Attributable Risk

Many diseases are caused by more than one exposure. For example, there is a high risk of developing CHD on the basis of cigarette smoking, elevated blood pressure and high blood cholesterol. For there to be a reduction in the incidence of CHD in the population, public health programs would be directed towards reducing or eliminating these causal exposures.

This is the aim of epidemiologic research; to identify and assess risk factors as well as planning and evaluating public health intervention or control measures so as to reduce the incidences of disease in the population. For this to be possible, the epidemiologist must be able to predict the impact of the removable of a particular exposure on the risk of developing a disease.

This then begs the question:

•      What amount of the risk of developing a disease is attributable to a particular exposure?
• ·   By what percent would the risk of developing disease be reduced if the exposure were eliminated?

It is very essential that these questions are answered and this is done using the attributable risk (AR).

Attributable Risk:

Attributable risk (AR) or risk difference (RD) is a measure of association that provides information about the absolute effect of the exposure or the excess risk of disease in those exposed compared to those non-exposed or the portion of the incidence of the a disease in the exposed that is due exposure. It is also defined as the difference between the incidence rates in the exposed and non-exposed groups. It is calculated as thus:

AR = I_e - I_o

I_e – Incidence in the exposed

I_o – Incidence in the non-exposed

In a cohort study, the attributable risk is calculated as difference between the cumulative incidences in the exposed and the non-exposed.

AR = CI_e - CI_o = a/(a + b) - c/(c + d)

 

CI_e – Cumulative incidence in the exposed

CI_o – Cumulative incidence in the non-exposed

 Table 1: Cohort Study of Smoking and Coronary Heart Disease among men

Coronary Heart Disease (CHD)                                                       Yes                    No                                     Total               Smoking Yes                                              140(a)                  669(b)                                    809 No                                                 10(c)                  413(d)                                    423 Total                                           150                       1082                                       1232 AR = CIe - CIo =  a/(a + b) - c/(c + d)                     = 140/809 - 10/423                           = 0.1731 –  0.0236                           = 0.1495                           = 1495/104

The table above is a hypothetical data from a cohort study of showing the relationship between coronary heart disease and smoking. Among the 1232 men who were free from coronary heart disease, 809 were smokers at the initial survey while 423 were not. At a second survey, 140 men who smoked had developed coronary heart disease as had 10 non-smokers.

From the data above the excess occurrence (incidence) of coronary heart disease among smokers attributable to their smoking is 1495 per 10000. 

Thus the attributable risk is used to quantify the risk of disease in the exposed group that are attributable to the exposure by removing the risk of disease that would have occurred anyway due to other causes (the risk of the non-exposed) or alternatively the number of cases of the disease among the exposed that could be eliminated if the exposure is eliminated. However it must be noted that the attributable risk is dependent on the assumption that a cause-effect relationship exist between exposure and disease. 

The attributable risk can also be expressed as a percentage and this referred to as the attributable rate percent, attributable proportion or etiologic fraction and is calculated as thus:

AR% =  AR/I_e* 100

AR% =  (I_{e -} I_o)/I_e * 100

Using the example above the etiologic fraction is:

AR% =  (0.1731 –  0.0236 )/0.1731* 100

AR% = 86.37%

Thus from this example, if smoking does cause coronary heart disease, 86.37% of the coronary heart disease in men who smoke can be attributed to their smoking and would be eliminated if they stopped smoking.

In case – control studies, the attributable risk cannot be calculated using this formula because the incidence rates of disease among the exposed and non-exposed are not available. However the attributable risk percent can be calculated using this formula:

AR% = (RR - 1)/RR * 100

RR – Relative risk. This is approximated using the odds ratio.

Here the incident rate among the unexposed is assigned the value 1. The numerator in this equation is termed the excess relative risk and is the segment of the relative risk among the exposed which exceeds the risk among the unexposed. Since relative risk reflects the total risk, thus expressing the group’s excess relative risk as a percentage of its relative risk yields the attributable risk percent.

Conversely, if the incidence rate in the total population of interest is known or can be estimated from other sources and the distribution of exposure among control is assumed to be representative of the whole population, these parameters can be used to estimate the incidence rates in exposed and non-exposed groups of case-control studies. The overall incidence rate of disease in a population (I_T) may be thought of as the weighted average of the incidence rates in various exposure categories, with the weights related to the proportions of individuals in each category, I_T can be calculated as the incidence rate among the exposed group (I_e) times the proportion of individuals in the total population who have the exposure (P_e), plus the incidence rate among the non-exposed (I_o) times the proportion of non-exposed person (P_o). This expressed as:

I_T = (I_e)(P_e) + (I_o)(P_o)

Remember,

RR =  I_e/I_o

Therefore;

I_e = RR * I_o

In case-control study the relative risk is estimated by the odds ratio (OR). Substituting I_e  in the formula:

I_T = (I_o)(OR)(P_e) + (I_o)(P_o)

  =  (I_o)[(OR)(P_e) + (P_o)]

To determine the incidence rate in the non-exposed, simply solve for I_o.

I_o = I_T/(OR)(P_e) + P_o

Once the incidence rate among the non-exposed is determined, it can then be multiplied by the odds ratio to provide an estimate of the incidence among the exposed. With these two incidence rates (I_e and I_o), the attributable risk can then be calculated.

Source: Epidemiology in Medicine by Charles H Hennekens and Julie E Buring