Risk Measures — DentalStats

From a 2x2 table

a = exposed & outcome+; b = exposed & outcome-; c = unexposed & outcome+; d = unexposed & outcome- Risk_exposed = a/(a+b) Risk_unexposed = c/(c+d) RR = Risk_exposed / Risk_unexposed RD = Risk_exposed - Risk_unexposed OR = (a/b) / (c/d) = ad/bc

RR is natural for cohort/RCTs; OR is common in case-control and logistic regression.

Interactive calculator + visualization

Outcome +

Outcome -

Exposed

Unexposed

RR

-

OR

-

RD

-

Risk comparison

Real Dental Scenario: Smoking & Periodontitis

Interactive animated cohort study walkthrough

Study Design

A dental research team followed 400 patients for 5 years to investigate the association between smoking and periodontitis development.

Smokers (n = 150)

80 developed periodontitis, 70 did not

Non-smokers (n = 250)

40 developed periodontitis, 210 did not

1

Risk in Smokers

Risk_smokers = 80 / 150 = 0.533 (53.3%)

53.3%

2

Risk in Non-smokers

Risk_nonsmokers = 40 / 250 = 0.160 (16.0%)

16.0%

3

Relative Risk (RR)

RR = Risk_smokers / Risk_nonsmokers = 0.533 / 0.160 = 3.33

Interpretation: Smokers are 3.33 times more likely to develop periodontitis compared to non-smokers.

4

Odds Ratio (OR)

OR = (a x d) / (b x c) = (80 x 210) / (70 x 40) = 16800 / 2800 = 5.71

Interpretation: The odds of periodontitis among smokers are 5.71 times the odds among non-smokers. Note: OR overestimates RR when the outcome is common (>10%).

5

Risk Difference (RD) / Attributable Risk

RD = Risk_smokers - Risk_nonsmokers = 0.533 - 0.160 = 0.373 (37.3%)

Interpretation: There is a 37.3 percentage point absolute increase in periodontitis risk attributable to smoking. For every 100 smokers, approximately 37 additional cases occur compared to non-smokers.

Summary: All Measures at a Glance

3.33

Relative Risk

Smokers 3.33x more likely

5.71

Odds Ratio

Odds 5.71x higher

37.3%

Risk Difference

37.3 pp absolute increase

Dental example

Example: smoking (exposure) and periodontitis (outcome). RR helps communicate "how many times more likely" the outcome is among smokers (in cohort-like data). Logistic regression reports adjusted ORs.