# Analysis of simple 2-stage freedom survey

Analyse data for a simple 2-stage survey for demonstrating disease freedom. This analysis calculates the overall system sensitivity for the survey and the resulting probability of population freedom from disease. It assumes that a random sample of clusters (or all clusters) has been selected for testing from the population and that a random sample of units has been tested within each selected cluster. It also assumes that the test system has a specificity of 100% (any positive results are further investigated to exclude false positives) and that no positive results were recorded. The analysis adjusts for imperfect sensitivity of the test used.

For this analysis, a fixed sample size per cluster is assumed. If sample size varies between clusters use the alternative option, which allows you to include individual cluster testing data.

The analysis calculates both cluster (the same for all clusters) assuming binomial sampling (large cluster size relative to sample size). System level sensitivity calculation depends on the available data:

- - where population size (number of clusters) is unknown or not specified the binomial calculation (sampling with replacement) is used; or
- - where population size (number of clusters) is specified the hypergeometric approximation (sampling without replacement) is used.

Design prevalence (specified level of disease to be detected) must be specified at both unit and cluster levels. Unit-level design prevalence must be specified as a proportion. Cluster-level design prevalence can be specified as either:

- - a proportion of the population infected; or
- - a specific (integer) number of clusters infected.

### Inputs

Inputs required include:

- - unit-level design prevalence (as a proportion);
- - cluster-level design prevalence as either a proportion or an integer number of clusters;
- - the number of clusters in the population (if known);
- - the number of clusters sampled;
- - the number of units sampled per cluster;
- - the estimated test sensitivity; and
- - the assumed prior probability that the population is free of disease.

### Outputs

Outputs from the analysis include:

- - The cluster-level sensitivity (SeH) for each cluster tested;
- - Overall system (population) sensitivity (probability of detecting disease if it was present at the specified unit and cluster-level design prevalences); and
- - Probability of freedom of the population from disease (at the specified unit and cluster-level design prevalences