A ratio is simply one number divided by another number; for example, the number of beers drunk in one year divided by the number of people in the population (beers per capita) or the number of cases observed divided by the number of cases expected.
A proportion is a special type of ratio in which everything or everyone in the numerator is also counted in the denominator; for example, the number of people who develop disease divided by the total number of people in the population (those with and without disease). A proportion can be expressed as a number between 0 and 1 or as a percentage between 0 and 100%. All proportions are ratios – not all ratios are proportions.
A rate should contain some measure of time, for example 60 km per hour, 17/100,000 per year.
As an example, the case–fatality ratio is a proportion and therefore also a ratio, but is not a rate (although it is often described as such) because it does not contain units of time.
total of 31,068 deaths (0.4%) were due to electrocution. This value was almost 12 times higher (PMR= 1,180) than the proportion of such deaths that would be expected in the general US population (Robinson et al., 1999). Proportional mor- tality ratios have fairly limited utility because they cannot easily be compared across different populations. They are usually calculated only when no popula- tion data are readily available and precise mortality rates cannot be calculated.
The case–fatality ratio (CFR)
The CFR (often called the case–fatality rate, although, strictly speaking, it is not a rate; see Box 2.9 above) is the proportion of people with a given disease or condi- tion who die from it in a given period. It is a common measure of the short-term severity of an acute disease and allows a direct assessment of the effectiveness of an intervention. For example, the CFR for myocardial infarction (heart attack) is usually measured over a period of 28 days. When deaths occur over a longer time period then it is more appropriate to consider the survival rate (see below). The CFR is usually expressed per 100 cases, i.e. as a percentage. As an example, the overall CFR in the 2003 SARS epidemic was estimated to be 14%–15%, i.e. approx- imately one in every seven people who contracted SARS died. However, this aver- age ratio hides the fact that, while patients under the age of 25 were unlikely to die (CFR= 1%), approximately half of patients over the age of 65 died (CFR = 50%). (Note that the mortality from SARS occurred so quickly that the particular time period the CFR refers to is generally not specified.)
Survival rate and relative survival rate
As we discussed above, the CFR is an appropriate measure for short-term mortal- ity (a month or so) but is less useful for conditions in which death may occur fur- ther down the track. For conditions such as cancer, mortality is often expressed in terms of the proportion of patients who are still alive a specified number of years after diagnosis – the survival rate. This proportion is often adjusted to allow for the fact that, depending on the age group being considered, some people would have been expected to die anyway from causes other than their cancer and this is known as the relative survival rate. A relative survival rate of 100% thus indi- cates that mortality does not differ from that experienced by the general pop- ulation. For example, in developed countries five-year relative survival rates for breast cancer are approximately 75%–80%, compared with only about 15% for lung cancer.
Measures of mortality related to childbirth and early life
In the second half of the twentieth century, organisations such as the World Health Organization started using a number of measures relating to maternal and, in particular, infant mortality as critical indicators of the general health of a community. This allowed comparison between regions and also tracking of improvements in health over time. Table 2.8 shows a number of these measures. (Note that, technically, they are proportions rather than true rates because they do not have units of time – see Box 2.8; they are, however, commonly described as rates and we will also use this terminology.)
The underlying concept of each rate is the same – it is the ratio of the actual number of deaths that occur in one year to the total population ‘at risk of death’ in the same year. Because it is not always possible to obtain an accurate figure for the number of people at risk, an approximation is sometimes used. For exam- ple, any woman who is pregnant is at risk of maternal death but the number of women who are pregnant in a given year is not routinely recorded, so in practice this is estimated by taking the number of live births in one year. It is also worth noting that the infant mortality rate is the number of infant deaths (age 0–1 year) relative to the number of live births in the same year. This means that the chil- dren in the numerator (deaths) are not the same as those in the denominator (births) because many of those who die will have been born in the previous year. This is not a problem if the birth rate is fairly stable.
For each rate we have given the most standard definition but, as you will see, there are some variations. For example, the stillbirth (or fetal death) rate should be calculated as the ratio of stillbirths to the number of live births plus the num- ber of stillbirths. This is because all of these children (live plus stillbirths) were at risk of being stillborn although not all of them were. This measure is, however,
Other measures commonly used in public health 57
Table 2.8 Measures of mortality related to childbirth and early life.
Deaths Population at risk
Measure (numerator) (denominator) Notes
Maternal mortality rate
Deaths among women from causes related to childbirth in 1 year (the WHO defines this as deaths up to 42 days after birth, but sometimes deaths up to 1 year are included)
Number of live births in the same year
Strictly speaking the denominator should be all pregnant women but this information is not recorded directly
Stillbirth or fetal death rate
Number of stillbirths in 1 year where a stillbirth is usually a fetal death after 28 weeks gestation although other time points may also be used (e.g. 20 weeks)
Live births+ fetal deaths in the same year
Sometimes calculated as the ratio of the number of fetal deaths to the number of live births (excluding fetal deaths). This is often called the fetal death ratio
Perinatal mortality rate
Fetal deaths (>28 weeks) and deaths up to 7 days of life
Live births+ fetal deaths in the same year
May be calculated as the ratio of the number of deaths to the number of live births (excluding fetal deaths) and called the perinatal death ratio May also include deaths up to 28 days of life
Neonatal mortality rate
Deaths in children aged less than 28 days
Number of live births in the same year
Only live births are included in the denominator because only babies born alive are at risk of dying before the age of 28 days
Post-neonatal mortality rate
Deaths in children from 28 days to 1 year
Number of live births in the same year
Strictly speaking the denominator should exclude children who die before age 28 days because they are no longer at risk.
Infant mortality rate Deaths in children up to 1 year of age
Number of live births in the same year
Probably the most widely used single indicator of the overall health of a community
Child death rate Deaths in children aged 1 to 4 years
Number of children aged 1–4 years in the population
An example of an age-specific mortality rate.
Child mortality rate Deaths in children up to 5 years of age
Number of live births in the same year
An alternative to the child death rate, preferable in countries where it is hard to enumerate the population of young children
1000 Sierra Leone Nigeria Uganda Ethiopia India China Sri Lanka Russia South Africa Brazil Vietnam Qatar Malaysia USA New Zealand UK Australia Japan Switzerland Singapore 100 10 1 100 1000 10000 100000 1000000 GDP per capita ($) In fa nt mor
tality (per 1000 bir
th
s)
Figure 2.4 Infant mortality rates in relation to GDP in 20 countries around the world. (Drawn from: The World Factbook 2009. Washington DC. Central Intelligence Agency, 2009. https://www.cia.gov/library/ publications/the-world- factbook/index.html, accessed 16 January 2010.)
sometimes presented as a stillbirth or fetal death ratio where only live births are counted in the denominator. The WHO in particular tends to use this variant. Because the number of live births will be less than the number of live births plus stillbirths, the fetal death or stillbirth ratio will always be slightly larger than the stillbirth rate. You will also notice that there is not always a standard definition of what constitutes a case (in this case a death). It just goes to reinforce how impor- tant it is to check exactly what the numbers refer to in order to make sure that you are always comparing like with like.
Figure 2.4 shows the enormous variation in infant mortality rates around the world, reflecting the great disadvantages under which many countries still labour. It also shows the very strong inverse correlation between GDP (gross domestic product) and infant mortality – the more wealthy a country the lower the infant mortality rate. In a poor country like Sierra Leone the rate is as high as 154 per 1,000 live births. In other words, more than one in 10 babies die before their first birthday, compared with less than 3 per 1,000 in Japan and Singapore.
It is important to remember that all of these measures just give an average pic- ture for the whole population. Low average rates can often hide much higher rates in some subgroups of the population. This is particularly true in coun- tries that include more than one ethnic group. For example, as you saw in Chap- ter 1, in Australia the Indigenous population has mortality rates that are several times higher than those of Australians as a whole, and in the USA in 2004 infant mortality was considerably higher among births to non-Hispanic black women
Measuring the ‘burden of disease’ 59
(13.6 per 1,000 live births) than for White or Asian and Pacific Islander mothers (5.7 and 4.7 per 1,000, respectively) (Mathews et al., 2007).
Measuring the ‘burden of disease’
In Table 2.6 we saw that age-standardised rates of heart disease were higher in Germany and Singapore than in Spain and Brazil, which, in turn, had higher rates than Japan, but this is only one disease; how does the overall health of these populations compare? The measures that we have looked at so far have focused on either morbidity (incidence) or mortality and many are only really useful for describing a single disease or group of diseases at a time. They can tell us how rates of cancer or mortality from heart disease vary between countries or over time but they are less useful if we want to look at the overall health of a popula- tion at a particular point in time and see how it compares with other time peri- ods and/or populations. Although global mortality measures such as the total mortality rate and the infant mortality rate give a broad view of this aspect of the health of a nation or group, they quite obviously tell us nothing about the many states of ill-health short of death. To make comparisons that are more inclusive of other aspects of health we need to use measures that allow us to combine the effects of multiple diseases as well as accounting for their severity and when they occur in life.
To solve this problem several different mortality- and morbidity-related mea- sures have been developed to describe the health of populations. New and more sophisticated variations are continually being introduced as organisations such as the WHO attempt not only to measure disease, but also to take into account related conditions such as pain, disability and loss of income that are associ- ated with ill-health. These measures bring us closer to measuring the overall ‘health’ of a population according to the WHO definition of health, and are being used increasingly by national and regional health departments for planning and resource allocation.
Life expectancy
A traditional mortality-based measure that accounts for the timing of death is
life expectancy, the average number of years that an individual of a given age
is expected to live if current mortality rates continue. For example, a boy born in the Russian Federation in 2002 has a life expectancy of 58.4 years, compared with 78.4 years for a boy born in Japan (WHO, 2003). Because it cannot take account of future changes in incidence and/or treatment of diseases, estimates of life expectancy are largely hypothetical. Mortality rates have been falling over time and, until recently, the expectation has been that this trend would continue into
100,000 90,000 80,000 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Age (years) Males N umber of su rviv or s Females Figure 2.5 Survivorship curve
for Australian males and females in 2005–2007. (Drawn from: Australian Bureau of Statistics, 2007.)
the future. Life expectancy figures therefore almost certainly underestimate the actual number of years someone could expect to live. However, the HIV/AIDS epidemic and other national phenomena, such as that seen for Russian men in Figure 1.2, have already reversed this situation in some countries; and this could become more generally true with the increasing ‘obesity epidemic’ in many Westernised countries predicted to lead to higher mortality rates and thus lower life expectancy in future (Olshansky et al., 2005).
Life expectancy can be presented for any age, but is used most commonly to describe life expectancy at birth. It is calculated using a ‘life-table’ similar in prin- ciple to that shown in Table 1.4. The starting point is a hypothetical group of new- borns (usually 100,000) and age-specific mortality rates are then used to estimate the number that would be expected to die at each year of life. The total number of years of life expected for the entire cohort can then be added up and the life expectancy at birth is this total divided by 100,000. Life expectancy at other ages is estimated by adding up the number of years of life after the age of interest and dividing by the number of people in the cohort who had reached that age (see Appendix 5 for the detailed calculations). If we draw a graph of the number or proportion of people expected to survive to each age we get what is called a sur- vival curve. Figure 2.5 shows the survival curves for Australian men and women in 2005–2007, illustrating the survival advantage that women still have over men.
Potential and expected years of life lost (PYLL and EYLL)
Life expectancy measures what is being achieved and is sometimes described as a measure of health expectancy. An alternative approach is to measure what
Measuring the ‘burden of disease’ 61
is being lost and this type of indicator is sometimes described as a health gap (Lopez et al., 2006 p. 47). One such measure looks not at the number of years someone can expect to live, but instead at the numbers of years of potential life they have lost if they die before a certain age. This age is frequently taken to be 65 although, with increasing numbers of people now living active lives well beyond this age, some reports now consider deaths before 70 to be ‘premature’ deaths. The number of potential years of life lost (PYLL) in a population is calculated by counting the total number of deaths from a specific cause in each age group and then multiplying this by the average number of years of life lost as a result of each of these deaths. For example, taking 65 as the cut-off age, a death from coronary heart disease at age 60 would contribute only 5 potential years of life lost compared with 15 years for a death at age 50. Thus, although there are fewer deaths among younger people, each contributes a greater number of PYLL than the deaths in the elderly.
One advantage this measure has over life expectancy is that it is possible to count the PYLL due to specific causes of death such as cancer or heart disease and thus to target those conditions with the highest PYLL. The years of life lost due to each cause of death can also be summed to give the total years of life lost. The same is not true for health expectancy measures because it is not possible to attribute years of life expectancy to the absence of a specific cause of death. The downside of calculating PYLL is that the choice of the age below which deaths are considered premature is arbitrary and deaths that occur above the speci- fied cut-off age are not counted at all. One way of getting around this is to cal- culate expected years of life lost (EYLL) where the number of years of life lost due to a death at any age is equal to the life expectancy at that age. It is also important to be aware that, unlike life expectancy measures, both PYLL and EYLL depend on the size of the population. Assuming two populations have similar life expectancy and mortality rates, the PYLL lost for the larger population will always be greater than that for the smaller population. It is, however, possible to get around this by calculating average PYLL to facilitate comparisons between populations.
Disability-free life expectancy
As we said at the beginning of this section, it is also important to consider mor- bidity to create a fuller picture of a population’s health. There is little point in working to extend life expectancy if the additional years of life are lived in very poor health. This concept is illustrated by the survival curves shown in Figure 2.6. As in Figure 2.5, the top line shows the proportion of people surviving at each age, but now the lower line shows the smaller proportion of people who are still in full health at each age. The combined areas A and B represent total life expectancy, but only a proportion of that life, the area A, is lived in full health, while area B
100 90 80 70
A
B
C
60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Age Survival % Sur viving Full health Figure 2.6 Survivorship curvesshowing years of life lived in full health (A), years lived in less than full health (B) and years of life lost (C). (Adapted from: Murray et al., 2000.)
indicates life lived with some degree of disability. Area C represents the potential years of life lost and the combined areas C and B represent the total health gap – the loss both of years of life and years of health. So how can we measure this?
One solution is to refine the calculations of total life expectancy to calculate
disability-free life expectancy, which takes into account not only age-specific
mortality rates but also the prevalence of disability at that age. This measure effectively adjusts the number of years of life expected for an individual at a given