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Child Mortality Estimation: Estimating Sex Differences in Childhood Mortality since the 1970s [1]

['Cheryl Chriss Sawyer', 'Population Division', 'Department Of Economic', 'Social Affairs', 'United Nations', 'New York', 'United States Of America']

Date: 2024-04 

The dataset used for this study builds upon datasets [28] – [30] that were developed for a 1998 United Nations publication on sex differentials in childhood mortality [1] and expanded for a 2011 report [2] (data collection for [2] was completed in 2010; the present study incorporates additional or revised data obtained through November 2011). Microdatasets from Demographic and Health Surveys (DHS) were processed to produce a time series from each survey of direct estimates of 5-y mortality rates by sex, extending back to a period 20–24 y before each survey. In addition, tabulations of children ever born and children surviving by age of the mother were calculated by sex of the child for each DHS survey to produce indirect estimates of 5 q 0 . An important new source of data since the mid-1990s is the Multiple Indicator Cluster Survey program, conducted by the United Nations Children's Fund, which has yielded additional sets of indirect estimates by sex, many for countries that had very limited data by sex from other sources. For other survey programs (including the World Fertility Survey, the Reproductive Health Survey, and the Pan Arab Project for Family Health), surveys not affiliated with the major survey programs, and censuses, the data used here are any direct or indirect estimates by sex available in published sources, or calculated from tabulations available therein. In addition, the number of data points from vital registration was greatly expanded. A large dataset of infant and under-five mortality by sex calculated from vital registration data was provided by the World Health Organization. These data were supplemented with registration data from the Human Mortality Database, the United Nations Demographic Yearbook, and other sources of life tables.

Indirect estimates of mortality in childhood are derived from summary data on the total number of children ever born and number surviving to women of reproductive age. The method used to derive indirect estimates (also known as the Brass method) is described in detail in a United Nations manual [27] . A large number of censuses and surveys have collected the required data, although the data are not always collected or published by sex (that is, the questionnaires do not always ask about sons and daughters separately, or, if they do, the separate tabulations may not be published). The Brass method translates proportions of children surviving classified by age of mother at the time of data collection into measures of survival to various childhood ages, which in turn can be transformed into standard indicators of childhood mortality using model life tables. Under-five mortality is the preferred indicator derived via the Brass method, because 5 q 0 is more robust to the choice of model life table than 1 q 0 , which can vary considerably according to the model selected. For this reason, indirect methods do not provide a satisfactory basis for estimating sex ratios of 1 q 0 , since the sex ratios obtained for this indicator through indirect methods are more affected by the choice of mortality model used than are differentials in 5 q 0 .

The three indicators of childhood mortality can be estimated directly or indirectly from demographic data sources. Direct estimates of 1 q 0 , 4 q 1 , and 5 q 0 are calculated from reported deaths and information on the population exposed to the risk of death, and do not require the use of models for their derivation. Direct estimates may be based either on vital events data—normally from a vital registration system or in some cases from information about household deaths collected in a census or large survey—or on survey questions posed to adult women about their childbearing histories. The childbearing histories collected in surveys comprise the date of each live birth and the age at death of children who have died before the survey date. Period-specific probabilities of dying calculated from birth histories are based on reported deaths and the numbers of children at risk of dying during a specific period, such as the 5 y preceding the survey [26] .

A final caveat refers to the availability of data for the 2000s. In many cases, the last available data point refers to 2005 or earlier ( Table S1 ), and the estimates for the latter part of the decade are a projection of the earlier trend.

Some important potential non-sampling biases in survey reports of childbearing histories include errors in the dating of births and deaths or omission of events from the birth history. Incorrect assignment of dates to events—for example, the heaping of date of death on 12 mo of age—can have an effect particularly on the relative levels of 1 q 0 and 4 q 1 . Fortunately, for the purposes of the present study, such misdating is unlikely to occur differentially for the deaths of boys and girls, so it is unlikely to have a major impact on the sex differentials in either of these indicators. Omission of children from the birth history, on the other hand, might be more likely to differ by sex of the child. In most cases, however, there was insufficient data from alternative sources to assess whether sex-differential omission from survey birth histories was occurring. The exception was in India, where examination of sex ratios of infant mortality (SR1) from the Sample Registration System and from the National Family Health Surveys revealed systematic differences in the sex ratio of infant mortality between the two sources, with SR1 estimates from the National Family Health Surveys being consistently higher than those from the Sample Registration System. For the sex ratio of child mortality, in contrast, the two sources produced consistent estimates. The discrepancy in SR1 could be due either to defects in the sample registration system that understate male mortality, or to omission from the survey birth histories of girls who died, thus inflating survey estimates of excess male mortality. The assessment was made that the difference in SR1 was most likely due to underreporting in the National Family Health Surveys birth histories of babies who died shortly after birth, with daughters who died more likely to be omitted than sons who died [2] , [32] .

Such large sampling errors, which are even larger when estimates are disaggregated for a subset of the sample, complicate the assessment of trends in differential mortality by sex. For example, the male-to-female ratio of infant mortality calculated from birth histories for the Haiti 2000 DHS survey was 141 for 1991–1995 and 93 for 1996–2000, while the corresponding ratios for child mortality were 88 and 105. If taken at face value, the reported ratios would imply that the situation in Haiti changed from one in which there was excess male mortality under age 1 y and excess female mortality between ages 1 and 4 y to a reverse situation in only 5 y. The trend estimates derived in this study smooth out such fluctuations through the application of regression techniques described below.

Compared to most measures estimated by sample surveys, deaths of children are relatively rare events. The sample sizes of typical household surveys are not large enough to produce very precise estimates of childhood mortality, even for both sexes combined at the national level. In a study of 50 DHS surveys, Curtis [31] showed that relative standard error for estimated infant and under-five mortality over a 5-y period for both sexes at the national level ranged from 0.04 to 0.08, implying that the 95% confidence interval ranged from 8% to 16% on each side of the point estimate. For child mortality, relative standard errors were higher, in the range of 0.06 to 0.15, because fewer deaths occur at ages 1 to 4 y.

Data derived from the complete registration of births and deaths are the ideal basis for the estimation of mortality, since they cover the full set of events of interest and permit the estimation of trends. Unfortunately, in most developing countries the coverage and completeness of registration by vital registration systems is insufficient to produce accurate estimates of the level of childhood mortality. However, in the absence of evidence that reporting of births and deaths differs by sex of the child in a way that would affect the ratio of male to female mortality, such ratios derived from vital registration may usefully inform trends of sex differentials. The sex differentials in 1 q 0 and 5 q 0 calculated from vital registration data were used without adjustment, even when overall births and child deaths were known to be under-registered, on the assumption that under-registration in vital registration systems did not differ by sex of the child. More study is required to assess whether this assumption is valid. For most countries, however, sex differentials estimated from vital registration are consistent with those calculated from survey birth history data and often have considerably less variability. The same assumption of sex-neutral underreporting was made for data from census or survey questions on household deaths.

Estimation Methods

The estimation of sex differentials in under-five, infant, and child mortality proceeded in three basic steps: (1) estimate trend in the sex ratio of 5 q 0 (SR5); (2) estimate, and adjust if appropriate, trend in the sex ratio of 1 q 0 (SR1); and (3) apply those trends to both-sexes estimates of 5 q 0 and 1 q 0 to derive estimate and sex ratio of 4 q 1 (SR4).

In the first step, a weighted trend line SR5 t was fitted to all available SR5 estimates. The weights for data points from surveys, censuses, and vital registration were determined using a weighting scheme used in previous work by the UN IGME [33],[34]. This weighting scheme assigns progressively lower weights to direct estimates from birth histories that refer to 5-y time periods more distant from the survey date, on the assumption that recall errors may affect distant periods more strongly. For indirect data, low or zero weights are assigned to indirect estimates that are based on reports of women in the early and late childbearing years, on the assumption that these estimates may be of lower quality or subject to systematic biases.

Because of variations between countries in the amount and consistency of data available, three different methods were ultimately employed to estimate sex ratios of mortality. Initially, loess regression was tested for all countries. The loess method fits a series of polynomials to localized subsets of the data centered on each point of the dataset. The weight of each data point in the localized regression is determined by its distance from the center. A bandwidth, denoted alpha, selected by the user, determines the proportion of the dataset used to fit each local regression. A number of different alpha values were tested, to impose varying degrees of smoothing. For countries where estimates were based on a time series of vital registration data, it was found that the loess with an alpha of 0.75 captured changes in trend without being overly sensitive to short-term variation. In addition, a re-descending M estimator with Tukey's biweight function was applied in the loess procedure in R (family = “symmetric”) to reduce the influence of more extreme data points. The case of Bulgaria is shown in Figure 2A to illustrate the loess fitting method.

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TIFF original image Download: Figure 2. Examples of data and fits for sex ratios of under-five and infant mortality using different methods. (A) Loess method, applied to Bulgaria. (B) Linear method, applied to the Dominican Republic. (C) Average method, applied to Lao People's Democratic Republic. Points shown in gray were assigned zero weight in the weighting scheme. The fitted SR1 was adjusted in the linear and average methods to account for the exclusion of indirect data. VR, vital registration. https://doi.org/10.1371/journal.pmed.1001287.g002

For countries where the primary sources of data were sample surveys, however, the degree of smoothing required to achieve plausible results with the loess often was so strong that the results differed little from a simpler linear regression. The linear regression line had the additional benefit of being more straightforward to adjust for SR1, as described below. Therefore, for many developing countries the results are based on robust linear regression (implemented with the rlm function in the R MASS package and hereafter referred to as the “linear method”), shown for the Dominican Republic in Figure 2B.

There were a number of countries where neither loess nor robust linear regression fitted to all data points was able to produce a result that was satisfactory for purposes of analysis or disaggregation. In a few of these countries, where time series of vital registration data were available to fit a stable trend and survey data had high sampling error, the decision was made to exclude the survey data and fit the loess or robust linear regression to the vital registration data only. In countries where such a stable time series was not available, a simple weighted average of all available SR5 data was computed (as in Figure 2C for Lao People's Democratic Republic). Such an average may be useful for disaggregating both-sexes estimates if no other method is available, but it does not give any information on time trends in SR5. For this reason, results from the average method are not analyzed at length, and countries where it was used are excluded from the time trend analysis for regional aggregations presented below. Table S2 indicates which of the methods—loess, linear, or average—was used to produce estimates of sex differentials for each country.

The second step of the estimation process was to fit a trend line SR1 t to available data on SR1. As was noted in the previous section on data sources, indirect data on SR1 were not included in the analysis because SR1 is less robust than SR5 to the choice of model life table. Yet, using only direct data for SR1 while using both direct and indirect data for SR5 could cause inconsistency between time series fitted for SR1 and SR5. This was particularly the case in countries where a number of surveys had collected indirect data only. Therefore, in order to best exploit the available information, direct and indirect estimates of SR5 were used to adjust direct estimates of SR1 in the linear and average methods. A preliminary trend line, SR1 t *, was fitted to SR1 from direct data using the same fitting method that had been selected for SR5 t . If no indirect data had been used to fit SR5 t , then SR1 t * was adopted as the final estimate SR1 t . If both direct and indirect data had been used to fit SR5 t , an additional trend line, SR5 t *, was fitted to SR5 points coming from direct data only. The ratio of SR5 t /SR5 t * was used to adjust SR1 t *, producing the final estimate SR1 t . Figure 2B and 2C show the results of this adjustment for the Dominican Republic and Lao People's Democratic Republic, respectively.

Predicted SR5 t and SR1 t were applied to estimates of 5 q 0 and 1 q 0 for both sexes to produce time series of infant and under-five mortality levels by sex. Levels of 5 q 0 by sex for time period t were derived from the both-sexes estimates using the formulas (2)and (3)where SRB is the sex ratio at birth as estimated for each country for the period 2000–2005 in World Population Prospects: The 2010 Revision [35]. Corresponding formulas were applied for infant mortality. Then, 4 q 1male and 4 q 1female were derived via the relationship in Equation 1. The resulting 4 q 1male and 4 q 1female were used to compute estimates of SR4 t . These derived estimates of SR4 t were compared to direct data on SR4 from surveys or vital registration and generally found to be consistent.

Estimates of under-five and infant mortality rates for both sexes combined were taken from two United Nations sources, World Population Prospects: The 2010 Revision, produced by the Population Division [35], and Levels & Trends in Child Mortality: Report 2011, produced by the UN IGME [36],[37]. The estimates from these two sources are generally quite similar for 5 q 0 —the indicator coordinated by the UN IGME—but can differ somewhat more for 1 q 0 , usually because of the use of different model life tables. The both-sexes estimates for 5 q 0 and 1 q 0 from World Population Prospects [35] were used in this report for most developing countries (noting that for 5 q 0 the estimates referring to periods prior to 1980 are unpublished). The choice of which series of both-sexes estimates to use does not affect the estimated trends SR5 t or SR1 t , as those come from the data, but it does affect estimated trends in SR4 t because the trend in the sex ratio of 4 q 1 derived from estimated 5 q 0 and 1 q 0 is dependent on the relative levels of 5 q 0 and 1 q 0 as well as the sex differentials in each. There were only a few cases where the choice of both-sexes estimate made an appreciable difference in SR4 t . For countries of the more developed regions, estimates from Levels & Trends in Child Mortality [36] were used because levels of 5 q 0 and 1 q 0 from this set of estimates are taken directly from annual vital registration.

For countries where averages of SR5 and SR1 were employed, these average ratios were applied to the whole series of both-sexes estimates. It should be noted that applying constant SR5 t and SR1 t to changing both-sexes estimates results in SR4 t values that change over time. However, these changes in SR4 t should not be interpreted as trends and will not be presented as such. As noted above, estimates for countries where the average method was used are not included in the aggregated trends for regions and development groups presented below.

Estimates were attempted for all countries or areas (hereafter referred to as countries) that had a population of 1 million or more in 2010. Out of the 156 countries with such a population, estimates were generated for 153 countries (Table 1). Of these, 113 were in less developed regions, comprising Africa, Asia excluding Japan, Latin America/Caribbean, and Oceania excluding Australia and New Zealand (the lists of countries located in the less developed regions and more developed regions as well as the other geographical groupings used for this study—sub-Saharan Africa, northern Africa/western Asia, eastern/southeastern Asia, Commonwealth of Independent States [CIS] Asia, Latin America/Caribbean, and developing Oceania—are shown in Table S3). Ninety-two countries in the less developed regions, containing 92% of the population of those regions, had sufficient data to apply the methods developed for trend analysis. For an additional 21 countries, holding 6% of the population of the less developed regions, enough data were available to estimate average sex differentials in under-five or infant mortality, which were assumed to apply to the entire time span under consideration.

Trends were estimated for 39 countries in the more developed regions (comprising Europe, northern America, Japan, Australia, and New Zealand), while for one developed country (Bosnia and Herzegovina), only average sex differentials could be estimated.

The methods and results presented in this article were developed as an analytical study separate from the production of United Nations mortality estimates published in Levels & Trends in Child Mortality [36] or World Population Prospects [35]. The mortality estimates by sex presented here may differ from estimates in forthcoming editions of those publications due to differences in data availability or other methodological considerations.

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[1] Url: https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1001287

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