By Fatima Ahmad Qureshy
In research study designs, one of the main goals often is to establish a relationship between two or more factors. For example in heathcare, physicians are mostly interested if one risk factor can lead towards a certain disease. To test if these two factors are really linked, we use measures of association.
Measures of association are tools in different study designs that measure association between exposure (e.g. risk factor, health characteristic) and outcome (e.g. disease, mortality) .
These include: Relative Risk, Attributable Risk, Odds Ratio, Rate Ratio etc. We will be discussing some of these in this article.
Before we start with the definitions of these measures, its important to have background knowledge of the study designs theycome up in: Case Control Study and Cohort Study.
Case Control study: A type of retrospective study in which two groups with different known outcomes are compared to see if the supposed exposure in the past was the causal factor. For example, comparing the subjects who have the disease (the “cases”) with subjects who do not have the disease (the “controls”), and examining the history to see association with a certain risk factor.
Cohort Study: Prospective Cohort study is a type of prospective study in which two groups of subjects with unknown outcomes are compared based on known exposure to risk factor. For example, two groups, one exposed and one unexposed group are compared to see if the exposure develops a certain outcome in future.
So now that we have background concept clear, lets discuss the measures of association:
Relative Risk:
- It compares disease development probability between exposed group, unexposed group on a relative scale, by dividing them.
- It is used in Cohort study, where there are two groups- exposed and unexposed.
Relative Risk = Probability of disease in exposed population / Probability of disease in non-exposed population
Attributable Risk
- Attributable risk (AR) or risk difference is the difference between the probabilities of disease in exposed and non-exposed groups. It compares the probabilities on an additive scale.
- Also, in cohort study.
- It is not a ratio like relative risk, it’s the difference.
ARR = Probability of disease (Unexposed) – Probability of disease (exposed)
EXAMPLE:
- Probability that someone has developed a disease when exposed P(D/E): 30/100 = 0.30
- Probability of developing the disease when NOT Exposed P (D/NE): 20/100= 0.20
RELATIVE RISK: P(D/E) / P(D/ND) = 0.30 / 0.20 = 1.5X
This means that exposed is 1.5 times more at risk of developing the disease.
ATTRIBUTABLE RISK: P(D/E)-P(D/NE) = 0.30-0.20= 0.10 (10%)
This means that risk of disease is 10% more in the exposed than in unexposed.
Odds Ratio
- Odds ratio is the ratio of odds of an event in one group vs the odds of event in the other group.
- The odds are itself a ratio of a probability that the event will occur to the probability that the event will not occur, so odds ratio is different from relative risk.
- Odds ratio is used in case control study. This means we study the odds of disease development due to exposure in Case (Diseased) Group, vs the odds of disease development due to exposure in Control (Non-Diseased) Group.
If disease and exposure status of two groups is put in a 2x2 contingency table, then we calculate Odds ratio as:
OR = A x D / B x C
Once we calculate OR, we can find out the association between exposer and outcome:
- 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
Number Needed to Treat (NNT)
- It is a number that determines how many individuals should be treated with an intervention (procedure, medication, lifestyle change), to prevent one person from developing disease.
- Gives an idea of the effectiveness of an intervention.
# needed to treat = 1 / Attributable risk (Absolute Risk Reduction)
- Here, we see that attributable risk is known as the Absolute risk reduction. This is because due to any intervention, the risk of disease outcome reduces, and that reduction gives us the idea of effectiveness of that treatment.
EXAMPLE
Let’s say that a research paper suggests that patients of Chronic Heart Disease need to be treated with beta blockers in order to reduce chances of mortality and presents following data in its study:
- Risk of Mortality in CHD patients WITHOUT the intervention of Carvedilol: 40%
- Risk of Mortality in CHD patients WITH the intervention of Carvedilol: 34%
- So, the risk reduces from 40%🡪34%
- Absolute Risk Reduction: 0.40 – 0.34 = 0.06
- Numbers Needed to Treat: 1/0.06 = 16.67
- This means that 17 people need to be given Carvedilol in order for one of them to be saved from death.
Therefore, these values are important in studying disease outcomes and various risk factors in research study designs.