Statistical Analysis
Levin’s Population Attributable Fraction (PAF) & Prevented Fraction Formula
Quantify public-health and operational defect impact using Morton Levin’s (1953) Population Attributable Fraction p_e*(RR - 1) / (1 + p_e*(RR - 1)) and protective Prevented Fraction p_cov*(1 - RR).
Distinguishing excess risk among the exposed (AF_e) from population-wide burden (PAF)
When a risk factor triples incidence (Relative Risk RR = 3.0), the Attributable Fraction Among the Exposed is AF_e = (RR - 1) / RR = 66.67%—meaning two-thirds of cases inside the exposed subgroup stem from that factor. Yet if only p_e = 25% of the overall population carries the exposure, Morton Levin’s (1953) formula shows that eliminating the exposure reduces total population incidence by PAF = p_e * (RR - 1) / (1 + p_e * (RR - 1)) = 0.50 / 1.50 = 33.33%.
Conversely, for a protective vaccine, safety control, or fraud filter with RR_prot < 1 (for example RR_prot = 0.40, i.e., 60% efficacy) deployed across coverage share p_cov = 60%, the Population Prevented Fraction is PF_pop = p_cov * (1 - RR_prot) = 0.60 * 0.60 = 36.00% of hypothetical unmitigated cases prevented.
| Epidemiologic / Quality Metric | Formula | Sample Value |
|---|---|---|
| Exposed Attributable Fraction AF_e | (RR - 1) / RR (at RR = 3.0) | 0.6667 (66.67% of exposed cases) |
| Levin Population PAF | p_e * (RR - 1) / (1 + p_e * (RR - 1)) (at p_e = 25%) | 0.3333 (33.33% of total cases) |
| Population Prevented Fraction PF | p_cov * (1 - RR_prot) (p_cov = 60%, RR = 0.40) | 0.3600 (36.00% prevented) |
Levin Population Attributable Fraction (PAF) Formula
Guard RR < 1 ("USE_PREVENTED_FRACTION") and evaluate (p_e * (RR - 1)) / (1 + p_e * (RR - 1)).
=IF(B3 < 1, "USE_PREVENTED_FRACTION", ROUND((B2 * (B3 - 1)) / (1 + B2 * (B3 - 1)), 4))Protective Population Prevented Fraction (PF_pop) Formula
Guard RR_prot > 1 ("NOT_PROTECTIVE") and multiply coverage share B4 by efficacy (1 - B5).
=IF(B5 > 1, "NOT_PROTECTIVE", ROUND(B4 * (1 - B5), 4))Try the example
Use the original values or change them to test your understanding.