In 1998, Botti et al. reported a trial of the use of pressure bandages for patients undergoing coronary angiography. Some of their results are shown in Table 5.3.
Table 5.3 Use of pressure bandages in patients undergoing coronary angiography. Pressure bandages Total Number with bleeding Cumulative incidence or event rate Yes 519 18 EERa= 3.5% No 556 37 CERb= 6.7% Total 1075 55 5.0%
aEER= experimental event rate or cumulative incidence in the treatment group. bCER= control event rate or cumulative incidence in the comparison group.
(Botti et al., 1998.)
The relative risk of bleeding among those given pressure bandages
compared with those without is 3.5÷ 6.7 = 0.52. This tells us that those given pressure bandages were about half as likely to develop bleeding as those who were not given bandages. The results of treatment trials are sometimes also reported as a relative risk reduction (RRR). This is the amount by which the treatment has reduced the relative risk and it is calculated by subtracting the relative risk from 1.0. It may then be expressed as a percentage by
multiplying by 100:
Relative risk reduction (RRR)= 1.0 − RR (5.4)
So the RRR = 1.0 – 0.52 = 0.48 or 48%.
Alternatively, it can be calculated directly from the cumulative incidence or event rates among the experimental (EER) and control (CER) groups:
Relative risk reduction (RRR)= (CER − EER) ÷ CER (5.5)
In this case the RRR= (6.7 – 3.5) ÷ 6.7 = 0.48.
In other words, use of the pressure bandages has reduced the risk of bleeding among patients undergoing coronary angiography by 48%. Obviously, the greater the RRR the better the intervention.
For studies with a positive association (RR> 1.0) the results are turned around to give what is logically called the relative risk increase (RRI). In the aspirin study discussed previously, aspirin increased the risk of bleeding by 40% (RR= 1.4).
Difference measures (attributable risk) 133
Box 5.2 (continued)
Note that you will see associations described in this way in all fields of epidemiology, e.g. ‘The risk of disease was 20% lower among those who exercised more’. It is a simple, informative mode of description that just happens to have been given a separate name in the area of clinical epidemiology.
Standardised incidence and mortality ratios
We discussed these measures in Chapter 2 (pages 52–54) because of the links between direct and indirect standardisation, but they also deserve a mention here since they compare the rate of disease (or death) in two populations and so, in effect, are also measures of relative risk.
Difference measures (attributable risk)
As we noted above, the relative risk tells us nothing about the actual amount of disease that is occurring. If the cumulative incidences or risks of disease in exposed and unexposed groups were 0.5% and 0.1%, respectively, the relative risk would be 5.0. Similarly, if the risks were 50% and 10% the relative risk would also be 5.0. The major difference between these two situations is obvious: the actual amount of disease that is occurring is vastly different – in fact in the second example it is 100 times greater. This vital public health information cannot be obtained from the relative risk.
The approach to measuring the excess amount of disease occurring among those exposed to a potential risk factor is just as intuitive and as simple to cal- culate as the relative risk. As you saw in the smoking and stroke example at the start of the chapter, we can calculate the extra amount of disease that is occur- ring in the exposed group by simply subtracting the incidence in the unexposed group (IRo, CIo or background risk) from the incidence in the exposed group (IRe, CIe). This can again be done using either of the measures of disease inci- dence (incidence rate or cumulative incidence) that you met in Chapter 2. If you are subtracting two incidence rates (as in the stroke example) you end up with a
rate difference, whereas if you are subtracting two measures of cumulative inci-
dence or risk (as in the immunisation example) you have a risk difference. These measures are also sometimes described as the excess rate and excess risk as they measure the extra disease that only occurs in the presence of the exposure. If we think that it is reasonable to assume that the excess disease can be attributed to the exposure, i.e. the exposure is causing the disease, then both of these
0 10 20 30 40 50 60
Never smoked Ex-smokers Current smokers
Incidence rate per 100,000 per
son-y
ear
s
Rate attributable to smoking Background rate
(a)
(b) (c)
Figure 5.1 Attributable risks: the results of a study of smoking and stroke (drawn from: Colditz
et al., 1988).
measures can also be described as the attributable risk (in the same way that relative risk is used to describe both rate ratios and risk ratios).
Rate differences
Consider the smoking and stroke example again (Table 5.1). Compared with never smokers, there were an extra 10.2 strokes (27.9 – 17.7) per 100,000 person- years in ex-smokers and an extra 31.9 strokes (49.6 – 17.7) per 100,000 person- years in current smokers. These effects are illustrated in Figure 5.1. The left-hand bar (a) shows the incidence rate of stroke in non-smokers. This is often called the background or reference rate because it reflects the natural occurrence of the disease in an unexposed population. We expect this to operate on all members of the population regardless of their smoking status, and this is shown for the ex- and current smokers. This lets us visualise directly the extra burden of stroke added by past and present smoking habits. Thus the second bar shows the extra incidence of stroke in ex-smokers (b) that is presumably due to the fact that the women had smoked in the past. Similarly, the third bar shows the far greater added rate of stroke in current smokers (c) that is attributable to their smoking. This extra disease is simply the difference between the rate in the exposed group (smokers) and the rate in the unexposed group (non-smokers). The total rate of disease in exposed individuals is therefore the sum of the background rate (due to other causes) and the additional rate due to the exposure in question.
If the groups differ only in their smoking habit and if we believe that smok- ing is actually causing strokes to occur then we can say that the extra disease in the smokers is attributable to their smoking – if they had not smoked then it
Difference measures (attributable risk) 135
would not have occurred.1This rate difference is also called the attributable risk (AR) because it measures the actual amount of disease that can be attributed to a particular exposure:
Rate difference or attributable risk = IRe− IR
= Incidence rate in exposed − Incidence rate in unexposed (5.6)
Risk differences
Look back to the example of immunisation against influenza in Table 5.2. What percentage of patients in the intervention group would have been expected to attend for immunisation even if they hadn’t received a phone call (background ‘risk’)?
What extra percentage of patients presumably attended only because they had received a call (i.e. how many attendances could be attributed to the phone call)? We would have expected 44% of patients in the intervention group to go for immunisation even if the practice receptionists had not called to offer them an appointment. We can therefore say that an extra 6% of patients (50% – 44%) in the intervention group presumably went for immunisation only because they had received a call, i.e. their immunisation can be attributed to this. Here we have calculated a risk difference (as opposed to a rate difference) since we are subtracting cumulative incidences (or risks):
Risk difference or attributable risk
= Cumulative incidence in exposed − Cumulative incidence in unexposed
= CIe− CIo (5.7)
Attributable fractions (AFs)
A further way to consider attributable risk that can also be informative is as the proportion or percentage of disease in the exposed group that would not have occurred in the absence of the exposure. This measure is often called the
attributable fraction or attributable proportion, although you will also come
across it described as the attributable risk per cent. To calculate the attributable fraction you simply divide the attributable risk by the incidence in the exposed
1 Note that although you will see the attributable risk described as the amount of disease caused by
the exposure, this is not technically correct because we can never know exactly how many cases are caused by a particular exposure. However, we can usefully use the attributable risk to estimate how much extra disease occurred in the presence of the exposure and thus presumably would not occur in the absence of that exposure.
group:
Attributable Fraction (AF) = Attributable Risk Incidence in exposed
or = Incidence in exposed− Incidence in unexposed Incidence in exposed
Again this can be done using either the incidence rate or the cumulative incidence:
Attributable Fraction (AF)= AR IRe or AR CIe (5.8) = IRe− IRo IRe or CIe− CIo CIe (5.9)
Consider the smoking and stroke example again. The rate of stroke among cur- rent smokers was 49.6/105person-years and the rate difference or attributable risk was 31.9/105person-years. The attributable fraction is therefore 0.64 or 64%, i.e. of all the strokes occurring among current smokers, about two thirds could be attributed to the fact that the women smoked:
Attributable Fraction (AF)= 49.6 − 17.7
49.6 = 0.64 = 64%
Interpretation of the attributable risk
The attributable risk tells us how much extra disease actually occurred in the exposed group as a result of the exposure. By implication, we can then say that, if the association is causal, this is the amount of disease that we could prevent in a comparable group of people in the future if we could prevent them from being exposed. This measure is, therefore, of direct use to health planning and policy setting. Note that in the field of clinical epidemiology, what we have called the attributable risk is often called the absolute risk reduction (ARR) or abso-
lute risk increase (ARI) depending on whether the event rate is reduced or
increased in the treatment group (See Box 5.3). The ARR and ARI are identical to the attributable risks used elsewhere in epidemiology and are calculated in exactly the same way – the only difference is in the names.
In practice, of course, it is often impossible to remove or prevent an expo- sure altogether. Someone who smokes cannot go back to being a never-smoker but they can become an ex-smoker. This means that current smokers who stop smoking will not realise the full benefit predicted by the standard attributable risk (which would compare smokers with the unexposed group, in this case never smokers). Rather, the best we could achieve with a 100% effective ‘stop smoking’
Difference measures (attributable risk) 137