computePValueRiskGroups {FFD}

FUNCTION to compute the probability of finding no testpositives in a sample of a certain size for a population stratified into risk groups.

Description

For a population that is stratified into risk groups the function computes the probability of finding no testpositives in a sample of given size using an imperfect diagnostic test. For each of the risk groups the population size nPopulationVec, the sample size nSampleVec and the relative infection risk nRelRiskVec must be specified. The discussed probability corresponds to the alpha-error (=error of the first kind) of the overall test with null hypothesis: prevalence = design prevalence.

Usage

computePValueRiskGroups(nPopulationVec, nSampleVec, 
    nRelRiskVec, nDiseased, sensitivity, 
    specificity = 1)

Arguments

nPopulationVec

Integer vector. Population sizes of the risk groups.

nSampleVec

Integer vector. Sample sizes of the risk groups.

nRelRiskVec

Numeric vector. (Relative) infection risks of the risk groups.

nDiseased

Integer. Number of diseased elements in the population according to the design prevalence.

sensitivity

Numeric between 0 and 1. Sensitivity (= probability of a testpositive result, given the tested individual is diseased) of the test (e.g., diagnostic test or herd test).

specificity

Numeric between 0 and 1. Specificity (= probability of a testnegative result, given the tested individual is not diseased) of the test (e.g., diagnostic test or herd test). The default value is 1.

Value

The return value is a numeric between 0 and 1. It is the probability of finding no testpositives (not diseased!) in the sample.

Author(s)

Ian Kopacka <[e-mail]>

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.

P.A.J.Martin, A.R. Cameron, M. Greiner, "Demonstrating freedom from disease using multiple complex data sources. : A new methodology based on scenario trees", Prev. Vet. Med. 79 (2007), pp. 71 - 97.

See Also

Calls computePValue

Examples

nPopulationVec <- c(500,700)
nSampleVec <- c(300,200)
nRelRiskVec <- c(1,1)
nDiseased <- round(sum(nPopulationVec)*0.01)
sensitivity <- 0.9
specificity <- 1
alphaError <- computePValue(sum(nPopulationVec), sum(nSampleVec),
	nDiseased, sensitivity, specificity)