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15 - Simulate sampling for fixed pool size

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:

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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Contents
1 Introduction
2 Overview
3 Bayesian vs Frequentist methods
4 Fixed pool size and perfect tests
5 Fixed pool size and known Se & Sp
6 Fixed pool size and uncertain Se & Sp
7 Variable pool size and perfect tests
8 Pooled prevalence using a Gibbs sampler
9 True prevalence using one test
10 Estimated true prevalence using two tests with a Gibbs sampler
11 Estimation of parameters for prior Beta distributions
12 Sample size for fixed pool size and perfect test
13 Sample size for fixed pool size and known test sensitivity and specificity
14 Sample size for fixed pool size and uncertain test sensitivity and specificity
15 Simulate sampling for fixed pool size
16 Simulate sampling for variable pool sizes
17 Important Assumptions
18 Pooled prevalence estimates are biased!

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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
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!