# propCI: Calculate confidence intervals for prevalences and other... In prevalence: Tools for Prevalence Assessment Studies

## Description

The propCI function calculates five types of confidence intervals for proportions:

• Wald interval (= Normal approximation interval, asymptotic interval)

• Agresti-Coull interval (= adjusted Wald interval)

• Exact interval (= Clopper-Pearson interval)

• Jeffreys interval (= Bayesian interval)

• Wilson score interval

## Usage

 1 propCI(x, n, method = "all", level = 0.95, sortby = "level") 

## Arguments

 x Number of successes (positive samples) n Number of trials (sample size) method Confidence interval calculation method; see details level Confidence level for confidence intervals sortby Sort results by "level" or "method"

## Details

Five methods are available for calculating confidence intervals. For convenience, synonyms are allowed. Please refer to the PDF version of the manual for proper formatting of the below formulas.

"agresti.coull", "agresti-coull", "ac"

\tilde{n} = n + z_{1-\frac{α}{2}}^2

\tilde{p} = \frac{1}{\tilde{n}}(x + \frac{1}{2} z_{1-\frac{α}{2}}^2)

\tilde{p} \pm z_{1-\frac{α}{2}} √{\frac{\tilde{p}(1-\tilde{p})}{\tilde{n}}}

"exact", "clopper-pearson", "cp"

(Beta(\frac{α}{2}; x, n - x + 1), Beta(1 - \frac{α}{2}; x + 1, n - x))

"jeffreys", "bayes"

(Beta(\frac{α}{2}; x + 0.5, n - x + 0.5), Beta(1 - \frac{α}{2}; x + 0.5, n - x + 0.5))

"wald", "asymptotic", "normal"

p \pm z_{1-\frac{α}{2}} √{\frac{p(1-p)}{n}}

"wilson"

\frac{p + \frac{z_{1-\frac{α}{2}}^2}{2n} \pm z_{1-\frac{α}{2}} √{\frac{p(1-p)}{n} + \frac{z_{1-\frac{α}{2}}^2}{4n^2}}} {1 + \frac{z_{1-\frac{α}{2}}^2}{n}}

## Value

Data frame with seven columns:

 x  Number of successes (positive samples) n  Number of trials (sample size) p  Proportion of successes (prevalence) method  Confidence interval calculation method level  Confidence level lower  Lower confidence limit upper  Upper confidence limit

## Note

In case the observed prevalence equals 0% (ie, x == 0), an upper one-sided confidence interval is returned. In case the observed prevalence equals 100% (ie, x == n), a lower one-sided confidence interval is returned. In all other cases, two-sided confidence intervals are returned.

## Author(s)

Brecht Devleesschauwer <[email protected]>

## Examples

 1 2 3 4 5 ## All methods, 95% confidence intervals propCI(x = 142, n = 742) ## Wald-type 90%, 95% and 99% confidence intervals propCI(x = 142, n = 742, method = "wald", level = c(0.90, 0.95, 0.99)) 

prevalence documentation built on May 29, 2017, 11:59 a.m.