His view: Australian men do three times more housework today than they did 40 years ago . . .
Her view: Australian men spend 5 minutes a day on laundry now compared to 1.6 minutes 40 years ago – an extra 31/2minutes a day . . .
(Maushart, 2003.)
As you learned in Chapter 1, one of the main uses of epidemiology is to identify the causes of disease and this is of fundamental importance in all areas of public health – if we can work out what is causing ill-health then we can work to prevent it. In Chapter 2 we looked at the ways in which we can measure the occurrence of disease and touched on some ways in which we can compare different pop- ulations. But while measuring the occurrence of a disease in a population can tell us about the health of that population, it does not directly shed much light on the underlying causes of the disease. To identify the aspects of people or their environment (exposures) that might lead to the onset of disease, we need to com- pare disease occurrence in groups with and without the exposures of interest. In Chapter 4 we looked at some of the study designs that we can use to do this; now we will look more closely at the measures we use to quantify the associa- tions between ‘exposures’, or potential causes of disease, and the disease itself. By quantifying the association between an exposure and disease we can start to make judgements as to whether the exposure might actually cause the disease (we will discuss causality in more detail in Chapter 10). If we believe that it is causing disease, we can then identify the importance of that exposure in terms of its overall effect on the health of a community.
In this chapter we will look at the ways in which we calculate, use and interpret these ‘measures of association’, so-called because they describe the association between an exposure and a health outcome. An understanding of these measures will help you to interpret reports regarding the causes of ill-health and the effects of particular exposures or interventions on the burden of illness in a commu- nity. Note that, while we will discuss the measures in the context of an ‘exposure’ and ‘disease’, they can be used to assess the association between any measure of health status and any potential ‘cause’.
Looking for associations
We all know that smoking is a cause of lung cancer but might it also increase the risk of stroke? To answer this question we could compare the incidence of stroke in a group of women who smoke with that in a group of non-smokers.
Table 5.1 displays data from a cohort study in which the investigators fol- lowed a large group of women for several years (person-years of observation). They classified the women as never smokers, ex-smokers and current smokers, recorded how many women had a stroke during the follow-up period and calcu- lated the incidence rate of stroke in each group.
How many times more likely was
(i) a current smoker to have a stroke than a never smoker and (ii) an ex-smoker to have a stroke than a never smoker?
Looking for associations 127
Table 5.1 Stroke incidence rates by smoking category in female nurses. Smoking category No. of cases of stroke Person-years of observation
Incidence rate per 100,000 person-years Never smoked 70 395,594 17.7 Ex-smoker 65 232,712 27.9 Current smoker 139 280,141 49.6 Total 274 908,447 30.2 (Colditz et al., 1988.)
Compared with non-smokers, how many extra strokes were there per 100,000 person-years in
(i) ex-smokers and (ii) current smokers?
There are two main ways in which we can compare smokers and non-smokers. First, ex-smokers were 1.6 times (27.9÷ 17.7) and current smokers were 2.8 times (49.6÷ 17.7) as likely to have a stroke as never smokers during the follow-up period. An alternative way to look at the data would be to say that, all other things being equal, if the smokers had never smoked we would have expected them to have the same rate of stroke as the never smokers, i.e. 17.7/100,000 person-years. This means that, compared with never smokers, there were an extra 10.2 strokes per 100,000 person-years (27.9 – 17.7) in ex-smokers and an extra 31.9 strokes per 100,000 person-years (49.6 – 17.7) in current smokers.
What we calculated above were, first, the rate ratio and, second, the rate dif-
ference for the association between smoking and stroke. These measures give
us two different ways of quantifying the relation between an exposure and a disease. The rate ratio tells us how many times higher the rate of disease is in one group than in another group (e.g. current smokers are almost three times as likely to have a stroke as never smokers). This gives an indication of the strength of the association and can help us to decide whether smoking could be a cause of stroke. The rate difference tells us how much extra disease occurred in one group compared with another group (e.g. there were an extra 32 strokes per 100,000 person-years among current smokers compared with non-smokers). If we believe that smoking is a cause of stroke then this extra disease can be attributed to the fact that the women had smoked in the past and, theoretically, it would not have occurred if they had never smoked. This information gives some sense of the potential value of a preventive intervention, in this case a pro- gramme aimed at stopping women from taking up smoking. (Of course, if such an intervention were successful it would reduce the incidence of many diseases, not just stroke.)
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It is important to remember that ratio and difference measures give us very different perspectives on a given situation. Look back to Box 5.1 at the start of the chapter. Men would probably prefer to look at the ratio or relative measure: they do three times more housework now than 40 years ago. In contrast, women would focus on the difference or absolute measure: men may do three times more laundry now than 40 years ago but they still do an average of only 5 minutes (3.5 minutes extra) per day.
Ratio measures (relative risk)
The cholera was therefore 14 times as fatal at this period amongst persons having the impure water of the Southwark and Vauxhall Company, as amongst those having the purer water from Thames Ditton (Snow, 1855).
People who ate cold chicken at the youth camp were almost four times more likely to become ill than people who did not eat cold chicken (from Table 1.2).
Ratio or relative measures tell us how many times more likely it is that some- one who is exposed to something will develop a certain disease or experience
Ratio measures (relative risk) 129
a particular health outcome than (or relative to) someone who is not exposed. They do not tell us anything about the actual amount of disease occurring in either group. They provide information about the strength of the association between the exposure and the outcome and, as you will see in Chapter 10, a strong asso- ciation is more suggestive that the exposure is actually causing the outcome. In the example above, the rate ratio for stroke and current smoking was 2.8. This is a fairly strong association and would add weight to an argument that smoking was actually causing strokes, although it is not as compelling as the much stronger relation between smoking and lung cancer, for which the rate ratio for current smoking is somewhere between 10 and 15.
As the example shows, ratio measures are very easy to calculate – you simply divide the frequency of disease (or of any health outcome) in the group that is exposed to the factor of interest by the frequency in the group that is not exposed to it. This can be done using either of the measures of disease incidence that you met in Chapter 2. If you divide two incidence rates you end up with a rate
ratio (as for the stroke example above); if you divide two measures of cumulative
incidence or risk then it is a risk ratio. It is also possible to divide two measures of prevalence to calculate a prevalence ratio. Note that you must always divide two measures of the same type – you cannot usefully divide an incidence rate by a measure of cumulative incidence.
Rate ratios
As you saw above, a rate ratio is calculated by simply dividing the incidence rate of disease in a group of people exposed to the factor of interest (often denoted by a subscript ‘e’) by the incidence rate in a group of people who are not exposed to the same factor (denoted by a subscript ‘o’):
Rate Ratio= Incidence Rate in exposed Incidence Rate in unexposed =
IRe IRo
(5.1) This factor could be a potential cause of disease, it could be a characteristic of a person, such as their age or where they live, or it could be something that influ- ences behaviour. Equally, it could be a preventive measure or, in the clinical con- text, a drug or other treatment that we hope will reduce the incidence of disease.
Risk ratios
Similarly, the risk ratio (also called the relative risk) is calculated by dividing the cumulative incidence or risk of disease in an exposed group by the cumulative incidence in an unexposed group:
Risk Ratio= Cumulative Incidence in exposed Cumulative Incidence in unexposed =
CIe CIo
Table 5.2 The results of a study evaluating the effects of calling patients on influenza immunisation rates.
Outcome
Exposure Immunised Not immunised % immunised
Received a call 328 332 50%
No call 288 370 44%
Total 616 702 47%
(Hull et al., 2002.)
In Chapter 2 we considered a randomised trial to evaluate whether taking aspirin would reduce the risk of blood clots in people with infective endocarditis. Look back at Table 2.3 on page 44 and calculate the risk ratio for the association between aspirin and blood clots.
In this trial, the risk ratio was 28.3%÷ 20.0% = 1.4; those who took aspirin were 1.4 times as likely to develop blood clots as those who did not take aspirin. A risk ratio of 1.0 would mean that there was no difference between the groups, so those taking aspirin were 40% more likely to develop blood clots than those not taking aspirin (in the context of clinical epidemiology this may be described as the rel- ative risk increase or RRI). If aspirin had reduced the risk of blood clots then we would have expected to see a risk ratio of less than 1.0. Clearly this intervention did not work the way the investigators had hoped it would.
This approach can be used much more widely than in the search for the causes of disease. As an example, a trial carried out in three general practices in the UK set out to find out whether telephoning patients to offer them an appointment for immunisation against influenza would increase immunisation uptake rates (Hull et al., 2002). In this study, attending for immunisation was the outcome of interest and receiving a telephone call was the exposure. A total of 1,318 patients aged 65 to 74 years were randomly assigned to two groups. Patients in one group (n= 660) received a telephone call from the receptionist at their general practice inviting them to make an appointment for immunisation (the intervention or exposed group). Patients in the other group (n= 658) were not called (the control or unexposed group). The investigators then waited to see who turned up for immunisation. They found that 328 of the patients who received a phone call attended, as did 288 of those who did not receive a call.
The easiest way to look at these data is in the form of a ‘2× 2 table’. These tables are usually set out so that the two columns show the numbers of people with and without the outcome of interest while the rows show the numbers in the exposed and unexposed groups (Table 5.2).
Ratio measures (relative risk) 131
What was the cumulative incidence of immunisation or, in other words, what percentage of patients attended for immunisation in each of the two groups? How many times more likely were patients to attend if they had received a per- sonal call to make an appointment than if they had not been telephoned? In the intervention group 50% of patients were immunised, compared with 44% of those in the control group (despite the intervention the immunisation rates were still below the government target of 60%). This means that patients who received an invitation were 1.14 times (50%÷ 44%) more likely to attend for immunisation. This measure is still a relative risk because it has the same struc- ture – the cumulative incidence (or risk) of a particular health outcome in one group is divided by the cumulative incidence in a second group. In this case the word ‘risk’ seems less appropriate but the term relative risk is still regularly used.
Prevalence ratios
As you saw when we discussed prevalence surveys in Chapter 3 and cross-
sectional studies in the previous chapter, it is also possible to use measures of
prevalence instead of incidence to compare the burden of disease in two groups and in this situation you end up with a prevalence ratio:
Prevalence Ratio= Prevalence in exposed Prevalence in unexposed=
Pe Po
(5.3) As we discussed in Chapter 2, measures of prevalence are harder to interpret than measures of incidence and for this reason prevalence ratios are used much less frequently than rate and risk ratios.
A note about relative risks
We noted above that the term relative risk is synonymous with risk ratio. In prac- tice, it is also commonly used to describe a rate ratio, since both the rate ratio and the risk ratio compare the amount of disease in one group relative to that in another. If a disease is rare (cumulative incidence or risk less than 1%), then the rate ratio and risk ratio will be almost identical; if it is not so rare then the risk ratio will be closer to 1.0 than the rate ratio although, in practice, there is little difference as long as the cumulative incidence is less than about 10%. The three terms rate ratio, risk ratio and relative risk are also commonly and conveniently abbreviated as RR. When we use the term relative risk it will refer to both the rate ratio and the risk ratio.
It is also worth noting that, although relative risks are also used in the con- text of clinical trials, several other related measures are also used in the field of clinical epidemiology (Box 5.2).