tools for prevalence assessment studies.
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"
|
Details
Five methods are available for calculating confidence intervals. For convenience, synonyms are allowed.
"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"
\[\frac{p + \frac{z_{1-\frac{\alpha}{2}}^2}{2n} \pm z_{1-\frac{\alpha}{2}} \sqrt{\frac{p(1-p)}{n} + \frac{z_{1-\frac{\alpha}{2}}^2}{4n^2}}}{1 + \frac{z_{1-\frac{\alpha}{2}}^2}{n}}\]
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.
Examples
## All methods, 95% confidence intervals
propCI(x = 142, n = 742)
#> x n p method level lower upper
#> 1 142 742 0.1913747 agresti.coull 0.95 0.1646432 0.2212853
#> 2 142 742 0.1913747 exact 0.95 0.1636684 0.2215588
#> 3 142 742 0.1913747 jeffreys 0.95 0.1643017 0.2208498
#> 4 142 742 0.1913747 wald 0.95 0.1630697 0.2196796
#> 5 142 742 0.1913747 wilson 0.95 0.1646876 0.2212409## Wald-type 90%, 95% and 99% confidence intervals
propCI(x = 142, n = 742, method = "wald", level = c(0.90, 0.95, 0.99))
#> x n p method level lower upper
#> 1 142 742 0.1913747 wald 0.90 0.1676204 0.2151289
#> 2 142 742 0.1913747 wald 0.95 0.1630697 0.2196796
#> 3 142 742 0.1913747 wald 0.99 0.1541757 0.2285736