# Measures of the effect of an exposure

## Introduction

**Learning objectives:** You will learn about:

- Attributable risk
- Population attributable risk
- Population attributable risk fraction

This section addresses measures of the excess risk caused by exposure to a factor, and the measure of the expected impact of a disease in a population that can be attributed to the exposure factor. This section presumes prior knowledge of basic risk measures.

Read the resource text now, which covers attributable risk and measures of population impact.

## Resource text

### Difference Measures^{1}

**Attributable Risk (risk difference)**

The attributable risk (AR) is a measure of association that provides information about the absolute effect of the exposure or excess risk of disease in those exposed compared with those unexposed, assuming that the risk is causal.

The risk or rate difference estimates the excess risk caused by exposure in the exposed group, that is, the risk attributable to the factor being investigated (e.g. smoking, alcohol).

Attributable risk (AR) = incidence risk **among exposed** - incidence risk among unexposed

Attributable rate (AR) = incidence rate **among exposed** - incidence rate among unexposed

**AR = r1-r0**

**r1 = incidence risk/rate amongst exposed**

**r0 = incidence risk/rate amongst unexposed**

e.g. in a cohort study the AR is calculated as the difference of incidence risks or incidence rates (depending on the study design used).

An AR greater than 0 indicates the number of cases of the disease among the exposed that can be attributed to the exposure, or the number of cases among the exposed that could be eliminated if the exposure were eliminated. The AR is a useful measure of the public health impact of an exposure in a population 1.

**Attributable risk %**

The AR may be expressed as a proportion.

**AR% = r1-r0 / r1 x 100**

**Issues in the use of measures of association**

- Good way of estimating the strength of an association between a risk factor and a disease.
- Not a good measure of how much of the disease present in a population was caused by a risk factor. Difference measures are used to estimate the excess risk caused by an exposure in the exposed group.

### Measures of Population Impact

In contrast to measures of effect (e.g. relative risk), which estimate the strength of the association between a risk factor and disease, or the attributable risk, which measures the extra risk or rate that is present in the exposed group compared to the unexposed group, measures of population impact estimate the expected impact (extra disease) in a population that can be attributed to the exposure.

- Estimate how much of the disease in the population is caused by the risk factor.
- Estimate the expected impact on a population of removing or changing the distribution of risk factors in that population.
- Measures of impact compare the
**population and unexposed**while measures of effect compare the exposed and unexposed. - Assume that the association between disease and risk factor are causal.

**There are two main measures of population impact:**

**The Population attributable risk (or rate) (PAR)**^{1}

The PAR is a similar measure to the attributable risk (or risk difference), but is concerned with the rate in the total study population (exposed and unexposed) compared with the rate in the exposed group.

The population attributable risk (PAR) estimates the excess rate of disease in the total study population of exposed and unexposed individuals that is attributable to the exposure. The PAR provides a measure of the public health impact of an exposure in the population (assuming that the association is causal).

The PAR is the absolute difference between the risk (or rate) in the whole population and the risk (or rate) in the unexposed group.

PAR = Risk (rate) in **total population** - Risk (rate) in unexposed

that is,

**PAR = r - r0**

r = rate in the total study population

r0 = rate in the unexposed

**Population attributable risk fraction (PAF) **^{1}

The population attributable risk fraction (PAF) is the **proportion** of all cases in the whole study population (exposed and unexposed) that may be attributed to the exposure.

PAF = **Population Attributable Risk (PAR)**

Overall rate in the population

that is,

**PAF = PAR/r**

**Issues in the calculation of measures of impact**

- The calculation of PAF assumes that all of the association between the risk factor and disease is causal.
- PAR varies according to how common an exposure to the risk factor is in the population.

**ReferencesM**

1. Hennekens CH, Buring JE. Epidemiology in Medicine. Lippincott Williams & Wilkins, 1987.

2. Farmer, R. Lawrenson, R. 2004. Lecture notes in Epidemiology and Public Health Medicine pp 67-68. Blackwell Publishing.

3. Kaelin, M.A. Bayona, M. 2004 Attributable Risk Applications in Epidemiology [online] [accessed 10/08/2008].

**Related links**

Kaelin, M.A. Bayona, M. 2004 Attributable Risk Applications in Epidemiology [online] [accessed 10/08/2008].

Kirkwood, B.R. Sterne, J.C. 2003. Essential Medical Statistics pp 451-452. Blackwell Science.