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Introduction

This chapter provides definitions and explanations of key DSS-generated mortality rates and measures, as well as describing the methodology employed in calculating them. It is intended for readers unfamiliar with these rates and measures. Their calculation is basic, and the various formulas can be found in standard textbooks (see for example, Shryock and Siegel 1976; Kpedekpo 1982; Newell 1994). These measures have been briefly discussed in this chapter for quick reference, as they form the basis for standardizing the results across DSS sites. Perhaps the most important reason for discussing them is the opportunity it affords to discuss the classic controversy over whether to define some of them as rates or ratios (for example, infant mortality, under-five mortality, and maternal mortality). Furthermore, this chapter provides an explanation of the need for a standard population and introduces the INDEPTH standard population for Africa south of the Sahara, discussed in greater detail in Part II.

Rates and ratios

Rates and ratios are frequently used in measuring demographic events. Rate refers to the frequency of events. A rate is estimated by taking the number of events in a given period and dividing it by the population at risk during that period. Pressat (1985, p. 194) stated that the term rate

is also used more loosely to refer to the ratio between a sub-population and the total. . . . In many other uses of rate, the measure in question would be better termed a ratio, proportion, or probability. The term can be justified only when a dynamic process is being measured, not a static description of a population at a given date, although its use in the latter sense is widespread. In general the word ratio is preferable to rate when the measure is not one relating events to a population at risk.

A ratio is the proportion between a numerator and a denominator that are related (for example, under-five child deaths per 1000 under-five person–years lived in a given year).

Crude death rate

The crude death rate (CDR) is defined as the number of deaths in a given period divided by the total population. Although the CDR can be computed for any segment of time, the period usually used is a year, and the denominator used in the rate calculation is the midyear population. The midyear population is the size of the population (or any specified group within the population) at the midpoint of a calendar year. This midpoint is often calculated as the arithmetic mean of the size of the population at the beginning and end of the year. Conventionally, the rate is expressed as a number per 1000 individuals.

In the case of a population under continuous surveillance, with possibly high in- and out-migration rates that may yield a strong variation in population size, the use of exact person–years lived is preferred. Person–years is the sum, expressed in years, of the time spent by all individuals in a given category of the population (Pressat 1985). Specifically, these years express the periods that eligible individuals spent in the DSA. Times or periods spent outside the DSA due to migration or death are excluded.

Age-specific death rate and ratio

Because of the differentials in exposure to the risk of dying, epidemiologists and demographers often use age-specific death rates (ASDRs) and sex-specific death rates, instead of the CDR. ASDRs are the most commonly used. The ASDR for an age group is defined as the number of deaths in the age group in a specific period divided by the total number of person–years lived in that age group during that period and multiplied by 1000. Demographers often use a slightly different notation. They express the ASDR of a particular age group as the deaths among individuals in that age group in the year, divided by the mid-year population of that age group and then multiplied by 1000. Five-year age groups are common, although age categories vary according to the purpose of study.

The following discussion of infant, under-five, and maternal mortality measures highlights the classic controversy over whether to define these measures as rates or ratios. The denominator used in calculating a measure determines whether it is a rate or a ratio. As stated earlier, the measure is a rate when the total number of individuals at risk is used as the denominator, and it is a ratio when some other event is used as the denominator.

Infant mortality

It is usually difficult to estimate the number of person–years lived for children <1 year old (infants). Consequently, the total number of live births is often used as the denominator to calculate the infant mortality rate. The total number of deaths among children <1 year old in a calendar year is divided by the live births in the same year, multiplied by 1000. Calculating the infant mortality rate in this way makes it more appropriately referred to as a ratio.

Infant deaths are unevenly distributed through the first year of life. A high proportion of infant deaths usually occurs in the first month of life. Of these deaths, a high proportion occurs during the first week of life; and of these, a high proportion

occurs during the first day. The conventional infant mortality rate or ratio may usefully be broken up into rates or ratios covering the early stages of life and a rate or ratio for the remainder of the year. The one for the first period is called the neonatal mortality rate or ratio, and that for the second period is called the postneonatal mortality rate or ratio. These concepts are briefly defined in the following paragraphs.

Neonatal mortality is defined as the number of deaths of infants <4 weeks old (or <1 month old) during a year. It is calculated by dividing the deaths of infants <28 days old during a year by the live births in the same year and multiplying by 1000. Early neonatal mortality is calculated by dividing the deaths of infants <7 days old during a year by live births in the same year and multiplying by 1000. Late neonatal mortality is calculated by dividing the deaths of infants 7–28 days old in a year by live births in the same year and multiplying by 1000. Postneonatal mortality is calculated by dividing the deaths of infants 4–51 weeks old during a year by live births in the same year and multiplying by 1000.

Infant mortality can also be expressed as a probability of dying before reaching the age of 1 year. Perinatal mortality is calculated by dividing the sum of stillbirths in the year and the deaths of infants <7 days old during the year by the sum of stillbirths in the year and live births in the same year.

Under-five mortality

Some consider the under-five mortality as a ratio expressing the number of deaths of children <5 years old divided by the number of live births in a year and then multiplied by 1000. Others treat it as a rate, calculating it by dividing the number of deaths of children <5 years old by the total number of person–years of children <5 years old and multiplying by 1000. When under-five mortality is presented as a probability of dying before age 5, it is expressed as ₅q₀.

Maternal mortality rate and ratio

Most DSSs record all pregnancies and their outcomes as well as deaths. As such, they have the potential to provide accurate, up-to-date estimates of maternal mortality rates and ratios. The maternal mortality ratio is conventionally defined as the number of deaths due to puerperal (pregnancy-related) factors per 100 000 live births. But strictly speaking, this is referred to as a ratio because the denominator is not the persons at risk of experiencing the event. In view of this, the following are the methods for estimating maternal mortality ratios and rates. The maternal mortality ratio is calculated by dividing the number of pregnancy-related deaths in a specified period by that of live births in the same period and multiplying by 100 000. The maternal mortality rate is calculated by dividing the number of pregancy-related deaths in a specified period by person–years lived by women of childbearing age and multiplying by 1000.

Maternal mortality can also be estimated by relating maternal deaths to women of reproductive age or to all pregnancies, including stillbirths and abortions.

Standardization

Age-standardized death rate

Crude mortality rates are inappropriate for comparing different populations within the DSS sites because of the different age structures within the sites. On the other hand, a single parameter is required for simple comparison. Therefore, standardized rates are used, in which the age-specific mortality rates are combined using a standard population. An INDEPTH standard population for sub-Saharan Africa (SSA) has been developed (see Table 6.2). More details on the INDEPTH standard population are provided in Chapter 6. The Segi (1960) and the new World Health Organization (WHO) standard age distributions are also shown in Table 6.2.

Age-specific rates are weighted averages of rates, where the weights are obtained as a proportion of the standard population in the respective age group. The summation goes over all age groups.

Confidence intervals for rates

Estimates of the mean and standard deviation of a population are usually needed if it is impossible to deal with the entire population. The standard deviation of a distribution of sample means is referred to as the standard error of the sample. It measures how precisely the sample mean estimates the population mean. For example, with a 95% confidence interval, about 95% of the sample means obtained by repeated sampling would lie within two standard errors below or above the population mean. Based on the sample mean and its standard error, a range of likely values can be constructed for a population mean that is not known. This range is referred to as a confidence interval. More precisely, there is a 95% probability that a particular sample mean lies within 1.96 standard errors above or below the population mean.

Confidence intervals can be calculated for the ASDRs. The variance of the CDRs or the ASDRs is used instead of the means. Estève et al. (1994) discussed the method in detail. For a small number of deaths or for small populations, however, confidence intervals for ASDRs are not reliable, because the formula used to calculate them is too imprecise. The question is then one of how large the numbers of deaths and populations must be to give reliable results. It is difficult to supply a rule of thumb, and as Estève et al. (1994, p. 58) noted,

It is however difficult to tell what “sufficiently large” means in the present context because the numerator of a standardised rate is no longer a Poisson variable. Its variance depends not only on the total number of observed cases but also weighting scheme and the accuracy of the age-specific rates.

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