Helper Functions for Calculating Proportion Confidence Intervals

Usage

prop_wilson(rsp, conf_level, correct = FALSE)

prop_strat_wilson(
  rsp,
  strata,
  weights = NULL,
  conf_level = 0.95,
  max_iterations = NULL,
  correct = FALSE
)

prop_clopper_pearson(rsp, conf_level)

prop_wald(rsp, conf_level, correct = FALSE)

prop_agresti_coull(rsp, conf_level)

prop_jeffreys(rsp, conf_level)

Arguments

rsp

(logical)
whether each subject is a responder or not.

conf_level

(proportion)
confidence level of the interval.

correct

(flag)
apply continuity correction.

strata

(factor)
variable with one level per stratum and same length as rsp.

weights

(numeric or NULL)
weights for each level of the strata. If NULL, they are estimated using the iterative algorithm proposed in Yan and Su (2010) that minimizes the weighted squared length of the confidence interval.

max_iterations

(count)
maximum number of iterations for the iterative procedure used to find estimates of optimal weights.

Value

Confidence interval of a proportion.

Functions

• prop_wilson(): Calculates the Wilson interval by calling stats::prop.test(). Also referred to as Wilson score interval.

• prop_strat_wilson(): Calculates the stratified Wilson confidence interval for unequal proportions as described in Yan and Su (2010)

• prop_clopper_pearson(): Calculates the Clopper-Pearson interval by calling stats::binom.test(). Also referred to as the exact method.

• prop_wald(): Calculates the Wald interval by following the usual textbook definition for a single proportion confidence interval using the normal approximation.

• prop_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.

• prop_jeffreys(): Calculates the Jeffreys interval, an equal-tailed interval based on the non-informative Jeffreys prior for a binomial proportion.

References

Yan X, Su XG (2010). “Stratified Wilson and Newcombe Confidence Intervals for Multiple Binomial Proportions.” Stat. Biopharm. Res., 2(3), 329--335.

See also

Examples

rsp <- c(
  TRUE, TRUE, TRUE, TRUE, TRUE,
  FALSE, FALSE, FALSE, FALSE, FALSE
)
prop_wilson(rsp, conf_level = 0.9)
#> [1] 0.2692718 0.7307282

# 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

prop_strat_wilson(
  rsp = rsp, strata = strata,
  conf_level = 0.90
)
#> $conf_int
#>     lower     upper 
#> 0.4072891 0.5647887 
#> 
#> $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 
#> 

# Not automatic setting of weights
prop_strat_wilson(
  rsp = rsp, strata = strata,
  weights = rep(1 / n_strata, n_strata),
  conf_level = 0.90
)
#> $conf_int
#>     lower     upper 
#> 0.4190436 0.5789733 
#> 

prop_clopper_pearson(rsp, conf_level = .95)
#> [1] 0.3886442 0.5919637

prop_wald(rsp, conf_level = 0.95)
#> [1] 0.3920214 0.5879786
prop_wald(rsp, conf_level = 0.95, correct = TRUE)
#> [1] 0.3870214 0.5929786

prop_agresti_coull(rsp, conf_level = 0.95)
#> [1] 0.3942193 0.5865206

prop_jeffreys(rsp, conf_level = 0.95)
#> [1] 0.3934779 0.5870917