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\name{epi.sssimpleestb}
\alias{epi.sssimpleestb}
\title{
Sample size to estimate a binary outcome using simple random sampling
}
\description{
Sample size to estimate a binary outcome using simple random sampling.
}
\usage{
epi.sssimpleestb(N = NA, Py, epsilon, error = "relative",
se, sp, nfractional = FALSE, conf.level = 0.95)
}
\arguments{
\item{N}{scalar integer, the total number of individuals eligible for inclusion in the study. If \code{N = NA} the number of individuals eligible for inclusion is assumed to be infinite.}
\item{Py}{scalar number, an estimate of the population proportion to be estimated.}
\item{epsilon}{scalar number, the maximum difference between the estimate and the unknown population value expressed in absolute or relative terms.}
\item{error}{character string. Options are \code{absolute} for absolute error and \code{relative} for relative error.}
\item{se}{the diagnostic sensitivity of the method used to detect positive outcomes (0 - 1).}
\item{sp}{the diagnostic specificity of the method used to detect positive outcomes (0 - 1).}
\item{nfractional}{logical, return fractional sample size.}
\item{conf.level}{scalar number, the level of confidence in the computed result.}
}
\details{
A finite population correction factor is applied to the sample size estimates when a value for \code{N} is provided.
}
\value{
Returns an integer defining the required sample size.
}
\references{
Getachew T, Getachew G, Sintayehu G, Getenet M, Fasil A (2016). Bayesian estimation of sensitivity and specificity of Rose Bengal, complement fixation, and indirect ELISA tests for the diagnosis of bovine brucellosis in Ethiopia. Veterinary Medicine International. DOI: 10.1155/2016/8032753
Humphry RW, Cameron A, Gunn GJ (2004). A practical approach to calculate sample size for herd prevalence surveys. Preventive Veterinary Medicine 65: 173 - 188.
Levy PS, Lemeshow S (1999). Sampling of Populations Methods and Applications. Wiley Series in Probability and Statistics, London, pp. 70 - 75.
Scheaffer RL, Mendenhall W, Lyman Ott R (1996). Elementary Survey Sampling. Duxbury Press, New York, pp. 95.
Otte J, Gumm I (1997). Intra-cluster correlation coefficients of 20 infections calculated from the results of cluster-sample surveys. Preventive Veterinary Medicine 31: 147 - 150.
}
\note{
The sample size calculation method implemented in this function follows the approach described by Humphry et al. (2004) accounting for imperfect diagnostic sensitivity and specificity.
If \code{epsilon.r} equals the relative error the sample estimate should not differ in absolute value from the true unknown population parameter \code{d} by more than \code{epsilon.r * d}.
}
\examples{
## EXAMPLE 1:
## We want to estimate the seroprevalence of Brucella abortus in a population
## of cattle. An estimate of the unknown prevalence of B. abortus in this
## population is 0.15. We would like to be 95\% certain that our estimate is
## within 20\% of the true proportion of the population seropositive to
## B. abortus. Calculate the required sample size assuming use of a test
## with perfect diagnostic sensitivity and specificity.
epi.sssimpleestb(N = NA, Py = 0.15, epsilon = 0.20,
error = "relative", se = 1.00, sp = 1.00, nfractional = FALSE,
conf.level = 0.95)
## A total of 545 cattle need to be sampled to meet the requirements of the
## survey.
## EXAMPLE 1 (continued):
## Why don't I get the same results as other sample size calculators? The
## most likely reason is misspecification of epsilon. Other sample size
## calculators (e.g., OpenEpi) require you to enter the absolute
## error (as opposed to relative error). For the example above the absolute
## error is 0.20 * 0.15 = 0.03. Re-run epi.simpleestb:
epi.sssimpleestb(N = NA, Py = 0.15, epsilon = 0.03,
error = "absolute", se = 1.00, sp = 1.00, nfractional = FALSE,
conf.level = 0.95)
## A total of 545 cattle need to be sampled to meet the requirements of the
## survey.
## EXAMPLE 1 (continued):
## The World Organisation for Animal Health (WOAH) recommends that the
## compliment fixation test (CFT) is used for bovine brucellosis prevalence
## estimation. Assume the diagnostic sensitivity and specficity of the bovine
## brucellosis CFT to be used is 0.94 and 0.88 respectively
## (Getachew et al. 2016). Re-calculate the required sample size
## accounting for imperfect diagnostic test performance.
n.crude <- epi.sssimpleestb(N = NA, Py = 0.15, epsilon = 0.20,
error = "relative", se = 0.94, sp = 0.88, nfractional = FALSE,
conf.level = 0.95)
n.crude
## A total of 1168 cattle need to be sampled to meet the requirements of the
## survey.
## EXAMPLE 1 (continued):
## Being seropositive to brucellosis is likely to cluster within herds.
## Otte and Gumm (1997) cite the intraclass correlation coefficient (rho) of
## Brucella abortus to be in the order of 0.09. Adjust the sample size
## estimate to account for clustering at the herd level. Assume that, on
## average, 20 animals will be sampled per herd:
## Let D equal the design effect and nbar equal the average number of
## individuals per cluster:
## rho = (D - 1) / (nbar - 1)
## Solving for D:
## D <- rho * (nbar - 1) + 1
rho <- 0.09; nbar <- 20
D <- rho * (nbar - 1) + 1
n.adj <- ceiling(n.crude * D)
n.adj
## After accounting for use of an imperfect diagnostic test and the presence
## of clustering of brucellosis positivity at the herd level we estimate that
## a total of 3166 cattle need to be sampled to meet the requirements of
## the survey.
}
\keyword{univar}% at least one, from doc/KEYWORDS
\keyword{univar}% __ONLY ONE__ keyword per line
|
