These utilities were developed as additional tools to help in the evaluation of the validity and precision of different pooling strategies for fixed pool sizes. Three different options are provided depending on assumptions about test sensitivity and specificity. The three options are:

- assuming both sensitivity and specificity are perfect (100%);
- assuming sensitivity and/or specificity are less than 100% but are known exactly; and
- assuming that sensitivity and/or specificity are uncertain.

These programs each use two separate pairs of values for sensitivity and specificity. The first pair of values are the values used in estimating true prevalence from the simulated testing results (for the perfect test option estimated sensitivity and specificity are both assumed to be 100% and cannot be entered in the input screen). The second pair of values ('True test sensitivity/specificity') are used to determine the actual results of testing during simulation. By specifying different values for the true test sensitivity (specificity) and estimated sensitivity (specificity) it is possible to evaluate the importance of potential errors in the assumed values used. For example, if prevalence is estimated assuming that the test is perfect (both sensitivity and specificity are 100%) but in fact the true sensitivity is say 80%, the true prevalence would be substantially underestimated, resulting in a biased estimate. This model allows estimation of the magnitude of this bias.

All three methods simulate sampling and prevalence estimation for up to 6 different pooling strategies for assumed values of prevalence and test sensitivity and specificity and for a specified level of confidence, assuming that a fixed pool size is used. The program runs multiple iterations of sampling and estimation and calculates the mean prevalence, confidence interval width and estimated bias across all iterations. By simulating alternative pooling strategies this utility allows the various strategies to be evaluated and compared to determine the optimum strategy that will give the desired level of precision in the prevalence estimate and also minimise the level of bias in the estimate.

For each pooling strategy, the program simulates sampling, pooling and testing of individuals from an infinite population with the specified prevalence, using a test of the specified true sensitivity and specificity. Sampling and testing is repeated for the specified number of iterations for each strategy and the prevalence, confidence interval width and variance are estimated for each iteration using the selected method and assumed values for sensitivity and specificity. The mean prevalence, bias, confidence interval width and variance are calculated across all iterations for each strategy, where mean bias is the mean prevalence estimate less the true (design) prevalence for the population. Mean square error (mean variance plus square of mean bias) is also calculated, and the magnitude of the mean bias is also calculated as proportions of the mean estimated prevalence, the true (design) prevalence and the mean square error.

Outputs for each method are summarised across all iterations for each strategy entered and presented in a summary
table. The main outputs are:

- mean prevalence;
- minimum and maximum prevalence estimates;
- mean bias in the estimated mean prevalence;
- mean confidence interval width;
- mean standard error of the estimated prevalence;
- mean squared error of the estimated prevalence (mean variance plus the square of the mean bias);
- relative bias as a proportion of the mean estimated (apparent) prevalence (AP);
- relative bias as a proportion of the specified design (true) prevalence (TP);
- squared mean bias as a proportion of the mean squared error;
- the proportion of 'valid' estimates, where the confidence interval for the estimated prevalence contains the true (design) prevalence.
- detailed results for all iterations for each strategy (download as a text file by clicking on the appropriate icon in the summary results table; and
- histogram of the distribution of prevalence estimates (view or download by clicking on the appropriate icon in the summary results table.

For fixed pool sizes and perfect tests or tests of known sensitivity and specificity, exact binomial confidence limits are used. For fixed pool sizes and tests of uncertain sensitivity and specificity, asymptotic confidence limits are used. For fixed pool sizes and tests of known sensitivity and specificity, the width of the simulated (exact) confidence intervals may be substantially wider than the corresponding asymptotic confidence intervals. Therefore, sample sizes calculated using asymptotic methods for known sensitivity and specificity may be inadequate to give the desired precision if exact confidence limits are calculated, and may need to be increased if the desired precision is to be achieved.

It is important to enter pool sizes and associated numbers of pools tested from the top of the table. You must enter at least one row of valid values, and any rows entered must be complete. All values must be positive integers. Any row in the input table that includes an invalid value will be ignored, as will any subsequent rows.

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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

HerdPlus: Calculate SeH and SpH for a single herd

HerdPlus: SeH and SpH comparison for varying herd sizes

HerdPlus: SeH and SpH for listed herd sizes and optimised sample sizes

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

Home

Likelihood ratios and probability of infection in a tested individual

Mantel-Haenszel chi-square test for stratified 2 by 2 tables

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

Paired t-test or Wilcoxon signed rank test on numeric data

Pooled Prevalence

Pooled Prevalence Calculator - Demonstration analyses

Pooled Prevalence Calculator - Demonstration analyses - 1

Pooled Prevalence Calculator - Demonstration analyses - 2

Pooled Prevalence Calculator - Demonstration analyses - 3

Pooled Prevalence Calculator - Demonstration analyses - 4

Pooled Prevalence Calculator - Demonstration analyses - 5

Pooled Prevalence Calculator - Demonstration analyses - 6

Pooled Prevalence Calculator - Demonstration analyses - 7

Pooled Prevalence Calculator - Demonstration analyses - 8

Pooled Prevalence Calculator - Demonstration analyses - 9

Pooled Prevalence Calculator - Demonstration analyses - 10

Pooled Prevalence Calculator - Demonstration analyses - 11

Pooled Prevalence Calculator - Demonstration analyses - 12

Pooled Prevalence Calculator - Demonstration analyses - 13

Pooled Prevalence Calculator - Demonstration analyses - 14

Pooled Prevalence Calculator - Demonstration analyses - 15

Pooled Prevalence Calculator - Demonstration analyses - 16

Pooled Prevalence Calculator - Demonstration analyses - 17

Pooled prevalence for fixed pool size and perfect tests

Pooled prevalence for fixed pool size and tests with known sensitivity and specificity

Pooled prevalence for fixed pool size and tests with uncertain sensitivity and specificity

Pooled prevalence for variable pool size and perfect tests

Pooled prevalence using a Gibbs sampler

Population (or cluster) sensitivity for varying unit sensitivity

Population level (or herd, flock, cluster, or other grouping) sensitivity

Population or cluster level sensitivity using pooled sampling

Positive and Negative Predictive Values for a test

Probability of infection in a test-negative sample

Random Geographic Coordinates Sampling

Random Number Sampling

Random sampling from a sampling frame

Random sampling from populations

Random sampling of animals

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

Sample size to detect a significant difference between 2 means with unequal sample sizes and variances

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

Simulate sampling for fixed pool size and assumed perfect test

Simulate sampling for fixed pool size and uncertain test sensitivity and specificity

Simulate sampling for variable pool sizes

Simulated true prevalence estimates from survey testing with an imperfect test

Statistical analysis of numeric data

Stochastic analysis of 2-stage freedom survey data

Summarise Beta probability distributions for specified alpha and beta parameters

Summarise Binomial probability distributions for specified sample size and probability

Summarise categorical or continuous data

Summarise continuous data (ungrouped)

Summarise continuous data by single grouping variable

Summarise measures of association from a 2x2 table

Summarise Pert probability distributions for specified minimum, mode and maximum values

Summarise probability distributions

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!