many (if not all) societies worldwide, infants are not given full status, for instance, they are not always named immediately. Thus we wish to allow for continued gradual acquisition after birth and up to some time T that signifies full standing or full ALP. Likewise, starting the acquisition only at birth but proceeding gradually afterward is perfectly possible.

Turning to the specifics, denote the ALP multiplier function by f(t), where t is measured in years and ranges from −0.25 (that is, 13 weeks before birth, the beginning of the third trimester) to T. The function is meaningfully defined for any finite value of T, though it is natural to assume that full life potential is achieved by puberty at the latest. Thus f(−0.25) = 0 and f(T) = 1. We let f⁰ = f(0) be the value at 0. Of course, starting times other than −0.25 are perfectly legitimate as well, but −0.25 is the natural choice given the standard definitions of stillbirth and the gathering and reporting of data using that definition.

We need a functional form that smoothly begins at 0 and rises to f⁰, which is at least weakly convex (following the intuition that life potential is acquired increasingly rapidly as birth is approached), and whose curvature is parametrizable. The natural choice is x^γ with γ ≥ 1. This has canonical endpoints of 0 and 1, where x^γ takes on the values 0 and 1, respectively, for any γ, so that as we change the curvature (or skewness), the endpoints remain fixed. Fitting this to our specific domain, we get x = 4t + 1 for −0.25 ≤ t < 0. Finally, if we wish the skewness parameter to lie between 0 and 1 as well (for clarity), we can define g so that g = 1/(1 − g) for 0 ≤ g < 1. This yields f_(t) = f⁰(4t + 1)^1/(1−g) for −0.25 ≤ t< 0. Thus g = 0 produces a straight line (zero curvature), while g = 1 (defined by fiat) is infinitely skewed: 0 until birth and then jumping to f⁰.

For t ≥ 0, we consider the symmetric version of the same polynomial, that is, 1 − (1 − x)^β. Again we fit this to our domain, namely, from t = 0 to t = T, and define b so that b = 1/(1 − b) for the skewness. This yields f₊ (t) = 1 − (1 − f⁰)[(T − t)/T]^1/(1−b) for 0 ≤ t ≤ T. We check that indeed f₊(0) = f⁰ and f₊(T) = 1 according to this formula for any 0 ≤ β ≤ 1. If T = 1, the formula simplifies to f₊(t) = 1 − (1 − f⁰)(1 − t)^1/(1−b). This leaves four parameters: f⁰, T, g, and b. We can additionally impose g = b if we wish, but this is unnecessary.

Summarizing, the function we use for ALP is

If f_D(t) is the standard DALY formulation (whether or not age weighting or discounting is used), then g = b = 1 (that is, discontinuous jumps around birth from 0 to 1) and f_D⁰= 1, so that technically at age 0 the value is already 1 (so the discontinuity is on the left side of age 0 only). Given these parameters, T is immaterial, because the function achieves its maximum immediately. However, the fact that we can replicate the standard DALY means that the gradual acquisition function does indeed generalize it.

Combining these equations with the standard definition of DALYs, the total loss L(a) for a death at age a ≥ −0.25 is

where β is the age-weighting parameter (typically 0.04) if age weighting is used, r is the discount rate (typically 0.03), s_a(x) is the survival probability for reaching age x ≥ a conditional on having reached age a, and C is the normalization parameter for the age weights (C = 0.16243, see the discussion in chapter 5).

The normalization parameter C in equation (6A.2) was chosen so that the total global burden of disease would be the same with and without age weighting. The index of age weighting referred to in the main text, K, is generated by having a weighted average—with weights of K and (1 − K), where 0 ≤ K ≤ 1—of loss functions L(a) that result from equation (6A.2) with the indicated values of β and C and a loss function assuming uniform age weights. That this is at least approximately the case is apparent from figure 6.4b, where the two functions cross at about age 40. Clearly this will not be true when any of the acquisition functions are used, because they reduce the YLL burden at younger ages with no corresponding increase elsewhere, leading to a reduced total burden as measured by absolute DALY levels.

Note, however, that the total burden is no longer the same even for DALYs(3,0) and DALYs(3,1), because the specific value of C was calibrated to 1990 morbidity and mortality statistics. One can readily imagine more neutral (and invariant) normalizations, such as requiring a constant integral over age of death for each of these YLL functions, or perhaps weighting this integral using an idealized survival table. Any variant along these lines would raise the total level of DALYs(3,0,.54) relative to both DALYs(3,0) and DALYs(3,1). Of course, we are for the most part interested only in the relative burden across ages or disease categories, so the absolute totals are of secondary importance.

Finally, to somewhat simplify the number of parameters in the ALP function, we introduce a notion of speed of acquisition, A. Recall that f⁰ can be anywhere between 0 and 1, regardless of whether the function f(t) takes on positive values before birth. If f⁰ = 1 (as in the original DALY), then f = 1 thereafter and the speed A is in some sense as large as possible. To generalize this idea, we look at the total area between the ALP function f(t) and the constant function 1.

Formally, this area is given by the integral of 1 − f(t), evaluated from t⁰ to T, where t⁰ is the first t s that f(t) > 0. It is thus typically either − 0.25 or 0, depending on whether we are including stillbirths. Call this integral I:

Substituting the second part of equation (6A.1), we can evaluate this integral as

Normalizing so that the speed A lies between 0 and 1 (and higher values denote faster acquisition), we define

For example, for b = 0.7 (a typical value) and t⁰ = 0, we obtain a simple formula for the speed parameter A, encapsulating the acquisition function in a single number: A = 1/[1 + 0.23T(1 − f⁰)]. There is still a trade-off between T and f⁰, that is, the relationship between the underlying parameters and A is not one-to-one. A single value for A could have arisen from multiple combinations parameter values, but it still serves as a useful summary statistic. Figure 6A.1 graphs (as a function of T, fixing b = 0.7 and t⁰ = 0) the value of f⁰ that yields various specified acquisition speeds A. The analogous figure 6.3 shows less variability in this ratio.

Figure 6A.1

Relationship between Time to Complete ALP and Life Potential at Age 0 for Several Values of A

We evaluate three specifications (parameter choices) for the acquisition function. These are, in order of value at birth: f₁, given by (f₁⁰ = 0.25, T₁ = 14, g₁ = 0.5, b₁ = 0.7); f₂, given by (f₂⁰ = 0.3, T₂ = 5, g₂ = 0.4, b₂ = 0.7); and f₃, given by (f₃⁰ = 0.5, T₃ = 2, g₃ = 0.3, b₃ = 0.8). The respective values for A (using t⁰ = −0.25) are 0.29, 0.54, and 0.84. These three acquisition functions were graphed in figure 6.4. Representative values for specific ages were listed in table 6.5, along with the corresponding values for f_D(t), the traditional formulation for DALYs. Figure 6A.2 shows how the ratio of years of life lost at age 20 to age 0 for these three functions varies with A. We view f₂ (with T = 5) as a reasonable intermediate choice and, with a 3 percent discount rate, have used f₂ to generate what we define as DALYs(3,0,.54). Complete burden of disease calculations are reported using DALYs(3,0,.54) in table 6B.8.

Figure 6A.2

Ratio of DALYs Lost at Age 20 to Age 0 as a Function of A

Annex B: Supplementary Tables

Table 6B.1. Deaths (Excluding Stillbirths) from Selected Causes, by Age, 2001 (thousands)

Table 6B.2. YLL(3,0) from Selected Causes, by Age, 2001 (thousands)

Table 6B.3. YLD from Selected Causes, by Age, 2001 (thousands)

Table 6B.4. The Burden of Disease—DALYs(3,0) from Selected Causes, by Age, 2001 (Excluding Stillbirths) (thousands)

Table 6B.5. YLL_SB(3,0,1) Calculated to Include Stillbirths (Valued the Same as Newborn Deaths) (thousands)

Table 6B.6. The Burden of Disease—DALYs_SB(3,0,1). Calculated to Include Stillbirths (Valued the Same as Newborn Deaths) (thousands)

Table 6B.7. YLL_SB(3,0,.54) Calculated to Include Stillbirths and Gradual ALP (in thousands)

Table 6B.8. The Burden of Disease—DALYs_SB(3,0,.54). Calculated to Include Stillbirths and Gradual ALP (A = .54) (thousands)

Annex C: Causes of Neonatal Mortality: Comparison of Numbers from the Global Burden of Disease with Those from the Child Health Epidemiology Reference Group

This chapter has examined the consequences of incorporating stillbirths and neonatal deaths (deaths in the 28 days following live birth) into the Global Burden of Disease (GBD) framework. Methods and results of the GBD are presented elsewhere in this book and, in particular, chapter 3 discusses the estimates of deaths by age and cause for 2001 that form the basis for results throughout this book and in this chapter. Estimates of deaths from specific causes undergo continual revision as new data and syntheses become available, yet establishing a time cutoff is a necessary (if somewhat arbitrary) condition for preparing a volume with consistent estimates across chapters. For this volume, the cutoff date for the estimates of deaths by cause in 2001 was late 2003. That date was itself established in response to the need for a separate book—Jamison and others (2006)—to have a consistent set of demographic and epidemiological numbers feeding into its highly diverse chapters.

During 2001, the World Health Organization (WHO) established the Child Health Epidemiology Reference Group (CHERG) to undertake a new synthesis of data on causes of death among children under five. While some early CHERG results influenced the GBD numbers in this volume, for the most part, CHERG's work became available well after the cutoff date for this iteration of the GBD. For this reason, the 2005 WHO estimates (Bryce and others 2005; WHO 2005b) of causes of death among children under five based on CHERG (CHERG/WHO) differ to some extent from the GBD ones used in this volume. Chapter 5 further discusses the two sets of estimates for under-five deaths, and the importance of envelope and epidemiological consistency constraints in generating the GBD numbers. In terms of data sources, the GBD uses epidemiological data together with vital registration data (where available), models extrapolating from vital registration data, and epidemiological consistency checks. CHERG relies relatively more on verbal autopsy based epidemiological data for causes of child death.

The work of CHERG, however, provides a critical input to this chapter not available from the GBD work, that is, a breakdown of the causes of death specifically for the neonatal period. One of the motivations of this chapter is that neonatal deaths account for fully 37 percent of the worldwide total of deaths among children under age five. In preparing this chapter, therefore, we needed to draw fully on the CHERG analyses of neonatal deaths while—to ensure consistency and comparability with numbers elsewhere in this volume—we use the GBD estimates of total deaths among children under five. This allows estimates of the neonatal burden to be inserted into the larger context of the GBD with its inclusion of 136 causes as well as all age groups older than age five. The specific assumptions we made to reconcile GBD and CHERG numbers are made clear in the text with table 6.4 and in the notes to table 6.4.

The CHERG/WHO results appear as percentages of deaths by one set of causes for neonates and by a mostly different set of causes for children ages 28 days to 5 years. This makes direct comparison with the GBD numbers difficult in the formats in which the two sets of numbers are presented. The difficulty is compounded by occasional differences in the labels (and content) of cause categories and by the fact that the GBD deals with far more causes than CHERG/WHO. Even the truncated GBD cause list used in this chapter uses 35 instead of 136 causes, in contrast to the 10 used by CHERG/WHO. To facilitate comparison of the two sets of findings, annex table 6C.1 uses the 6 of the 10 CHERG/WHO cause categories that are relevant to neonates to compare this chapter's and CHERG's findings for neonatal deaths. To construct table 6C.1 we took proportional allocations of deaths from CHERG/WHO presented in figure 2 of Bryce and others (2005) and applied those proportions to the estimated number of neonatal deaths (3.896 million) used in this chapter. The table is for the world as a whole.

Table 6C.1

Causes of Neonatal Mortality, Worldwide in 2001 (thousands).

Acknowledgments

The authors are indebted to many individuals for valuable inputs, comments, and encouragement. The late José Luis Bobadilla encouraged us concerning the importance of this work and provided guidance to the literature on causes of death among the very young. Kenji Shibuya of WHO provided helpful inputs to an early draft. At an earlier stage of this work, Nancy Hancock and Jia Wang provided valuable inputs for which we are very grateful. Elisabeth Aahman, also of WHO, provided invaluable inputs to the estimates of stillbirth and neonatal mortality rates that this chapter draws on; we owe her particular thanks. Participants at seminars at the Harvard Center for Population and Development and at the Centers for Disease Control and Prevention provided valuable comments, and in particular we would like to thank Sevgi Aral and Lincoln Chen. The editors of this volume and two peer reviewers, Arnab Acharya and Linda Martin, provided detailed and valuable critical reaction. Robert Black provided additional important critical reaction.

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Footnotes

1

The term child mortality rate is sometimes used to denote what we call the under five mortality rate. We try to avoid confusion by being explicit about the age range covered.

2

Murray and Lopez (1998) and Shibuya and Murray (1998a, 1998b, 1998c) provide an earlier overall assessment of the burden from some of the major causes of neonatal mortality. Low birthweight as a risk factor is further discussed in Fishman and others (2004) and in chapter 4 of this volume.

3

Allowing the use of negative age weights could achieve some of the same effects as gradual ALP.