epi.sssimpleestb {epiR}

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

N

scalar integer, the total number of individuals eligible for inclusion in the study. If N = NA the number of individuals eligible for inclusion is assumed to be infinite.

Py

scalar number, an estimate of the population proportion to be estimated.

epsilon

scalar number, the maximum difference between the estimate and the unknown population value expressed in absolute or relative terms.

error

character string. Options are absolute for absolute error and relative for relative error.

se

the diagnostic sensitivity of the method used to detect positive outcomes (0 - 1).

sp

the diagnostic specificity of the method used to detect positive outcomes (0 - 1).

nfractional

logical, return fractional sample size.

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 N is provided.

Value

Returns an integer defining the required sample size.

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 epsilon.r equals the relative error the sample estimate should not differ in absolute value from the true unknown population parameter d by more than epsilon.r * d.

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.

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.