Confidence interval for a single binomial proportion

Vectorized computation of a two-sided confidence interval for a single proportion x / n, using one of five standard methods. All methods are computed in closed form or via qbeta (no per-row binom.test loop), so the function scales to a full count table's worth of cells at once.

Usage

proportion_ci(
  x,
  n,
  method = c("clopper_pearson", "wilson", "wald", "agresti_coull", "jeffreys"),
  level = 0.95
)

Arguments

x: Numeric vector of event counts (numerators).
n: Numeric vector of trial counts (denominators). Recycled against x following the usual R rules.
method: One of "clopper_pearson" (default), "wilson", "wald", "agresti_coull", or "jeffreys".
level: Numeric coverage probability (default 0.95).

Value

A data.table with two columns, lower and upper, giving the interval bounds as proportions in [0, 1] (multiply by 100 for the percentage scale).

Details

The methods and their references:

clopper_pearson: Exact interval based on the beta distribution. Matches stats::binom.test() and SAS PROC FREQ ... EXACT (the clinical convention). This is the default.
wilson: Wilson score interval without continuity correction. Matches stats::prop.test(correct = FALSE).
wald: Normal-approximation ("simple asymptotic") interval, clamped to [0, 1].
agresti_coull: Adds z^2/2 pseudo-successes and pseudo-failures, then applies the Wald interval to the adjusted counts.
jeffreys: Bayesian interval using the Jeffreys Beta(0.5, 0.5) prior, with the standard boundary adjustments at x == 0 and x == n.

Edge cases: when n == 0 (or either input is NA) both bounds are NA; when x == 0 the lower bound is exactly 0; when x == n the upper bound is exactly 1.

Examples

proportion_ci(c(0, 12, 40), c(40, 40, 40), method = "clopper_pearson")
#>        lower     upper
#>        <num>     <num>
#> 1: 0.0000000 0.0880973
#> 2: 0.1656272 0.4653163
#> 3: 0.9119027 1.0000000