rsu.sssep.rsfreecalc: Sample size to achieve a desired surveillance system sensitivity to detect disease at a specified design prevalence assuming representative sampling, imperfect unit sensitivity and specificity

Description

Calculates the sample size to achieve a desired surveillance system sensitivity to detect disease at a specified design prevalence assuming representative sampling, imperfect unit sensitivity and specificity .

Usage

rsu.sssep.rsfreecalc(N, pstar, mse.p, msp.p, se.u, sp.u, method = "hypergeometric", 
   max.ss = 32000)

Value

A list comprised of two data frames: summary and details. Data frame summary lists:

n: the minimum number of individuals to be sampled.
N: the total number of individuals eligible to be sampled.
c: the cut-point number of positives to achieve the specified surveillance system (population-level) sensitivity and specificity.
pstar: the design prevalence.
p1: the probability that the population has the outcome of interest at the specified design prevalence.
se.p: the calculated population level sensitivity.
sp.p: the calculated population level specificity.

Data frame details lists:

n: the minimum number of individuals to be sampled.
se.p: the calculated population level sensitivity.
sp.p: the calculated population level specificity.

Arguments

N: scalar, integer representing the total number of subjects eligible to be sampled.
pstar: scalar, numeric, representing the design prevalence, the hypothetical outcome prevalence to be detected. See details, below.
mse.p: scalar, numeric (0 to 1) representing the desired population level sensitivity. See details, below.
msp.p: scalar, numeric (0 to 1) representing the desired population level specificity. See details, below.
se.u: scalar (0 to 1) representing the sensitivity of the diagnostic test at the surveillance unit level.
sp.u: scalar, numeric (0 to 1) representing the specificity of the diagnostic test at the surveillance unit level.
method: a character string indicating the calculation method to use. Options are binomial or hypergeometric.
max.ss: scalar, integer defining the maximum upper limit for required sample size.

Details

Type I error is the probabilty of rejecting the null hypothesis when in reality it is true. In disease freedom studies this is the situation where you declare a population as disease negative when, in fact, it is actually disease positive. Type I error equals 1 - SeP.

Type II error is the probabilty of accepting the null hypothesis when in reality it is false. In disease freedom studies this is the situation where you declare a population as disease positive when, in fact, it is actually disease negative. Type II error equals 1 - SpP.

Argument pstar can be expressed as either a proportion or integer. Where the input value for pstar is between 0 and 1 the function interprets pstar as a prevalence. Where the input value for pstar is an integer greater than 1 the function interprets pstar as the number of outcome-positive individuals in the population of individuals at risk. A value for design prevalence is then calculated as pstar / N.

References

Cameron A, Baldock C (1998a). A new probability formula for surveys to substantiate freedom from disease. Preventive Veterinary Medicine 34: 1 - 17.

Cameron A, Baldock C (1998b). Two-stage sampling in surveys to substantiate freedom from disease. Preventive Veterinary Medicine 34: 19 - 30.

Cameron A (1999). Survey Toolbox for Livestock Diseases --- A practical manual and software package for active surveillance of livestock diseases in developing countries. Australian Centre for International Agricultural Research, Canberra, Australia.

Examples

Run this code

## EXAMPLE 1:
## A cross-sectional study is to be carried out to confirm the absence of 
## brucellosis in dairy herds using a bulk milk tank test assuming a design 
## prevalence of 0.05. Assume the total number of dairy herds in your study 
## area is 5000 and the bulk milk tank test to be used has a diagnostic 
## sensitivity of 0.95 and a specificity of 1.00. How many herds need to be 
## sampled to be 95% certain that the prevalence of brucellosis in dairy herds 
## is less than the design prevalence if less than a specified number of 
## tests return a positive result?

rsu.sssep.rsfreecalc(N = 5000, pstar = 0.05, mse.p = 0.95, msp.p = 0.95, 
   se.u = 0.95, sp.u = 0.98, method = "hypergeometric", max.ss = 32000)$summary

## A system sensitivity of 95% is achieved with a total sample size of 194 
## herds, assuming a cut-point of 7 or more positive herds are required to 
## return a positive survey result.

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