Measures of association

Measures of association: It quantifies the relationship between exposure or risk factors and disease among groups. The following types are seen:

1. Relative risk or risk ratio or RR: It compares the risk of a health event (disease, injury, risk factor, or death) among one group with the risk among another group. It compares the risk between exposed and unexposed groups.

   RR = Risk of disease (incidence proportion, attack rate) in group of primary interest

   Risk of disease (incidence proportion, attack rate) in comparison group

   Applying it to 2 X 2 table, RR = [a/a+b] / [c/c+d]

   A risk ratio of 1.0 indicates identical risk among the two groups. A risk ratio greater than 1.0 indicates an increased risk for the group in the numerator, usually the exposed group. A risk ratio less than 1.0 indicates a decreased risk for the exposed group, indicating that perhaps exposure actually protects against disease occurrence.

2. Odds ratio: It is a measure of association between an exposure and an outcome. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.

It is given by the formula, (from 2x2 table),

Odds ratio = (a/b) / (c/d) OR ad/bc

In other words, ratio of exposed persons with disease / ratio of unexposed persons with disease

Where,

a = number of persons exposed and with disease

b = number of persons exposed but without disease

c = number of persons unexposed but with disease

d = number of persons unexposed and without disease

The odds ratio is the measure of choice in a case-control study. In a case control study, when a disease is uncommon in the population, the odds ratio approximates the relative risk.

OR =1 Exposure does not affect odds of outcome

OR >1 Exposure associated with higher odds of outcome

OR <1 Exposure associated with lower odds of outcome

A RR of 3 means the risk of an outcome is increased threefold. But an Odds Ratio of 3 doesn’t mean the risk is threefold, rather the odds is threefold greater. For example if you compare the association between cigarette smoking and lung cancer and find out that the OR is 3, that means the odds of a person with lung cancer being a smoker is 3 times greater than the odds of being a non-smoker.

3. Hazard ratio: It is a measure of association used in prospective studies like clinical trials. It is calculated a follows:

   Hazard ratio = Chance of an event or outcome occurring in the treatment group/ Chance of an event or outcome occurring in the control group

The numerical value of the hazard ratio expresses the relative hazard reduction achieved by the study drug compared to the hazard reduction by the control treatment. A hazard ratio of 1 means lack of association, a hazard ratio > 1 suggests an increased risk, and a hazard ratio < 1 suggests a decreased risk. For example, a hazard ratio of 0.70 means that the study drug provides 30% risk reduction compared to the control treatment.

4. Attributable proportion or attributable risk or percent (AR) : It is the amount of disease in the exposed group that is attributable to the exposure.

AR (%) = (Risk for exposed group − risk for unexposed group) / Risk for exposed group X 100

Another way of calculating attributable proportion is RR-1 / RR, where RR is relative risk.

From 2 x 2 table, AR = [a/a+b] - [c/c+d]

Population attributable risk (PAR) is the proportion of the incidence of a disease in the population (exposed and unexposed) that is due to exposure.

PAR = Incidence in the total population - incidence in the unexposed group

PAR % = PAR/ Incidence in total population x 100

Problem 1: Calculate the attributable risk percent in the following example. In a study, the lung cancer mortality rate among nonsmokers was 0.07 per 1,000 persons per year. The lung cancer mortality rate among persons who smoked 1–14 cigarettes per day was 0.57 lung cancer deaths per 1,000 persons per year. Calculate the attributable proportion.

Attributable proportion = (0.57 − 0.07) ⁄ 0.57 × 100% = 87.7%

5. Absolute risk reduction or ARR or risk difference: ARR, RRR and NNT (see below), are used to quantify the effect size of an intervention. The absolute risk reduction is the arithmetic difference between the event or outcome rates in two groups.

   ARR = Risk of an unwanted outcome in group 1 - risk of the same outcome in group 2

   For example if you take two groups, group 1 has taken the flu vaccine while group 2 has not taken the flu vaccine. Incidence of flu in group 1 is 10% and incidence of flu in group 2 is 45%. Then ARR for flu vaccination will be,

   45% - 10% = 35%.

   According to 2 x 2 table, ARR = [c/c+d] - [a/a+b]

6. Number needed to treat or NNT : It is the number of individuals that need to be treated in order to prevent one event. In the example of flu vaccination above, it is the number of people who need to be vaccinated to prevent one case of flu. Lower the NNT, more is the treatment efficacy.

   NNT = 1/ARR

   For the previous example, as ARR is 35%, NNT = 1/35 % = 7, which means that 7 people need to be vaccinated with the flu vaccine to prevent one case of flu.

7. Relative risk reduction or RRR: It tells you by how much the treatment reduced the risk of bad outcomes relative to the control group who did not have the treatment. It is similar to ARR, but given in a ratio or proportion format rather than an absolute number (as in ARR). RRR measures the amount of risk reduction compared to a baseline risk.

   RRR = difference in risk between the two groups / risk in the control group*

   *a control group is the unexposed or untreated group.

   It can also be calculated as 1-RR.

   Compared to RRR, ARR is a better index to measure effect size.

8. Number needed to harm or NNH: It is a measure of how many people need to be treated (or exposed to a risk factor) in order for one person to have a particular adverse effect. Higher the NNH, safer the intervention or treatment.

   NNH = 1/Absolute risk increase or 1/Attributable risk