Approximate 95% confidence interval for the fold enrichment

Log-scale Wald interval. Only k is random (K/N is the fixed population fraction), so with p_hat = k/n: SE(log FE) = SE(log p_hat), approximately sqrt(1/k - 1/n) by the delta method. A Jeffreys-style continuity correction (k+0.5 successes, n+1 trials) keeps the interval finite at k = 0. Bounds are exponentiated back. Byte-parity port of the TypeScript `foldEnrichmentCI` (packages/core/src/statistics.ts); coverage is validated by Monte Carlo under the null in scripts/bio_validation.py.

Usage

fold_enrichment_ci(N, K, n, k)

Arguments

N

Population size (total items in the universe). Integer >= 1.

K

Number of success states in the population (e.g. inclusive |A|). Integer >= 0.

n

Number of draws (e.g. inclusive |B|). Integer >= 0.

k

Observed successes (e.g. |A intersection B|). Integer >= 0.

Value

Numeric length-2 vector `c(low, high)` (>= 0).

Examples

fold_enrichment_ci(20000, 138, 581, 126)
#> [1] 27.00011 36.75119