# The lifetime risk of maternal mortality: concept and measurement

## John Wilmoth ^{a}

a. Department of Demography, University of California, Berkeley, CA, United States of America.

Correspondence to John Wilmoth (e-mail: jrw@demog.berkeley.edu).

*(Submitted: 05 October 2007 – Revised version received: 14 July 2008 – Accepted: 28 July 2008 – Published online: 13 February 2009.)*

*Bulletin of the World Health Organization* 2009;87:256-262. doi: 10.2471/BLT.07.048280

### Introduction

The importance of quantifying the loss of life caused by maternal mortality in a population is widely recognized. In 2000, the UN Millennium Declaration identified the improvement of maternal health as one of eight fundamental goals for furthering human development. As part of Millennium Development Goal 5, the UN established the target of reducing the maternal mortality ratio by three-quarters between 1990 and 2015 for all national and regional populations.^{1}

The maternal mortality ratio (*MMR*atio) is obtained by dividing the number of maternal deaths in a population during some time interval by the number of live births occurring in the same period. Thus, the *MMR*atio depicts the risk of maternal death relative to the frequency of childbearing. A related measure, the maternal mortality rate (*MMR*ate), is found by dividing the average annual number of maternal deaths in a population by the average number of women of reproductive age (typically those aged 15 to 49 years) who are alive during the observation period. Thus, the *MMR*ate reflects not only the risk of maternal death per pregnancy or per birth, but also the level of fertility in a population.

In addition to the *MMR*atio and the *MMR*ate, the lifetime risk, or probability, of maternal death in a population is another possible measure. Whereas the *MMR*atio and the *MMR*ate are measures of the frequency of maternal death in relation to the number of live births or to the female population of reproductive age, the lifetime risk of maternal mortality describes the cumulative loss of human life due to maternal death over the female life course. Because it is expressed in terms of the female life course, the lifetime risk is often preferred to the *MMR*atio or *MMR*ate as a summary measure of the impact of maternal mortality.

However, despite its interpretive appeal, the lifetime risk of maternal mortality can be defined and calculated in more than one way. A clear and concise discussion of both its underlying concept and measurement methods is badly needed. This article addresses these issues and is intended to serve as a basis for official estimates of this important indicator of population health and well-being. In fact, the measure recommended here was adopted for use with the 2005 maternal mortality estimates published by the UN.^{2}

### Basic concepts

The lifetime risk, or probability, of maternal mortality could reflect at least three different underlying concepts, which can be summarized briefly as follows:

- The fraction of infant females who would die eventually from maternal causes in the absence of competing causes of death from birth until menopause.
- The fraction of infant females who would die eventually from maternal causes when competing causes of death are taken into account.
- The fraction of adolescent females who would die eventually from maternal causes when competing causes of death are taken into account.

In formulae, these three concepts of lifetime risk can be defined as follows:

(1)

(2)

(3)

where each summation is over an age range, with *x* = 15 to 49 years. Each formula yields a probability of maternal death over some portion of the female life course, given a particular set of assumptions about other causes of death.

In these three equations, *MMR*atio* _{x}* is the maternal mortality ratio at age

*x*,

*MMR*ate

*is the maternal mortality rate at age*

_{x}*x*,

*f*is the fertility rate at age

_{x}*x*, ℓ

*is the number of survivors at age*

_{x}*x*in a female life table, and

*L*is the number of woman-years of exposure to the risk of dying from maternal or other causes between ages

_{x}*x*and

*x +*1 for the hypothetical cohort of women whose lifetime experience is depicted in the same life table. The equivalence between the two expressions in each equation follows from observing that

and

where, for a given time period, *MD _{x}* is the number of maternal deaths occurring among women aged

*x*,

*W*is the number of woman-years of exposure at age

_{x}*x*in the observed population (in contrast to

*L*, which refers to the hypothetical population of a female life table), and

_{x}*B*is the number of live births in women aged

_{x}*x*. Therefore,

*MMR*ate

*atio*

_{x}= MMR

_{x}× f_{x}.
Note that *LR*_{2} and *LR*_{3} are related as follows:

(4)

where ℓ_{15}/ℓ_{0} is the probability that a woman will survive from birth (i.e. 0 years) to age 15 years, as derived from a female life table. Equation 4 can be used for computing *LR*_{2} from *LR*_{3}, or vice versa.

To understand Equation 2 better, observe that each element of the sum can be represented verbally as follows:

Note that “woman-years lived at age *x*” refers in one case to the observed population and in the other to the hypothetical population of a female life table. Thus, the observed age-specific maternal mortality rates are applied to the fictitious life-table population as a means of constructing a synthetic measure of lifetime risk for a given time period.

Summing Equation 2 across age (i.e. *x* = 15 to 49 years) yields the number of maternal deaths over the life course per female live birth, or in other words, the *full* lifetime probability of maternal mortality, with other causes of death taken into account. A similar analysis of Equation 3 illustrates that it represents the *adult* lifetime probability of maternal mortality per 15-year-old female.

By contrast, Equation 1 contains the implicit assumption that the number of woman-years lived between ages *x* and *x +* 1 per female live birth (*L _{x}*/ℓ

_{0}) is one for all ages, so in effect it ignores all forms of mortality, including that from maternal causes. Thus, it is theoretically possible within this model for a woman to die more than once from a maternal cause over her lifetime (similar to having more than one birth). This imprecision is unimportant, however, since

*MMR*ate

*is typically quite small at all ages, usually less than 1 per 1000, and thus higher-order terms are negligible.*

_{x}Since

in all human life tables, it follows that:

(5)

Therefore, of the three concepts of lifetime risk, the first one, *LR*_{1}, yields the largest probability of maternal death over a lifetime. However, this value is inflated because deaths due to other causes are ignored. If such deaths are factored into the calculation, the resulting lifetime risk of maternal death is reduced. A variant of *LR*_{1} was used for computing the lifetime risk of maternal mortality in UN estimates for the year 2000.^{3}

The second concept, *LR*_{2}, yields the smallest probability of maternal death over a lifetime, while the third concept, *LR*_{3}, yields a value that lies between the other two. Both *LR*_{2} and *LR*_{3} take account of competing risks due to other causes of mortality. However, many deaths from other causes occur in childhood, before the risk of maternal death becomes relevant. If childhood deaths are eliminated from the calculation, *LR*_{3} reflects the *adult* lifetime risk of maternal death.

The size of the differences between the three measures in Equation 5 depends strongly on the level of overall mortality in a population. In populations with a high probability of survival to adulthood, there is very little difference between them; the three measures differ most in populations with relatively high levels of mortality from all causes, including maternal causes.

For all three concepts, the measures of lifetime risk are hypothetical in the sense that they rely on the demographic patterns observed in a population during a single period of time. Thus, they represent the lifetime risk of maternal mortality for a cohort of females who, hypothetically, are subject throughout their lives to prevailing demographic conditions, as reflected by age-specific rates of fertility and mortality, including maternal mortality. Like life expectancy at birth, they are examples of “period” measures of population characteristics as used in standard demographic analysis.^{4}^{–}^{6}

### Age-specific maternal mortality data

The Bangladesh Maternal Health Services and Maternal Mortality Survey of 2001 was a nationally representative survey that collected information about mortality in general and about maternal deaths in particular.^{7} The data presented here are based on births and deaths that occurred within interviewed households during a period of 3 years before the survey. For each reported death, information was gathered on the age and sex of the deceased. In addition, if the deceased was a woman aged 13–49 years, follow-up questions were asked to determine whether the death was due to a maternal cause.

Using such information, it was possible to compute various age-specific measures of fertility and mortality, including maternal mortality. Table 1 illustrates the results obtained when all three measures of lifetime risk were calculated for Bangladesh during 1998–2001 using data derived from the 2001 survey and Equation 1, Equation 2 and Equation 3. In these calculations, when age-specific information about maternal deaths was used to compute the lifetime risk, the value of each measure was the same whether based on *MMR*atio* _{x}* or

*MMR*ate

*.*

_{x}### Summary maternal mortality data for ages 15–49 years

In most situations, the age distribution of maternal deaths is not known and information is limited to summary measures, such as the *MMR*atio or the *MMR*ate, which are computed using data on maternal deaths, live births and woman-years of exposure for ages 15–49 years combined. To obtain the formulae for lifetime risk that are used in practice from Equation 1, Equation 2 and Equation 3, one must assume that either the *MMR*atio or the *MMR*ate is constant across all ages.

For example, if one assumes the *MMR*atio is constant across all ages, Equation 1, Equation 2 and Equation 3 can be simplified as follows:

(1a)

(2a)

(3a)

Here, *TFR* is the total fertility rate, or the number of children per woman implied by age-specific fertility rates, *f _{x}* , if we assume death does not occur until at least the age when menopause is reached, and

*NRR*is the net reproduction rate, or the expected number of female children per newborn girl given current age-specific fertility and mortality rates. The factor of 2.05 in Equation 2a and Equation 3a comes from assuming a typical sex ratio at birth (i.e. 105 boys per 100 girls) and is needed here because the

*NRR*is expressed in terms of female births only.

Alternatively, if we assume the *MMR*ate is constant across age, the three equations become the following:

(1b)

(2b)

(3b)

Here, *T*_{15} – *T*_{50} is a life-table quantity representing the number of woman-years lived between ages 15 and 50 years, and the factor of 35 in Equation 1b corresponds to the reproductive interval from age 15 to 50 years. If a different reproductive interval were used for computing the *MMR*ate, these equations would need to be modified accordingly.

These two sets of formulae can be considered as alternative approximations for Equation 1, Equation 2 and Equation 3. Their accuracy depends on the validity of the underlying assumptions: that either *MMR*atio* _{x}* or

*MMR*ate

*has a constant value across the age range. In this regard, it is clear which of the two sets of approximations is preferable:*

_{x}*MMR*ate

*tends to be more stable over age than*

_{x}*MMR*atio

*, as illustrated in Table 1, for the population of Bangladesh between 1998 and 2001. This pattern is expected to be observed in general and follows from the relationship linking these two measures at a given age*

_{x}*x*. Recall that

*MMR*atio

*ate*

_{x}× f_{x}= MMR*. Thus, the relative stability of*

_{x}*MMR*ate

*over age occurs because the sharp age-related increase in the risk of maternal death per live birth,*

_{x}*MMR*atio

*, is balanced by a sharp decline in the fertility rate,*

_{x}*f*, at older ages.

_{x}
The greater accuracy of approximations based on the *MMR*ate is confirmed in Table 2, which shows all three measures of lifetime risk computed for Bangladesh from 1998 to 2001 using three types of information about maternal mortality: age-specific data, the *MMR*atio and the *MMR*ate. The differences between rows in the table are consistent with the inequality in Equation 5. The differences between columns confirm that estimates of lifetime risk derived using age-specific data are closer to approximations derived using the *MMR*ate than to those derived using the *MMR*atio. Observe that, in this example, estimates based on the *MMR*ate have a small but consistent upward bias of around 2–3% in relative terms. However, estimates based on the *MMR*atio have a much larger downward bias, about 16–17%.

Finally, it is important to note that none of the lifetime risk measures in Table 2 is identical to the one used in the published report of UN maternal mortality estimates for the year 2000.^{3} That measure, here called *LR*_{0}, equals 1.2 × *LR*_{1}, as computed using Equation 1a. The factor of 1.2 was intended to serve as a means of incorporating maternal deaths associated with pregnancies that did not result in a live birth. However, this adjustment is inappropriate, since the *MMR*atio depicts the frequency of maternal deaths in relation to the number of live births, not the number of pregnancies.

### Discussion

In summary, the choice between possible measures of the lifetime risk of maternal death has two dimensions: the desired concept of lifetime risk and the accuracy of the calculation method. Of the three concepts of lifetime risk considered here, the first should be rejected as inappropriate because it ignores other forms of mortality (i.e. competing risks) and consequently exaggerates the lifetime risk of maternal mortality. The other two concepts both take competing risks into account and differ only in terms of their starting point: either birth or age 15 years, with the latter representing an approximate minimum age of reproduction.

There seem to be few precedents to guide the choice between the second and third concepts of lifetime risk. One source defined the “lifetime risk of maternal death” as the “probability of maternal death during a woman’s reproductive lifetime”.^{8} This definition seems to imply a conditional probability in which the pool of women at risk should include only those who survived to the age when reproduction starts. Members of the working group that produced the UN estimates of maternal mortality for 2005 came to the same conclusion; namely, that the concept of “lifetime risk of maternal mortality” should refer to the probability of maternal death conditional on survival to age 15 years, with other forms of mortality taken into account (i.e. *LR*_{3}).

Ideally, measures of lifetime risk should be computed using age-specific data. In most situations, however, one does not possess age-specific information about maternal mortality. For international comparisons, therefore, one needs a method that produces reliable results using either the *MMR*atio or the *MMR*ate computed for ages 15–49 years. I have demonstrated here that *MMR*ate* _{x}* tends to be more stable as a function of age than

*MMR*atio

*and, therefore, that the*

_{x}*MMR*ate yields more accurate estimates of the lifetime risk of maternal death.

Based on these two conclusions about concept and accuracy, I recommend that *LR*_{3} computed using the *MMR*ate be used for international comparisons of the lifetime risk of maternal mortality. As noted already, this approach was used to derive the 2005 UN estimates.^{2}

Table 3 compares estimates, for the world as a whole and for various regional groupings, of the lifetime risk of maternal mortality in 2005 derived using all the calculation methods discussed here, except those that rely on age-specific data. Taking sub-Saharan Africa as an example, the range of estimates extends from 3.41% to 5.76%, or from 1 in 29 to 1 in 17. Note that the measure of lifetime risk used for the 2000 UN estimates, *LR*_{0}, gives the highest value of the lot, whereas the measure recommended here and used for the 2005 estimates (i.e. *LR*_{3} based on the *MMR*ate) gives an intermediate value of 4.47%, or 1 in 22.

For the population groupings shown in Table 3, the measure of lifetime risk used for the 2000 UN estimates exaggerates the lifetime risk relative to the measure used for the 2005 estimates by an average of around 20%.

Thus, the two sets of estimates are not directly comparable: a trend analysis based on the 2000 and 2005 estimates of lifetime risk would exaggerate the pace of decline in some cases, while it would understate the speed of increase or reverse the direction of change in others. For this reason, and because of other changes in the methods used between the 2000 and 2005 UN studies of maternal mortality, the two sets of estimates should not be used for trend analysis. Any such analysis should focus on the 1990 and 2005 regional estimates of the *MMR*atio.^{2} ■

##### Acknowledgements

The analysis presented here was initiated while the author was working for the UN Population Division. The author thanks his colleagues in the Maternal Mortality Working Group for their constructive comments about this work. Special thanks to Emi Suzuki of the World Bank for assistance with data. The comments of two anonymous reviewers were very helpful.

**Funding:** Final data analysis and preparation of this article for publication were supported by a grant from the United States National Institute on Aging (R01 AG11552).

**Competing interests:** None declared.

#### References

*The Millennium Development Goals report 2007*. New York, NY: United Nations; 2007.*Maternal mortality in 2005: estimates developed by WHO, UNICEF, UNFPA, and the World Bank*. Geneva: World Health Organization; 2007.*Maternal mortality in 2000: estimates developed by WHO, UNICEF, and UNFPA*. Geneva: World Health Organization; 2004.- Keyfitz N, Caswell H.
*Applied mathematical demography*, 3rd ed. New York, NY: Springer; 2005. - Preston SH, Heuveline P, Guillot M.
*Demography: measuring and modeling population processes*. Oxford: Blackwell; 2001. - Leridon H, Toulemon L.
*Démographie: approche statistique et dynamique des populations*[in French]. Paris: Economica; 1997. - National Institute of Population Research and Training (NIPORT), ORC Macro, Johns Hopkins University and ICDDR. B.
*Bangladesh maternal health services and maternal mortality survey 2001*. Dhaka and Calverton, MD: ORC Macro & ICDDR,B; 2003. - Ronsmans C, Graham WJ. Maternal mortality: who, when, where, and why.
*Lancet*2006; 368: 1189-200 doi: 10.1016/S0140-6736(06)69380-X pmid: 17011946. *World population prospects: the 2004 revision, extended dataset (CD-ROM edition)*. New York, NY: United Nations; 2005.