# Sample size for demonstration of freedom (detection of disease) using pooled testing

This utility calculates the number of pools required to be tested to provide a desired probability of detecting disease (cluster-sensitivity) at the specified
design prevalence, for a **large (infinite)**
population, using pooled testing and assuming a fixed pool size and a test of known sensitivity and 100% specificity. These analyses are an
adaptation of the method from Christensen and Gardner (2000). (Prev Vet Med, **45**:83-106), assuming known test sensitivity,
perfect test specificity and 1 or more pools positive to declare a population infected (i.e. to be recognised as free there must be zero positive pools).

Inputs are the pool size used, pool-level test sensitivity, desired cluster-sensitivity and design (target) prevalence (as a proportion). Test sensitivity is measured at the pool level (i.e. the probability that a pool will test positively if it represents one or more infected units).

Outputs are:

- - the number of pools of the specified size that must be tested to achieve the desired cluster-sensitivity for the given design prevalence;
- - a table and graph of various pool sizes and corresponding numbers of pools that must be tested to provide the desired cluster-sensitivity for a range of design prevalence values, assuming the same test sensitivity applies to all pool sizes.