R/proportion_ci.R
proportion_ci.RdFunctions to calculate different proportion confidence intervals for use in ard_proportion().
proportion_ci_wald(x, conf.level = 0.95, correct = FALSE)
proportion_ci_wilson(x, conf.level = 0.95, correct = FALSE)
proportion_ci_clopper_pearson(x, conf.level = 0.95)
proportion_ci_agresti_coull(x, conf.level = 0.95)
proportion_ci_jeffreys(x, conf.level = 0.95)
proportion_ci_strat_wilson(
x,
strata,
weights = NULL,
conf.level = 0.95,
max.iterations = 10L,
correct = FALSE
)
is_binary(x)(binary numeric/logical)
vector of a binary values, i.e. a logical vector, or numeric with values c(0, 1)
(scalar numeric)
a scalar in (0,1) indicating the confidence level.
Default is 0.95
(scalar logical)
include the continuity correction. For further information, see for example
stats::prop.test().
(factor)
variable with one level per stratum and same length as x.
(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.
(positive integer)
maximum number of iterations for the iterative procedure used
to find estimates of optimal weights.
Confidence interval of a proportion.
proportion_ci_wald(): Calculates the Wald interval by following the usual textbook definition
for a single proportion confidence interval using the normal approximation.
$$\hat{p} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$$
proportion_ci_wilson(): Calculates the Wilson interval by calling stats::prop.test().
Also referred to as Wilson score interval.
$$\frac{\hat{p} + \frac{z^2_{\alpha/2}}{2n} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n} + \frac{z^2_{\alpha/2}}{4n^2}}}{1 + \frac{z^2_{\alpha/2}}{n}}$$
proportion_ci_clopper_pearson(): Calculates the Clopper-Pearson interval by calling stats::binom.test().
Also referred to as the exact method.
$$ \left( \frac{k}{n} \pm z_{\alpha/2} \sqrt{\frac{\frac{k}{n}(1-\frac{k}{n})}{n} + \frac{z^2_{\alpha/2}}{4n^2}} \right) / \left( 1 + \frac{z^2_{\alpha/2}}{n} \right)$$
proportion_ci_agresti_coull(): Calculates the Agresti-Coull interval (created by Alan Agresti and Brent Coull) by
(for 95% CI) adding two successes and two failures to the data and then using the Wald formula to construct a CI.
$$ \left( \frac{\tilde{p} + z^2_{\alpha/2}/2}{n + z^2_{\alpha/2}} \pm z_{\alpha/2} \sqrt{\frac{\tilde{p}(1 - \tilde{p})}{n} + \frac{z^2_{\alpha/2}}{4n^2}} \right)$$
proportion_ci_jeffreys(): Calculates the Jeffreys interval, an equal-tailed interval based on the
non-informative Jeffreys prior for a binomial proportion.
$$\left( \text{Beta}\left(\frac{k}{2} + \frac{1}{2}, \frac{n - k}{2} + \frac{1}{2}\right)_\alpha, \text{Beta}\left(\frac{k}{2} + \frac{1}{2}, \frac{n - k}{2} + \frac{1}{2}\right)_{1-\alpha} \right)$$
proportion_ci_strat_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).
$$\frac{\hat{p}_j + \frac{z^2_{\alpha/2}}{2n_j} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}_j(1 - \hat{p}_j)}{n_j} + \frac{z^2_{\alpha/2}}{4n_j^2}}}{1 + \frac{z^2_{\alpha/2}}{n_j}}$$
is_binary(): Helper to determine if vector is binary (logical or 0/1)
x <- c(
TRUE, TRUE, TRUE, TRUE, TRUE,
FALSE, FALSE, FALSE, FALSE, FALSE
)
proportion_ci_wald(x, conf.level = 0.9)
#> $N
#> [1] 10
#>
#> $n
#> [1] 5
#>
#> $estimate
#> [1] 0.5
#>
#> $conf.low
#> [1] 0.2399258
#>
#> $conf.high
#> [1] 0.7600742
#>
#> $conf.level
#> [1] 0.9
#>
#> $method
#> Wald Confidence Interval without continuity correction
#>
proportion_ci_wilson(x, correct = TRUE)
#> $N
#> [1] 10
#>
#> $n
#> [1] 5
#>
#> $conf.level
#> [1] 0.95
#>
#> $estimate
#> p
#> 0.5
#>
#> $statistic
#> X-squared
#> 0
#>
#> $p.value
#> [1] 1
#>
#> $parameter
#> df
#> 1
#>
#> $conf.low
#> [1] 0.2365931
#>
#> $conf.high
#> [1] 0.7634069
#>
#> $method
#> Wilson Confidence Interval with continuity correction
#>
#> $alternative
#> [1] "two.sided"
#>
proportion_ci_clopper_pearson(x)
#> $N
#> [1] 10
#>
#> $n
#> [1] 5
#>
#> $conf.level
#> [1] 0.95
#>
#> $estimate
#> probability of success
#> 0.5
#>
#> $statistic
#> number of successes
#> 5
#>
#> $p.value
#> [1] 1
#>
#> $parameter
#> number of trials
#> 10
#>
#> $conf.low
#> [1] 0.187086
#>
#> $conf.high
#> [1] 0.812914
#>
#> $method
#> [1] "Clopper-Pearson Confidence Interval"
#>
#> $alternative
#> [1] "two.sided"
#>
proportion_ci_agresti_coull(x)
#> $N
#> [1] 10
#>
#> $n
#> [1] 5
#>
#> $estimate
#> [1] 0.5
#>
#> $conf.low
#> [1] 0.2365931
#>
#> $conf.high
#> [1] 0.7634069
#>
#> $conf.level
#> [1] 0.95
#>
#> $method
#> [1] "Agresti-Coull Confidence Interval"
#>
proportion_ci_jeffreys(x)
#> $N
#> [1] 10
#>
#> $n
#> [1] 5
#>
#> $estimate
#> [1] 0.5
#>
#> $conf.low
#> [1] 0.2235287
#>
#> $conf.high
#> [1] 0.7764713
#>
#> $conf.level
#> [1] 0.95
#>
#> $method
#> Jeffreys Interval
#>
# Stratified Wilson confidence interval with unequal probabilities
set.seed(1)
rsp <- sample(c(TRUE, FALSE), 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)
n_strata <- ncol(table(rsp, strata)) # Number of strata
proportion_ci_strat_wilson(
x = rsp, strata = strata,
conf.level = 0.90
)
#> $N
#> [1] 100
#>
#> $n
#> [1] 49
#>
#> $estimate
#> [1] 0.49
#>
#> $conf.low
#> [1] 0.4072891
#>
#> $conf.high
#> [1] 0.5647887
#>
#> $conf.level
#> [1] 0.9
#>
#> $weights
#> a.x b.x a.y b.y a.z b.z
#> 0.2074199 0.1776464 0.1915610 0.1604678 0.1351096 0.1277952
#>
#> $method
#> Stratified Wilson Confidence Interval without continuity correction
#>
# Not automatic setting of weights
proportion_ci_strat_wilson(
x = rsp, strata = strata,
weights = rep(1 / n_strata, n_strata),
conf.level = 0.90
)
#> $N
#> [1] 100
#>
#> $n
#> [1] 49
#>
#> $estimate
#> [1] 0.49
#>
#> $conf.low
#> [1] 0.4190436
#>
#> $conf.high
#> [1] 0.5789733
#>
#> $conf.level
#> [1] 0.9
#>
#> $method
#> Stratified Wilson Confidence Interval without continuity correction
#>