prevalence (version 0.4.1)

propCI: Calculate confidence intervals for prevalences and other proportions

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

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"

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

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"

$$\tilde{n} = n + z_{1-\frac{\alpha}{2}}^2$$ $$\tilde{p} = \frac{1}{\tilde{n}}(x + \frac{1}{2} z_{1-\frac{\alpha}{2}}^2)$$ $$\tilde{p} \pm z_{1-\frac{\alpha}{2}} \sqrt{\frac{\tilde{p}(1-\tilde{p})}{\tilde{n}}}$$

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

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

"jeffreys", "bayes"

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

"wald", "asymptotic", "normal"

$$p \pm z_{1-\frac{\alpha}{2}} \sqrt{\frac{p(1-p)}{n}}$$

"wilson"

$$ \frac{p + \frac{z_{1-\frac{\alpha}{2}}^2}{2n} \pm z_{1-\frac{\alpha}{2}} \sqrt{\frac{p(1-p)}{n} + \frac{z_{1-\frac{\alpha}{2}}^2}{4n^2}}} {1 + \frac{z_{1-\frac{\alpha}{2}}^2}{n}} $$

Examples

# NOT RUN {
## 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))
# }