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2-Stage surveys for demonstration of freedom

Calculate sample sizes for 2-stage freedom survey where individual cluster details are available


Paste cluster testing data in the space below. Data columns can be in any order but must include columns for cluster size (labeled "ClusterSize") and cluster id (labeled "ClusterID"). A header row specifying column names must also be included.

Download example data


Calculate least-cost sample sizes for 2-stage surveys for demonstrating disease freedom. This analysis calculates the number of clusters and the number of units within each cluster to be tested to provide a specified system sensitivity (probability of detecting disease) for the given unit and cluster-level design prevalences and test sensitivity. Calculations are based on actual cluster sizes provided (for the entire population) and a list of randomly selected clusters, along with the number of units to sample for each selected cluster is included in the outputs. Test specificity is assumed to be 100% (or follow-up testing of any positive will be undertaken to confirm or exclude disease).

Sample sizes are optimised to minimise overall cost for given cluster and unit-level testing costs. A maximum sample size per cluster can be specified, if desired and calculations can be specified to ensure either a fixed sample size per cluster or a fixed (minimum) cluster sensitivity.

Sample sizes are calculated using the hypergeometric probability approximation (assuming sampling without replacement).

Design prevalence (specified level of disease to be detected) must be specified at both unit and cluster levels. Design prevalence can be specified as either:

  • a proportion of the population infected; or
  • a specific (integer) number of clusters or units (within clusters) infected.

Inputs

Inputs required include:

  • unit-level design prevalence as either a proportion or an integer number of units;
  • cluster-level design prevalence as either a proportion or an integer number of clusters;
  • the estimated test sensitivity;
  • the relative cost of testing at both cluster and unit levels;
  • the target system sensitivity (SSe) which is the probability of detecting disease if it is present at the specified design prevalences;
  • an optional maximum sample size to be tested per cluster;
  • whether calculations are to be based on maintaining a fixed sample size per cluster or a fixed (minimum) cluster sensitivity (SeH);
  • sampling frame data for all clusters in the population, including cluster id (labelled "ClusterID") and cluster size (labelled "ClusterSize").

Note: Any clusters with a cluster size < 1 or where clusters size is missing are excluded from the calculations.

Outputs

Outputs from the analysis include:

  • A summary of the total numbers of clusters and units to be sampled, target number of units to test per selected cluster, mean SeH and achieved SSe;
  • A list of clusters randomly selected for testing, the number of units to be tested for each cluster and the corresponding SeH;
  • A graph of required numbers of clusters to test, SeH and relative costs for varying numbers of units tested per cluster; and
  • An excel spreadsheet of the summary results and cluster list.

If it is not possible to achieve the desired system sensitivity by testing all (or the specified maximum number of) units in all of the clusters, a message will be returned, along with a summary of the achieved mean SeH and SSe if all units were tested. In this case a list of all clusters, and the SeH achieved if all or the maximum number of units were tested.


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2-sample t-test for summary data
2-sample z-test to compare sample proportion
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Glossary
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HerdPlus: SeH and SpH comparison for varying herd sizes
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HerdPlus: SeH and SpH for varying sample sizes
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HerdPlus: SeH for varying design prevalence
Home
Likelihood ratios and probability of infection in a tested individual
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McNemar's chi-squared test for association of paired counts
Numbers of false positives to a test
One-sample test to compare sample mean or median to population estimate
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Pooled Prevalence
Pooled Prevalence Calculator - Demonstration analyses
Pooled Prevalence Calculator - Demonstration analyses - 1
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References
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Sample size calculation for fixed pool size and uncertain sensitivity and specificity
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User guide - Home
User guide 1 - Introduction
User guide 2 - Overview
User guide 3 - Bayesian vs frequentist methods
User guide 4 - Pooled prevalence for fixed pool size and perfect tests
User guide 5 - Pooled prevalence for fixed pool size and tests with known sensitivity and specificity
User guide 6 - Pooled prevalence for fixed pool size and tests with uncertain sensitivity and specificity
User guide 7 - Pooled prevalence for variable pool size and perfect tests
User guide 8 - Pooled prevalence using a Gibbs sampler
User guide 9 - Estimated true prevalence using one test with a Gibbs sampler
User guide 10 - Estimated true prevalence using two tests with a Gibbs sampler
User guide 11 - Estimation of alpha and beta parameters for prior Beta distributions and summarisation of Beta distributions for specified alpha and beta parameters
User guide 12 - Sample size for fixed pool size and perfect test
User guide 13 - Sample size for fixed pool size and known test sensitivity and specificity
User guide 14 - Sample size for fixed pool size and uncertain test sensitivity and specificity
User guide 15 - Simulate sampling for fixed pool size
User guide 16 - Simulate sampling for variable pool sizes
User guide 17 - Important Assumptions
User guide 18 - Pooled prevalence estimates are biased!