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Helper Functions for Calculating Proportion Confidence Intervals

Source: R/estimate_proportion.R
h_proportions.Rd

[Stable]

Functions to calculate different proportion confidence intervals for use in estimate_proportion().

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.

Functions

  • prop_wilson(): the Wilson interval calls 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(): the Clopper-Pearson interval calls stats::binom.test(). Also referred to as the exact method.

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

  • prop_agresti_coull(): the Agresti-Coull interval was created by Alan Agresti and Brent Coull and can be understood (for 95% CI) as adding two successes and two failures to the data, and then using the Wald formula to construct a CI.

  • prop_jeffreys(): the Jeffreys interval is 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

estimate_proportions, descriptive function d_proportion(), and helper functions strata_normal_quantile() and update_weights_strat_wilson().

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