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11 - Simulate sampling for fixed pool size and assumed perfect test

This program simulates sampling and prevalence estimation for a specified (design) prevalence value and level of confidence. The program runs multiple iterations of sampling, pooling and testing from an infinite population with the specified prevalence, estimates true prevalence assuming a prefect test (using Method 2) for each iteration and calculates the mean prevalence and estimated bias across all iterations. It assumes fixed pool sizes and a test with 100% sensitivity and specificity. Values for the true sensitivity and specificity that are different to the assumed values of 100% can also be entered if desired, to check the importance of the assumption of a perfect test.

For this analysis, six alternative pooling strategies were evaluated for the estimation of prevalence in a population with an assumed true prevalence of 0.14 (14%). Pool sizes and numbers of pools were previously estimated to provide 95% confidence of estimating a true prevalence of 0.14 with a precision of 0.055 (see sample size examples). This is equivalent to the observed prevalence and precision when 162 samples from little red flying foxes in Queensland were tested individually, with 22 positive results (H. Field, pers com). The true sensitivity and specificity of the test were both assumed to be 1 (100%), equal to the assumed values for prevalence estimation. Input values, pooling strategies and results are summarised in the tables below.

Input Value
Method Fixed pool size and known Se and Sp
Assumed Prevalence 0.14
Assumed Sensitivity 1
Assumed Specificity 1
True Sensitivity 1
True Specificity 1
Confidence 0.95
Number of strategies 6
Number of iterations 1000
Strategy Pool size Number of pools
1 2 83
2 3 60
3 4 49
4 5 42
5 10 33
6 20 46
Strategy Mean prevalence Minimum prevalence Maximum prevalence Mean bias Mean CI width Mean standard error Mean square error Bias/AP Bias/TP Bias/MSE Proportion valid
1 0.14101 0.06862 0.23165 0.00101 0.11593 0.02794 0.00079 0.00719 0.00724 0.0013 0.968
2 0.14017 0.06528 0.22434 0.00017 0.1161 0.02787 0.00079 0.00124 0.00124 4e-05 0.96
3 0.14037 0.06782 0.25617 0.00037 0.11666 0.02789 0.00079 0.0026 0.00261 0.00017 0.967
4 0.14123 0.06508 0.23506 0.00123 0.11878 0.02826 0.00081 0.00872 0.0088 0.00187 0.965
5 0.14534 0.06983 1 0.00534 0.12772 0.02923 0.00092 0.03671 0.03811 0.03097 0.972
6 0.23773 0.08374 1 0.09773 0.22332 0.02911 0.01046 0.41109 0.69804 0.91322 0.974

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Contents
1 Fixed pool size and perfect tests
2 Fixed pool size and tests with known sensitivity and specificity
3 Fixed pool size and tests with uncertain sensitivity and specificity
4 Variable pool size and perfect test
5 Pooled prevalence using a Gibbs sampler
6 Estimated true prevalence using one test (unpooled) with a Gibbs sampler
7 Estimated true prevalence using two tests (unpooled) with a Gibbs sampler
8 Sample size calculation for fixed pool size and perfect tests
9 Sample size calculation for fixed pool size and tests with known sensitivity and specificity
10 Sample size calculation for fixed pool size and tests with uncertain sensitivity and specificity
11 Simulate sampling for fixed pool size and assumed perfect test
12 Simulate sampling for fixed pool size and test with known sensitivity and specificity
13 Simulate sampling for fixed pool size and test with uncertain sensitivity and specificity
14 Simulate sampling for variable pool size and assumed perfect test
15 Demonstration of freedom using pooled testing with tests of known sensitivity and fixed pool size
16 Estimation of alpha and beta Parameters for Prior Beta distributions
17 Estimation of Beta probability distributions for specified alpha and beta parameters

Search
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!