Question 1

What is the difference between relative risk and odds ratio?

Accepted Answer

Relative risk (RR) = ratio of the probability of outcome in exposed vs unexposed: RR = P(outcome|exposed)/P(outcome|unexposed). Odds ratio (OR) = ratio of the odds of outcome: OR = (a/b)/(c/d). When the outcome is rare (< 10%), RR ≈ OR. When the outcome is common, OR exaggerates the effect compared to RR. RR is easier to interpret for absolute risk communication; OR is required for logistic regression and case-control studies.

Question 2

What does RR = 2.0 mean?

Accepted Answer

RR = 2.0 means the exposed group is twice as likely to experience the outcome as the unexposed group. RR = 1.0 means no association. RR < 1.0 means the exposure is protective (reduced risk). The 95% CI for RR: if it includes 1.0, the result is not statistically significant at α = 0.05.

Question 3

What is the Number Needed to Treat (NNT)?

Accepted Answer

NNT = 1/ARR where ARR (absolute risk reduction) = risk_control − risk_treated. NNT is the number of patients you need to treat to prevent one additional bad outcome. NNT = 1 is perfect (everyone benefits); NNT = 100 means treating 100 patients prevents 1 event. NNT < 10 is generally considered clinically meaningful. For harmful exposures, the analogous measure is NNH (number needed to harm).

Question 4

When should I use OR instead of RR?

Accepted Answer

Use OR when: (1) the study design is case-control (RR cannot be computed from case-control data; OR can), (2) the outcome is rare (< 10% prevalence — OR ≈ RR in this case), (3) you are running logistic regression (which models log-odds and produces OR naturally). Use RR when: the study is prospective (cohort or RCT) and you want a direct ratio of risks, especially for common outcomes.

Question 5

How do I interpret confidence intervals for RR and OR?

Accepted Answer

For RR and OR, the null value is 1.0 (not 0). If the 95% CI for RR includes 1.0 (e.g., [0.7, 2.1]), the result is not statistically significant. If the entire CI is above 1.0 (e.g., [1.3, 3.2]), there is a significant increased risk. If the entire CI is below 1.0 (e.g., [0.3, 0.8]), there is a significant protective effect. Always report CIs alongside RR/OR — point estimates alone are insufficient.

Question 6

What is relative risk reduction (RRR) vs absolute risk reduction (ARR)?

Accepted Answer

ARR = risk_control − risk_treated (absolute difference in risk). RRR = ARR / risk_control = 1 − RR (proportional reduction in risk). Example: control risk = 40%, treated risk = 30%. ARR = 10%, RRR = 25%, NNT = 10. Drug companies often report RRR because it sounds more impressive (25% vs 10%). ARR and NNT give a more direct sense of clinical benefit.

Cell	Meaning	Example
a	Exposed AND outcome (true positive)	Treated patients with event
b	Exposed AND no outcome	Treated patients without event
c	Unexposed AND outcome	Control patients with event
d	Unexposed AND no outcome	Control patients without event

	Event (a/c)	No event (b/d)	Total	Risk
Treated	a = 20	b = 80	100	20%
Control	c = 40	d = 60	100	40%

Measure	Best for	Interpretation
Relative Risk (RR)	Cohort studies, clinical trials	More intuitive: RR=0.5 means "half the risk"
Odds Ratio (OR)	Case-control studies, logistic regression output	Approximates RR when outcome is rare (<10%)
ARR / NNT	Clinical decision-making	NNT=5 is always easier to communicate than RR=0.5
RRR	Marketing, reporting	Always more impressive — NNT communicates real impact better

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RR, OR & NNT Formulas

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RR vs OR: When to Use Each

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