Measures of association: Measures of association quantify the relationship between an exposure (or other risk factor) and a disease by comparing groups. The following types are commonly used:
Relative risk or risk ratio or RR: Relative risk compares the risk of a health event (disease, injury, risk factor, or death) in one group with the risk in another group. Most often, you compare the risk in an exposed group to the risk in an unexposed group.
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 means the two groups have the same risk. A risk ratio greater than 1.0 means the group in the numerator (usually the exposed group) has a higher risk. A risk ratio less than 1.0 means the exposed group has a lower risk, suggesting the exposure may be protective.
Odds ratio: The odds ratio (OR) is a measure of association between an exposure and an outcome. It compares:
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 does not mean the risk is threefold; it means the odds are threefold greater. For example, if you study the association between cigarette smoking and lung cancer and find that the OR is 3, that means the odds of a person with lung cancer being a smoker are 3 times the odds of being a non-smoker.
Hazard ratio: A hazard ratio is a measure of association commonly used in prospective studies such as clinical trials, especially when time-to-event is important. 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 no association, a hazard ratio > 1 suggests increased risk, and a hazard ratio < 1 suggests decreased risk. For example, a hazard ratio of 0.70 means that the study drug provides 30% risk reduction compared to the control treatment.
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%
Absolute risk reduction or ARR or risk difference: ARR, RRR and NNT (see below), are used to quantify the effect size of an intervention. Absolute risk reduction (also called the risk difference) is the arithmetic difference between the event (outcome) rates in two groups.
ARR = Risk of an unwanted outcome in group 1 - risk of the same outcome in group 2
For example, suppose group 1 received the flu vaccine and group 2 did not. If the incidence of flu is 10% in group 1 and 45% in group 2, then ARR for flu vaccination is:
45% - 10% = 35%.
According to 2 x 2 table, ARR = [c/c+d] - [a/a+b]
Number needed to treat or NNT : NNT is the number of individuals who need to be treated to prevent one event. In the flu vaccination example above, it is the number of people who need to be vaccinated to prevent one case of flu. A lower NNT indicates higher treatment efficacy.
NNT = 1/ARR
For the previous example, since ARR is 35%, NNT = 1/35 % = 7. This means 7 people need to be vaccinated with the flu vaccine to prevent one case of flu.
Relative risk reduction or RRR: Relative risk reduction tells you how much the treatment reduced the risk of bad outcomes relative to the control group (the unexposed or untreated group). It is similar to ARR, but it is expressed as a ratio or proportion rather than an absolute difference. 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.
Number needed to harm or NNH: NNH is the number of people who need to be treated (or exposed to a risk factor) for one person to experience a particular adverse effect. A higher NNH indicates a safer intervention or treatment.
NNH = 1/Absolute risk increase or 1/Attributable risk
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