MKinfer (version 1.2)

binomDiffCI: Confidence Intervals for Difference of Two Binomial Proportions

Description

This function can be used to compute confidence intervals for the difference of two binomial proportions. It includes methods for the independent and the paired case.

Usage

binomDiffCI(a, b, c, d, conf.level = 0.95, paired = FALSE, 
            method = ifelse(paired, "wilson-cc", "wilson"), 
            R = 9999, bootci.type = "all", 
            alternative = c("two.sided", "less", "greater"), ...)

Value

A list with class "confint" containing the following components:

estimate

the estimated probability of success.

conf.int

a confidence interval for the probability of success.

Arguments

a

independent: number of successes of group 1; paired: number of cases with success in group 1 and 2.

b

independent: number of successes of group 2; paired: number of cases with success in group 1 and failure in group 2.

c

independent: number of failures of group 1; paired: number of cases with failure in group 1 and success in group 2.

d

independent: number of failures of group 2; paired: number of cases with failure in group 1 and 2.

conf.level

confidence level

paired

a logical value indicating whether the two groups are paired.

method

character string specifing which method to use; see details.

R

number of bootstrap replicates.

bootci.type

type of bootstrap interval; see boot.ci.

alternative

a character string specifying one- or two-sided confidence intervals. Must be one of "two.sided" (default), "greater" or "less" (one-sided intervals). You can specify just the initial letter.

...

further arguments passed to function boot, e.g. for parallel computing.

Author

Matthias Kohl

Details

The Wald intervals (independent and paired) are obtained by applying the normal approximation. There are also Wald intervals with continuity correction.

The Wilson intervals are recommended by Newcombe and Altman (2000); see Chapter 6 of Altman et al. (2000). In the paired case, the continuity corrected version of the interval is recommended. The intervals are proposed in Newcombe (1998a) and Newcombe (1998b).

The bootstrap interval is calculated by using function boot.ci.

References

D. Altman, D. Machin, T. Bryant, M. Gardner (eds). Statistics with Confidence: Confidence Intervals and Statistical Guidelines, 2nd edition. John Wiley and Sons 2000.

R.G. Newcombe (1998a). Interval estimation for the difference between independent proportions: comparison of eleven methods. Stat Med, 17(8), 873-890.

R.G. Newcombe (1998b). Improved confidence intervals for the difference between binomial proportions based on paired data. Stat Med, 17(22), 2635-2650.

See Also

prop.test, boot.ci

Examples

## Example 1: Altman et al. (2000, p. 49)
## the confidence interval computed by prop.test
prop.test(c(63, 38), c(93, 92))$conf.int
## wald / simple asymptotic interval
binomDiffCI(a = 63, b = 38, c = 30, d = 54, method = "wald")
## wald / simple asymptotic interval with continuity correction
binomDiffCI(a = 63, b = 38, c = 30, d = 54, method = "wald-cc")
## wilson
binomDiffCI(a = 63, b = 38, c = 30, d = 54)
## bootstrap intervals (R = 999 to reduce computation time for R checks)
binomDiffCI(a = 63, b = 38, c = 30, d = 54, method = "boot", R = 999)
## one-sided
binomDiffCI(a = 63, b = 38, c = 30, d = 54, alternative = "greater")
## bootstrap intervals (R = 999 to reduce computation time for R checks)
binomDiffCI(a = 63, b = 38, c = 30, d = 54, method = "boot", R = 999,
            bootci.type = "bca", alternative = "greater")


## Example 2: Altman et al. (2000, p. 50)
## the confidence interval computed by prop.test
prop.test(c(5, 0), c(56, 29))$conf.int
## wald / simple asymptotic interval
binomDiffCI(a = 5, b = 0, c = 51, d = 29, method = "wald")
## wald / simple asymptotic interval with continuity correction
binomDiffCI(a = 5, b = 0, c = 51, d = 29, method = "wald-cc")
## wilson
binomDiffCI(a = 5, b = 0, c = 51, d = 29)
## bootstrap intervals (R = 999 to reduce computation time for R checks)
binomDiffCI(a = 5, b = 0, c = 51, d = 29, method = "boot", R = 999)
## one-sided
binomDiffCI(a = 5, b = 0, c = 51, d = 29, alternative = "less")
## bootstrap intervals (R = 999 to reduce computation time for R checks)
binomDiffCI(a = 5, b = 0, c = 51, d = 29, method = "boot", R = 999,
            bootci.type = "perc", alternative = "less")


## Example 3: Altman et al. (2000, p. 51)
## wald / simple asymptotic interval
binomDiffCI(a = 14, b = 5, c = 0, d = 22, paired = TRUE, method = "wald")
## wald / simple asymptotic interval with continuity correction
binomDiffCI(a = 14, b = 5, c = 0, d = 22, paired = TRUE, method = "wald-cc")
## wilson
binomDiffCI(a = 14, b = 5, c = 0, d = 22, paired = TRUE, method = "wilson")
## wilson with continuity correction
binomDiffCI(a = 14, b = 5, c = 0, d = 22, paired = TRUE)
## bootstrap intervals (R = 999 to reduce computation time for R checks)
binomDiffCI(a = 14, b = 5, c = 0, d = 22, paired = TRUE, method = "boot", R = 999)

## Example 4: Altman et al. (2000, p. 51)
## wald / simple asymptotic interval
binomDiffCI(a = 212, b = 144, c = 256, d = 707, paired = TRUE, method = "wald")
## wald / simple asymptotic interval with continuity correction
binomDiffCI(a = 212, b = 144, c = 256, d = 707, paired = TRUE, method = "wald-cc")
## wilson
binomDiffCI(a = 212, b = 144, c = 256, d = 707, paired = TRUE, method = "wilson")
## wilson with continuity correction
binomDiffCI(a = 212, b = 144, c = 256, d = 707, paired = TRUE)
## bootstrap intervals (R = 999 to reduce computation time for R checks)
binomDiffCI(a = 212, b = 144, c = 256, d = 707, paired = TRUE, method = "boot",
            bootci.type = c("norm", "basic", "stud", "perc"), R = 999) ## type = "bca" gives error

# \donttest{
binomDiffCI(a = 63, b = 38, c = 30, d = 54, method = "boot", R = 9999, 
        parallel = "multicore", ncpus = 2)
# }