epi.sssimpleestb {epiR} R Documentation

## 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 = 1E+06, Py, epsilon, error = "relative",
se, sp, nfractional = FALSE, conf.level = 0.95)
```

### Arguments

 `N` scalar integer, the total number of individual listing units in the population. `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.

### 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.

n.crude <- epi.sssimpleestb(N = 1E+06, Py = 0.15, epsilon = 0.20,
error = "relative", se = 1.00, sp = 1.00, nfractional = FALSE,
conf.level = 0.95)
n.crude

## 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:

n.crude <- epi.sssimpleestb(N = 1E+06, Py = 0.15, epsilon = 0.03,
error = "absolute", se = 0.94, sp = 0.88, nfractional = FALSE,
conf.level = 0.95)
n.crude

## A total of 545 cattle need to be sampled to meet the requirements of the
## survey.

## EXAMPLE 1 (continued):
## The OIE 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 = 1E+06, 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