Relative Risk, Odds Ratio, NNT & Incidence for Step 1

bolt The 60-second version

check_circleIncidence = new cases during a period ÷ population at risk. Prevalence = all existing cases at a point in time ÷ total population.
check_circleIn a steady state, prevalence ≈ incidence × average disease duration. Longer survival without cure raises prevalence; a cure lowers it.
check_circleRelative risk (cohort studies) = risk in exposed ÷ risk in unexposed = [a/(a + b)] ÷ [c/(c + d)].
check_circleOdds ratio (case-control studies) = ad/bc; it approximates relative risk when the disease is rare.
check_circleAbsolute risk reduction (ARR) = control event rate − treatment event rate; relative risk reduction = ARR ÷ control event rate.
check_circleNumber needed to treat = 1 ÷ ARR; number needed to harm = 1 ÷ attributable risk (absolute risk increase).

target What you'll be able to do · aligned to USMLE Step 1 · Biostatistics & Epidemiology

BIOSTATDistinguish incidence from prevalence and predict how prevalence changes.
BIOSTATCalculate relative risk and odds ratio and match each to its study design.
BIOSTATCalculate ARR, RRR, attributable risk, NNT, and NNH.
BIOSTATInterpret confidence intervals around ratio measures.

How risk measures are tested on Step 1

Set up the table with exposure in the rows and outcome in the columns, then pick the measure that matches the design.

	Outcome +	Outcome −
Exposed	a	b
Unexposed	c	d

Relative risk uses rows (risk within exposed and unexposed groups); the odds ratio uses the cross product ad/bc.

RR vs OR. Values above 1 mean the exposure is associated with more of the outcome; below 1, less.

Think of a bathtub: incidence is the faucet, prevalence is the water level.

Prevalence. A new drug that prolongs life in an incurable disease raises prevalence without changing incidence.

Absolute measures tell you how many patients benefit.

NNT. Round the number needed to treat up to the next whole patient.

Relative risk reduction (RRR) = ARR ÷ CER = 1 − RR. Relative measures can make small absolute benefits look large.
Attributable risk (AR) = risk in exposed − risk in unexposed; AR% = (RR − 1) ÷ RR.
Number needed to harm (NNH) = 1 ÷ AR for an adverse outcome.

Most errors come from mixing up formulas.

Do not calculate relative risk from a case-control study: the investigator chose how many cases and controls to include, so true risks are unknown.
Use percentages as decimals when calculating NNT: an ARR of 5% gives NNT = 1 ÷ 0.05 = 20.
Confidence intervals for RR or OR that include 1 mean the association is not statistically significant.