Stratified Wilson CI — ci_prop_wilson

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.

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

Details

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

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
)
#> 
#> ── Stratified Wilson Confidence Interval without continuity correction ─────────
#> • 49 responses out of 100
#> • Weights: FALSE.a.x = 0.054, TRUE.a.x = 0.095, FALSE.b.x = 0.106, TRUE.b.x =
#> 0.151, FALSE.a.y = 0.061, TRUE.a.y = 0.064, FALSE.b.y = 0.072, TRUE.b.y =
#> 0.095, FALSE.a.z = 0.089, TRUE.a.z = 0.081, FALSE.b.z = 0.061, TRUE.b.z = 0.072
#> • Estimate: 0.49
#> • 90% Confidence Interval:
#>   (0.4155, 0.5689)

# Not automatic setting of weights
ci_prop_wilson_strata(
  x = rsp, strata = strata,
  weights = rep(1 / n_strata, n_strata),
  conf.level = 0.90
)
#> 
#> ── Stratified Wilson Confidence Interval without continuity correction ─────────
#> • 49 responses out of 100
#> • Weights: 0.083, 0.083, 0.083, 0.083, 0.083, 0.083, 0.083, 0.083, 0.083,
#> 0.083, 0.083, 0.083
#> • Estimate: 0.49
#> • 90% Confidence Interval:
#>   (0.4231, 0.5827)