# rsu.sssep.rsfreecalc: Sample size to achieve a desired surveillance system... In epiR: Tools for the Analysis of Epidemiological Data

## 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

 ```1 2``` ```rsu.sssep.rsfreecalc(N, pstar, mse.p, msp.p, se.u, sp.u, method = "hypergeometric", max.ss = 32000) ```

## 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`.

## 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.

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```## 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. ```

epiR documentation built on Oct. 11, 2021, 9:08 a.m.