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Stratified Newcombe Common Risk Difference Confidence Interval

ci_prop_diff_nc_strata.Rd

Calculates the stratified Newcombe confidence interval for unequal proportions as described in Yan X, Su XG. Stratified Wilson and Newcombe confidence intervals or multiple binomial proportions. Weights are estimated using CMH or Wilson methods.

Usage

ci_prop_diff_nc_strata(
  x,
  by,
  strata,
  conf.level = 0.95,
  correct = FALSE,
  weights_method = c("wilson", "cmh"),
  data = NULL
)

Arguments

x

(binary/numeric/logical)
vector of a binary values, i.e. a logical vector, or numeric with values c(0, 1)

by

(string)
A character or factor vector with exactly two unique levels identifying the two groups to compare. Can also be a column name if a data frame provided in the data argument.

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.

conf.level

(scalar numeric)
a scalar in (0,1) indicating the confidence level. Default is 0.95

correct

(scalar logical)
include the continuity correction. For further information, see for example [ci_prop_diff_nc())].

[ci_prop_diff_nc())]: R:ci_prop_diff_nc())

weights_method

(character)
Can be either "wilson" or "cmh" and directs the way weights are estimated.

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 calculated as per the specified "weights_method" argument.

method

Type of method used

Details

$$ L = \hat{d}_{\rm MH} - z_{\alpha/2} \sqrt{ \sum_h w_h^2 L_{2h} (1 - L_{2h}) + \sum_h w_h^2 U_{1h} (1 - U_{1h}) } $$

$$ U = \hat{d}_{\rm MH} + z_{\alpha/2} \sqrt{ \sum_h w_h^2 L_{2h} (1 - L_{2h}) + \sum_h w_h^2 U_{1h} (1 - U_{1h}) } $$

Where:

  • \(\hat{d}_{\rm MH}\): Mantel-Haenszel common risk difference

  • \(z_{\alpha/2}\): standard normal critical value

  • \(w_h\): stratum weights

  • \(L_{2h}\), \(U_{1h}\): Wilson-type CI limits for stratum h

Examples

set.seed(1)
rsp <- sample(c(TRUE, FALSE), 100, TRUE)
grp <- sample(c("Placebo", "Treatment"), 100, TRUE)
strata_data <- data.frame(
  "f1" = sample(c("a", "b"), 100, TRUE),
  "f2" = sample(c("x", "y", "z"), 100, TRUE),
  stringsAsFactors = TRUE
)
strata <- interaction(strata_data)

ci_prop_diff_nc_strata(
  x = rsp, by = grp, strata = strata, weights_method = "cmh",
  conf.level = 0.95
)
#> 
#> ── Stratified Newcombe Confidence Interval without continuity correction, CMH ──
#> • 49 responses out of 100
#> • Weights: a.x = 0.122, b.x = 0.273, a.y = 0.132, b.y = 0.14, a.z = 0.193, b.z
#> = 0.14
#> • Estimate: 0.042
#> • 95% Confidence Interval:
#>   (-0.1508, 0.2314)