1. Module appendix - Attributable risk
Principles of Epidemiology for Public Health (EPID600)
Module appendix - Attributable risk
Victor J. Schoenbach, PhD home page
Department of Epidemiology Gillings School of Global Public Health University of North Carolina at Chapel Hill
Amedauwa, Ya’-teh habeen, Bienvenidos, Ni-hau, Bagunara, Karibu, Aloha
6/24/2013
Attributable risk

2. Attributable risk - conceptual
Assume that we know that a factor causes a disease.
How can we answer the “so what?” questions:
“How much risk is attributable to that factor?”
“How many cases are attributable to that factor?”
The answers depend on: (1) by how much the factor increases risk and (2) how common the risk factor is. A strong risk factor that is common has a large impact.
Assume that we know that a factor causes a disease.
How can we answer the “so what?” questions:
“How much risk is attributable to that factor?”
“How many cases are attributable to that factor?”
These questions concern the impact of the factor.
The magnitude of the impact depends on (1) by how much the factor increases risk and (2) how common the risk factor is.
A strong risk factor that is common has a large impact.
6/24/2013
Attributable risk

3. Background risk – 8 cases / 200 people (1/25 = 4%)


 O O O




 O O
Here is the example population we used in the lecture on incidence and prevalence, though I’ve altered the number of cases to make the numbers work out. Suppose that these are the cases that would occur in this population during a 5-week period. Assuming that the whole population was at risk at the beginning of the five weeks, so that all 8 cases shown are new cases, what would the 5-week incidence proportion be? 8/200 = 0.04 = 4%. So the “background risk” in this population is 4%. O O
6/24/2013
Attributable risk

4. Risk in exposed vs. unexposed (4/75 = 5.3%) vs. (5/125 = 4%)


 O O O O




 O O
Now consider an alternate reality – the same people, observed during the same 5-week interval, but the 75 people in the top three rows were exposed to a risk factor and experienced four cases instead of three. Comparing the two realities, it’s clear that the additional case, in the red circle, is “attributable” to the risk factor. Had the risk factor not been present, that case would not have occurred.
So in this idealized example, one case – 25% of the 4 cases observed in the exposed group, 11% of all 9 cases – is attributable to the exposure.
Putting the observation in terms of risk, the background risk was 4%, which is also the risk in the people who are unexposed (5/125). The risk in the exposed group is 4 cases / 75 people = 5.33%. So the amount of risk that is attributable to the risk factor is the risk difference, 5.33% − 4.00% = 1.33%. O O
6/24/2013
Attributable risk

5. Attributable risk – proportion of risk in exposed population (PAR)


 O O O O




 O O
We can express this same additional risk by expressing it is as proportion of the risk in the exposed persons or as a proportion of the risk in the entire population. The attributable risk of 1.33% is 25% of the risk in the exposed group (which was 4/75=5.33%). We found the same result when dividing the number of attributable cases (1) by the number of exposed cases (4). The attributable risk (or cases) as a proportion of the risk (or cases) in the exposed answers the question, “what proportion of the risk in persons exposed to the risk factor could be eliminated by preventing their exposure to the risk factor”. This number is referred to as the “attributable risk proportion” (PAR) or “attributable risk percent”. O O
6/24/2013
Attributable risk

6. Attributable risk – proportion of risk in the entire population (PARP)


 O O O O




 O O
We might also be interested in estimating the proportion of risk in the entire population that could be eliminated if we prevented their exposure to the risk factor. But, of course, the overall risk in the entire population reflects the fact that some – but not all – of the population is exposed. Obviously, preventing the risk factor will have no effect on the people who were never exposed to it in the first place. So in order to estimate the proportion of population risk that could be eliminated, we need to use a calculation that takes account of the prevalence of exposure.
There are a number of formulas we can use, but if we know the number of cases that are attributable to the exposure, then we can easily calculate what proportion they make up of the total number of cases. There was only one attributable case, so 1/9 = 11% of the total number of cases was attributable. If we prevented the exposure, we return to the baseline scenario, several slides back, which had 8 cases. This percentage is the “population attributable risk proportion” (PARP). If the entire population were exposed, then the PAR and the PARP will be equal. To verify that, try creating such a scenario. O O
6/24/2013
Attributable risk

7. Attributable risk – counterfactual comparison


 O O O O




 O O
In this artificial example, we could make the counterfactual comparison – the cases in the exposed group compared to the cases we would have seen among the same people if they had not been exposed. In that way we could be certain how many cases were due to the exposure – and even which case! In real life, of course, we would not know which case(s) were due to the exposure. (Because we cannot tell which cases are attributable to the exposure, some epidemiologists prefer to speak of attributable “case load”.) We would also have to employ a substitute population for the counterfactual. O O
6/24/2013
Attributable risk

8. Attributable risk measures
Absolute comparison
Relative comparison
Among exposed persons
Attributable risk (AR)
Attributable risk proportion (ARP)
Among all persons
Population attributable risk (PAR)
Population attributable risk proportion (PARP)
The four attributable risk measures are shown in the table. Measures in the left-hand column show absolute comparisons and yield an amount of risk. Measures in the right-hand column show relative comparisons and yield a proportion of risk.
A key take-home concept is that the amount of risk attributable to a factor is a function of: (1) how strongly the factor is associated with the disease and, unless we are speaking only of exposed persons, (2) the prevalence of the exposure.
10/10/2012
Attributable risk

9. Attributable risk – substitute population required
4 cases in 75 exposed persons, risk = 5.33%
5 cases in 125 unexposed persons, risk = 4.00%
In actuality we would know only that there were 4 cases in 75 persons who were exposed and 5 cases in 125 persons who were not exposed. We would first have to decide whether we can regard the unexposed as an adequate substitute population for a comparison of risk – or we would have to consider what adjustments might enable a valid comparison.
Even so we would still not know which of the four cases is due to the exposure. But we can still estimate the attribute risk, the attributable risk proportion (PAR), and the population attributable risk proportion (PARP), using the same calculations just illustrated and summarized on the next slide.
9 cases in 200 persons (total), risk = 4.50%
10/10/2012
Attributable risk

10. Attributable risk calculations
4 cases in 75 exposed persons, risk = 5.33%
5 cases in 125 unexposed persons, risk = 4.00%
9 cases in 200 persons (total), risk = 4.50%
Attributable risk = 5.33% − 4.00% = 1.33% (risk difference)
Population attributable risk (PAR) = 4.50% − 4.00% = 0.50%
Attributable risk proportion (ARP) = 1.33% / 5.33% = 25% (attributable cases / exposed cases = 1/4 = 25%)
Population attributable risk proportion (PARP) = 0.50% / 4.50% = 11% (attributable cases / all cases = 1/9 = 11%)
This slide illustrates the attributable risk calculations just presented. I’ve also included something called the “population attributable risk” (PAR), a different quantity than the population attributable risk proportion. One sees the PAR only infrequently, but it completes the pattern, since it provides an absolute comparison between the risk in the exposed and the risk in the entire population. In the two “absolute” measures, the background risk is subtracted from the observed risk (in the exposed or in the population). In the two relative measures, the absolute attributable risk measure is expressed as a proportion of the observed risk. The relative measures can also be calculated more simply dividing attributable cases by total cases (in the exposed or in the population). If we didn’t know attributable cases, we can estimate them by multiplying the attributable risk (i.e., risk difference) by the number of exposed people: (5.33%−4.00%) x 75 = 1.33% x 75 = 1. The greater the increase in risk, the more attributable cases. The greater the number of people exposed, the more attributable cases.
10/10/2012
Attributable risk

11. Attributable risk – assumption, perspectives
We are assuming that the exposure is a cause of the disease.
The “attributable risk” for an exposure is the risk that would not have occurred without the exposure.
Can use either of two perspectives:
1. difference in risk between exposed and unexposed people
2. difference in risk between total population and unexposed people
If we can assume that we know that a factor is a cause of a disease, then conceptually, the “attributable risk” for that factor is the amount of risk for which it is responsible, i.e., the risk that would not have existed had the factor not been present or, if the risk is reversible, the amount by which risk would be reduced if the factor were eliminated. Conceptually, we are comparing the risk we observe to the counterfactual situation of the same people at the same time but with a different exposure status.
We can calculate attributable risk among those who are exposed to the factor or in the total population by comparing to a substitute population to represent the counterfactual comparison. Since only people exposed to the causal factor can have risk attributable to it, attributable risk in the population will reflect the fact that not everyone in the population is exposed,.
If, as is usually the case, some risk for the disease exists even in the absence of the causal factor, then the amount of risk attributable to the factor is the difference between the risk in people who are exposed and that “background risk”.
So the “attributable risk” for a factor is the:
1. difference in risk or incidence in exposed and unexposed people or
2. difference in risk or incidence in the total population and unexposed people
3/20/2013
Attributable risk

12. Attributable risk – relative or absolute
Attributable risk can be presented as:
1. an “absolute” number, e.g., “80,000, or 20 per 100 cases/year of stroke are attributable to smoking”
2. a “relative” number, e.g., “20% of stroke cases are attributable to smoking”.
(analogy: a wage increase in a part-time job: $ increase, % increase in wage, % increase in income)
As always, an amount of risk can be expressed as an absolute value or relative to some risk of interest. For example, we can speak of the amount of risk attributable to smoking or the proportion of risk that is attributable.
Attributable risk can be presented as:
1. an “absolute” number, e.g., “80,000, or 20 per 100 cases/year of stroke are attributable to smoking”
2. a “relative” number, e.g., “20% of stroke cases are attributable to smoking”.
By way of analogy, suppose you work two part-time jobs and receive an increase in pay from one of them. You might think about the increase as the additional amount of money you will receive (e.g., another $50/week), or as a percentage increase in your wage (e.g., a 10% increase), or a percentage increase in your total income (e.g., a 5% increase). Each expression is a legitimate way of quantifying the increase, and each expression answers a different implicit question.
10/7/2008
Attributable risk

13. How much risk is attributable: absolute perspective
New cases
Noncases
Total
Risk
Exposed
100
900
1,000
(n1)
10%
(R1)
Unexposed 50
1,950
2,000
(n0)
2.5%
(R0)
Attributable
risk = R1 –
R0 = 10% –
2.5% =
7.5%
Incidence proportion (risk)
Suppose that there are n1 people exposed to the causal factor and n0 people who are not exposed. In the numerical example there are 1,000 exposed and 2,000 unexposed. Suppose also that the disease incidence is R1 in people exposed to the factor and R0 in people who are not exposed.
The risk difference, 10% - 2.5% = 7.5%, is the amount of the risk that is “attributable” to the exposure, on the assumption that both groups would have had the 2.5% risk if the exposure had not occurred.
People
6/24/2013
Attributable risk

14. How many cases are attributable? (absolute)
New cases
Noncases
Total
Risk
Exposed
100
900
1,000
(n1)
10%
(R1)
Unexposed 50
1,950
2,000
(n0)
2.5%
(R0)
Incidence proportion (risk)
How many cases are expected without the exposure?
(2.5% x 3,000 = 75)
The rectangle in the lower left shows the number of cases (sometimes called the “caseload”) that would be expected in the substitute population, the n0 unexposed people: R0n0, the risk for the unexposed times the number of people. The risk of 2.5% reflects 50 cases in a population of 2,000.
The taller rectangle, on the right, shows the caseload among the n1 exposed people: the risk of 10% in the exposed population reflects 100 cases in the 100 exposed people.
To estimate how many of the 150 total cases observed are “attributable” to the exposure, we need to estimate how many cases we would have expected in the exposed group if the exposure had not occurred.
If the exposure had been avoided, we would expect the incidence proportion among the n1 people who would have been exposed to be the same as that in the substitute population (R0). 50 25
People
10/9/2012
Attributable risk

15. Absolute perspective: amount of caseload
New cases
Noncases
Total
Risk
Exposed
100
900
1,000
(n1)
10%
(R1)
Unexposed 50
1,950
2,000
(n0)
2.5%
(R0)
Incidence proportion (risk)
How many cases are attributable?
(150 – 75 = 75) 75
If the exposed group had not experienced the exposure and had had the risk of the unexposed group (2.5%), then we would expect 2.5% x 1,000 = 25 cases in the exposed group. So of the 100 exposed cases, 75 are “attributable” to the exposure. Note that we cannot know which of the 75 case are caused by the exposure. For that reason my colleague Charlie Poole prefers to refer to “75% of the caseload” rather than 75 cases. 50 25
People
10/9/2012
Attributable risk

16. For relative measures, think of % of cases
So if the exposure were absent or innocuous, we would expect the cases in the exposed to be R0 n1, rather than R1n1 cases. Thus, the caseload above the line at R0 is “attributable cases” (represented by the darker shading). This area represents the caseload “attributable” to the exposure in that these cases would not be expected if the exposure were innocuous. If we desire to estimate attributable risk as a proportion, then we simply divide the number of attributable cases, (R1 – R0) n1, by all exposed cases, I1n1 (for attributable risk among those exposed), or we can divide those same attributable cases by all cases [R0n0 + R1n1] (for attributable risk in the population as a whole).
10/7/2008
Attributable risk

17. Relative perspective: % of caseload
Exposed
Unexposed
Total
Risk
New cases
100
900
1,000 n1
10% R1
Noncases 50
1,950
2,000 N0
2.5% R0
Incidence proportion (risk)
Express attributable cases as a % of all exposed cases
“Attributable risk proportion or %”
75%
If we express the attributable case load as a proportion or percentage of all cases in the exposed group, we get the “attributable risk proportion” or the “attributable risk percent”. This figure estimates the proportion of the case load in the exposed group that would not have occurred if the exposure had been prevented.
10/9/2012
People
Attributable risk

18. Relative perspective: % of caseload
Exposed
Unexposed
Total
Risk
New cases
100
900
1,000 n1
10% R1
Noncases 50
1,950
2,000 N0
2.5% R0
Incidence proportion (risk)
Express attributable cases as a % of all cases
“Population attributable risk proportion or %”
50%
If we express the attributable case load as a proportion or percentage of all cases (i.e., in the entire population, both exposed and unexposed), we get the “population attributable risk proportion” or the “population attributable risk percent” (PARP). This figure estimates the proportion of the case load in the population that would not have occurred if the exposure had been prevented.
10/9/2012
Attributable risk