FUNCTION to compute the optimal sample size.

Description

Computes the optimal sample size for a survey to substantiate freedom from disease. The optimal sample size is the smallest sample size that produces an alpha-error less than or equal to a prediscribed value alpha. The population is considered as diseased if at least one individual has a positive test result. The sample size is computed using a bisection method. The function either computes the sample size for a fixed population (lookupTable == FALSE) or a lookup table with sampling sizes depending on the population size for individual sampling (lookupTable == TRUE); see Ziller et al., 2002.

Usage

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computeOptimalSampleSize(nPopulation, prevalence, alpha = 0.05, 
    sensitivity = 1, specificity = 1, lookupTable = FALSE)

Arguments

nPopulation

Integer. Population size if lookupTable == FALSE or the largest considered herd size for the lookup table if lookupTable == TRUE .

prevalence

Numeric between 0 and 1. Design prvalence. The number of diseased is then computed as max(1,nPopulation*prevalence).

alpha

Numeric between 0 and 1. Alpha-Error (=error of the first kind, significance level) of the underlying significance test. Default value = 0.05.

sensitivity

Numeric between 0 and 1. Sensitivity of the diagnostic (for one-stage sampling) or herd test (for two stage sampling). Default value = 1.

specificity

Numeric between 0 and 1. Specificity of the diagnostic (for one-stage sampling) or herd test (for two stage sampling). Default value = 1.

lookupTable

Logical. TRUE if a lookup table of sample sizes for individual sampling (see, Ziller et al., 2002) should be produced. FALSE if the sample size is desired for a fixed population size (default).

Value

The return value is either an integer, the minimal sample size that produces the desired alpha-error if lookupTable == FALSE or a matrix with columns N_lower, N_upper, sampleSize containing the sample sizes for the different herd sizes N.

E.g., N_lower = 17, N_upper = 21, sampleSize = 11 means that for holdings with 17-21 animals 11 animals need to be tested in order to achieve the desired accuracy (=herd sensitivity).

Author(s)

Ian Kopacka <ian.kopacka@ages.at>

References

A.R. Cameron and F.C. Baldock, "A new probablility formula to substantiate freedom from disease", Prev. Vet. Med. 34 (1998), pp. 1-17.

M. Ziller, T. Selhorst, J. Teuffert, M. Kramer and H. Schlueter, "Analysis of sampling strategies to substantiate freedom from disease in large areas", Prev. Vet. Med. 52 (2002), pp. 333-343.

See Also

computePValue

Examples

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## Compute the number of herds to be tested for limited sampling
## with sampleSizeLtd = 7:
#################################################################
data(sheepData)
## Compute the average herd sensitivity:
alphaList <- computeAlphaLimitedSampling(stockSizeVector = 
    sheepData$nSheep, sampleSizeLtd = 7, 
    intraHerdPrevalence = 0.13, diagSensitivity = 0.9, 
    diagSpecificity = 1)
sensHerd <- 1 - alphaList$meanAlpha
## Number of herds to be tested:
nHerds <- computeOptimalSampleSize(nPopulation = dim(sheepData)[1], 
    prevalence = 0.002, alpha = 0.05, sensitivity = sensHerd, 
    specificity = 1)

## Compute the number of animals to be tested for individual 
## sampling:
#################################################################
sampleSizeIndividual <- computeOptimalSampleSize(nPopulation = 300, 
    prevalence = 0.2, alpha = 0.05, sensitivity = 0.97, 
    specificity = 1, lookupTable = TRUE)