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2-Stage surveys for demonstration of freedom

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.

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1-sample t-test for summary data
1-sample z-test for a population proportion
1-Stage Freedom analysis
2-sample t-test for summary data
2-sample z-test to compare sample proportion
2-Stage surveys for demonstration of freedom
Analyse test repeatability
Analyse two-stage prevalence data
Analysis of 2-stage freedom survey data
Analysis of simple 2-stage freedom survey
Bioequivalence analysis - two-period, two-treatment crossover trial
Calculate Cluster-level sensitivity and specificity for range of sample sizes and cut-points for given cluster size and imperfect tests
Calculate confidence limits for a sample proportion
Calculate sample sizes for 2-stage freedom survey where individual cluster details are available
Calculate sample sizes for 2-stage freedom survey where individual cluster details are NOT available
Calculate sample sizes for 2-stage freedom survey with fixed cluster-level sensitivity
Calculate test Sensitivity and Specificity and ROC curves
Capture-Recapture analysis
Chi-squared test for contingency table from original data
Chi-squared test for homogeneity of a sample
Chi-squared test for r x c contingency table
Chi-squared test for trend
Cluster-level sensitivity and specificity with variable cut-points
Compare prevalence values
Compare two tests
Complex 2-stage risk-based surveillance - calculation of surveillance sample size
Complex 2-stage risk-based surveillance - calculation of surveillance sensitivity
Complex 2-stage risk-based surveillance - calculation of surveillance sensitivity based on herd testing data
Complex risk-based surveillance - calculation of surveillance sample size
Complex risk-based surveillance - calculation of surveillance sensitivity
Confidence of population freedom (NPV) for a surveillance system
Confidence of population freedom for multiple time periods
Contact
Design prevalence required to achieve target population (cluster or system) sensitivity
Diagnostic test evaluation and comparison
Estimate 95% confidence limits for a median
Estimate alpha and beta Parameters for Beta distributions from count data
Estimate confidence limits for a mean
Estimate parameters for multiple Beta probability distributions or summarise distributions for specified parameters
Estimated true prevalence and predictive values from survey testing
Estimated true prevalence using one test with a Gibbs sampler
Estimated true prevalence using two tests with a Gibbs sampler
Estimating prevalence
Estimation of alpha and beta parameters for prior Beta distributions
"EUFMD - Demonstration of FMD freedom": 2-stage risk-based surveillance with 1 herd-level risk factor, 1 animal-level risk factor and multiple surveillance components
FreeCalc: Analyse results of freedom testing
FreeCalc: Calculate sample size for freedom testing with imperfect tests
Get P and critical values for the Chi-squared distribution
Get P and critical values for the F distribution
Get P and critical values for the normal distribution
Get P and critical values for the t distribution
Glossary
HerdPlus utilities
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HerdPlus: SeH and SpH comparison for varying herd sizes
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HerdPlus: SeH and SpH for optimised sample sizes for range of herd sizes
HerdPlus: SeH and SpH for range of sample sizes and cut-points for given herd size
HerdPlus: SeH and SpH for varying sample sizes
HerdPlus: SeH for fixed sample size and cut-point
HerdPlus: SeH for optimised sampling strategy
HerdPlus: SeH for varying design prevalence
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Likelihood ratios and probability of infection in a tested individual
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Pooled Prevalence
Pooled Prevalence Calculator - Demonstration analyses
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Pooled prevalence for fixed pool size and tests with known sensitivity and specificity
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Pooled prevalence using a Gibbs sampler
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Population or cluster level sensitivity using pooled sampling
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References
Risk-based surveillance
Sample size calculation for fixed pool size and perfect tests
Sample size calculation for fixed pool size and uncertain sensitivity and specificity
Sample size calculations
Sample size for a case-control study
Sample size for a cohort study
Sample size for demonstration of freedom (detection of disease) using pooled testing
Sample Size for survival analysis to compare median times since last outbreak
Sample size required to achieve target confidence of freedom
Sample size to achieve specified population level (or herd, flock, cluster, etc) sensitivity
Sample size to detect a significant difference between 2 means with equal sample sizes and variances
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Sample size to detect a significant difference between 2 proportions
Sample size to estimate a proportion or apparent prevalence with specified precision
Sample size to estimate a single mean with specified precision
Sample size to estimate a true prevalence with an imperfect test
Sample size to estimate a true prevalence with an imperfect test
Simple 2-stage risk-based surveillance - calculation of sample size
Simple 2-stage risk-based surveillance - calculation of surveillance sensitivity
Simple 2-stage risk-based surveillance - calculation of surveillance sensitivity based on herd testing data
Simple risk-based surveillance - calculation of minimum detectable prevalence
Simple risk-based surveillance - calculation of sample size
Simple risk-based surveillance - calculation of surveillance sensitivity
Simple risk-based surveillance with differential sensitivity - calculation of sample size with two sensitivity groups
Simple risk-based surveillance with differential sensitivity - calculation of surveillance sensitivity
Simulate sampling for fixed pool size and assumed known test sensitivity and specificity
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Simulate sampling for fixed pool size and uncertain test sensitivity and specificity
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Simulated true prevalence estimates from survey testing with an imperfect test
Statistical analysis of numeric data
Stochastic analysis of 2-stage freedom survey data
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Summarise Binomial probability distributions for specified sample size and probability
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Survey Toolbox for livestock diseases
Survival analysis of herd incidence data
Test evaluation against a gold standard
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!