\name{epi.prev}

\alias{epi.prev}

\title{
Estimate true prevalence
}

\description{
Computes the true prevalence of a disease in a population on the basis of an imperfect test.
}

\usage{
epi.prev(pos, tested, se, sp, method = "wilson", conf.level = 0.95)
}

\arguments{
  \item{pos}{the number of positives.}
  \item{tested}{the number tested.}
  \item{se}{test sensitivity (0 - 1).}
  \item{sp}{test specificity (0 - 1).}
  \item{method}{a character string indicating the method to use. Options are \code{"c-p"} (Cloppper-Pearson), \code{"sterne"} (Sterne), \code{"blaker"} (Blaker) and \code{"wilson"} (Wilson).}
  \item{conf.level}{magnitude of the returned confidence interval. Must be a single number between 0 and 1.}
}

\details{
Appropriate confidence intervals for the adjusted prevalence estimate are provided, accounting for the change in variance that arises from imperfect test sensitivity and specificity (see Reiczigel et al 2010 for details). 

The Clopper-Pearson method is known to be too conservative for two-sided intervals (Blaker 2000, Agresti and Coull 1998). Blaker's and Sterne's methods (Blaker 2000, Sterne 1954) provide smaller exact two-sided confidence interval estimates. 
}

\value{
A list containing the following: 
   \item{ap}{the point estimate of apparent prevalence and the lower and upper bounds of the confidence interval around the apparent prevalence estimate.}
   \item{tp}{the point estimate of the true prevalence and the lower and upper bounds of the confidence interval around the true prevalence estimate.}
}


\references{
Abel U (1993). DieBewertung Diagnostischer Tests. Hippokrates, Stuttgart. 

Agresti A, Coull BA (1998). Approximate is better than 'exact' for interval estimation of binomial proportions. American Statistician 52: 119 - 126. 

Blaker H (2000). Confidence curves and improved exact confidence intervals for discrete distributions. Canadian Journal of Statistics 28: 783 - 798. 

Clopper CJ, Pearson ES (1934). The use of confidence of fiducial limits illustrated in the case of the binomial. Biometrika 26: 404 - 413. 

Gardener IA, Greiner M (1999). Advanced Methods for Test Validation and Interpretation in Veterinary Medicince. Freie Universitat Berlin, ISBN 3-929619-22-9; 80 pp. 

Messam L, Branscum A, Collins M, Gardner I (2008) Frequentist and Bayesian approaches to prevalence estimation using examples from Johne's disease. Animal Health Research Reviews 9: 1 - 23. 

Reiczigel J, Foldi J, Ozsvari L (2010). Exact confidence limits for prevalence of disease with an imperfect diagnostic test. Epidemiology and Infection 138: 1674 - 1678. 

Rogan W, Gladen B (1978). Estimating prevalence from results of a screening test. American Journal of Epidemiology 107: 71 - 76. 

Sterne TE (1954). Some remarks on confidence or fiducial limits. Biometrika 41: 275 - 278. 
}


\note{This function uses apparent prevalence, test sensitivity and test specificity to estimate true prevalence (after Rogan and Gladen, 1978). Confidence intervals for the apparent and true prevalence estimates are based on code provided by Reiczigel et al. (2010). 
}

\examples{
## A simple random sample of 150 cows from a herd of 2560 is taken.
## Each cow is given a screening test for brucellosis which has a 
## sensitivity of 96% and a specificity of 89%. Of the 150 cows tested
## 23 were positive to the screening test. What is the estimated prevalence 
## of brucellosis in this herd (and its 95% confidence interval)?

epi.prev(pos = 23, tested = 150, se = 0.96, sp = 0.89, method = "blaker",
   conf.level = 0.95)

## The estimated true prevalence of brucellosis in this herd is 5.1 cases per 
## 100 cows (95% CI 0 -- 13 cases per 100 cows).

## Moujaber et al. (2008) analysed the seroepidemiology of Helicobacter pylori 
## infection in Australia. They reported seroprevalence rates together with 
## 95% confidence intervals by age group using the Clopper-Pearson exact 
## method (Clopper and Pearson, 1934). The ELISA test they applied had 96.4% 
## sensitivity and 92.7% specificity. A total of 151 subjects 1 -- 4 years
## of age were tested. Of this group 6 were positive. What is the estimated 
## true prevalence of Helicobacter pylori in this age group?

epi.prev(pos = 6, tested = 151, se = 0.964, sp = 0.927, method = "c-p",
   conf.level = 0.95)

## The estimated true prevalence of Helicobacter pylori in 1 -- 4 year olds is
## 0 cases per 100 (95% 0 -- 1.3 cases per 100).
}

\keyword{univar}