ci_prop_wilson_strata: Stratified Wilson CI

In cicalc: Calculate Confidence Intervals

Stratified Wilson CI

Description

Calculates the stratified Wilson confidence interval for unequal proportions as described in Xin YA, Su XG. Stratified Wilson and Newcombe confidence intervals for multiple binomial proportions. Statistics in Biopharmaceutical Research. 2010;2(3).

Usage

ci_prop_wilson_strata(
  x,
  strata,
  weights = NULL,
  conf.level = 0.95,
  max.iterations = 10L,
  correct = FALSE,
  data = NULL
)

Arguments

x	(binary/numeric/logical) vector of a binary values, i.e. a logical vector, or numeric with values c(0, 1)
strata	(numeric) A vector specifying the stratum for each observation. It needs to be the length of x or a multiple of x if multiple levels of strata are present. Can also be a column name (or vector of column names NOT quoted) if a data frame provided in the data argument.
weights	(numeric) weights for each level of the strata. If NULL, they are estimated using the iterative algorithm that minimizes the weighted squared length of the confidence interval.
conf.level	(⁠scalar numeric⁠) a scalar in (0,1) indicating the confidence level. Default is 0.95
max.iterations	(positive integer) maximum number of iterations for the iterative procedure used to find estimates of optimal weights.
correct	(scalar logical) include the continuity correction. For further information, see for example stats::prop.test().
data	(data.frame) Optional data frame containing the variables specified in x and by.

Details

\frac{\hat{p}_j + \frac{z^2_{\alpha/2}}{2n_j} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}_j(1 - \hat{p}_j)}{n_j} + \frac{z^2_{\alpha/2}}{4n_j^2}}}{1 + \frac{z^2_{\alpha/2}}{n_j}}

Value

An object containing the following components:

n	Number of responses
N	Total number
estimate	The point estimate of the proportion
conf.low	Lower bound of the confidence interval
conf.high	Upper bound of the confidence interval
conf.level	The confidence level used
weights	Weights of each strata, will be the same as the input unless unspecified, then it will be the dynamically calculated weights.
method	Type of method used

Examples

# Stratified Wilson confidence interval with unequal probabilities

set.seed(1)
rsp <- sample(c(TRUE, FALSE), 100, TRUE)
strata_data <- data.frame(
  x = sample(c(TRUE, FALSE), 100, TRUE),
  "f1" = sample(c("a", "b"), 100, TRUE),
  "f2" = sample(c("x", "y", "z"), 100, TRUE),
  stringsAsFactors = TRUE
)
strata <- interaction(strata_data)
n_strata <- ncol(table(rsp, strata)) # Number of strata

ci_prop_wilson_strata(
  x = rsp, strata = strata,
  conf.level = 0.90
)

# Not automatic setting of weights
ci_prop_wilson_strata(
  x = rsp, strata = strata,
  weights = rep(1 / n_strata, n_strata),
  conf.level = 0.90
)

cicalc documentation built on Aug. 8, 2025, 7 p.m.