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14 - Sample size for fixed pool size and uncertain test sensitivity and specificity

This program calculates the approximate numbers of pools required for a range of pool sizes and specified values for estimated prevalence and desired confidence and precision of the estimate, assuming fixed pool sizes and a test with unknown (uncertain) sensitivity and specificity. Uncertainty associated with the point estimates of test sensitivity and specificity is incorporated through the inclusion of additional variance associated with the sample size used to determine the values used for these parameters. The smaller the sample size, the greater the uncertainty about the true values for sensitivity and/or specificity and hence the greater the uncertainty about the resulting prevalence estimate, resulting in an increased overall sample size to provide the same level of confidence in the estimate. These calculations are based on a re-arrangement of the formulae use to estimate asymptotic confidence limits for pooled prevalence estimates with unknown test sensitivity and specificity (Method 4).

The required number of pools (m) to estimate the true prevalence with the desired precision is calculated as:

where:

  • p = assumed true prevalence;
  • k = pool size;
  • Se = test sensitivity;
  • Sp = test specificity;
  • n1 = the sample size for estimating the sensitivity of the test;
  • n2 = the sample size for estimating the specificity of the test;
  • e = the acceptable error (desired precision); and
  • Z = the standardised normal variate corresponding to the desired level of confidence.



and:

Prevalence estimates calculated from pooled testing may be upwardly biased, particularly as the probability of all pools testing positive increases (high prevalence and/or small numbers of large pools). Therefore, it is advisable to select a lower value for pool size and test a larger number of smaller pools to minimise potential bias in the result, particularly if prevalence is likely to be high. Unlike the situation with a perfect test, it is not possible to determine an optimum pool size to minimise the variance of the estimate if test sensitivity and specificity are uncertain.

Required inputs for this analysis are:

  • the assumed true prevalence;
  • assumed test sensitivity;
  • assumed test specificity;
  • sample size for estimating the sensitivity of the test;
  • sample size for estimating the specificity of the test;
  • the desired level of precision (or acceptable error); and
  • the desired level of confidence in the result.

For example, you might wish to estimate the prevalence where the true value is assumed to be about 0.01 (1%), and you wish to have 95% (0.95) confidence that the true value is within +/- 0.005 (0.5%) of your estimate, with a test that has a sensitivity of 0.9 (90%) and specificity of 0.99 (99%) and where sensitivity and specificity were estimated using sample sizes of 100 and 1000 respectively. The assumed prevalence, desired precision and level of confidence must all be >0 and <1. Test sensitivity and specificity must both be >0 and <=1. Sample sizes for estimating sensitivity and specificity must be positive integers. The larger the sample size the lower the uncertainty and hence the greater the confidence achieved in the estimate.

You can also input a suggested pool size if desired, and the program will calculate the corresponding number of pools to be tested for that pool size (in addition to predetermined pool sizes). Suggested pool size is ignored if it is zero.

Output from the analysis is:

  • the number of pools required for the input-scenario and the suggested pool size;
  • a table of the numbers of pools (and total number of samples) required for the input-scenario for various pool sizes ranging from 1 to 500; and
  • a graph of number of pools vs pool size.


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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
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Design prevalence required to achieve target population (cluster or system) sensitivity
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Estimate 95% confidence limits for a median
Estimate alpha and beta Parameters for Beta distributions from count data
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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
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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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Pooled Prevalence Calculator - Demonstration analyses
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Pooled Prevalence Calculator - Demonstration analyses - 11
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Pooled Prevalence Calculator - Demonstration analyses - 13
Pooled Prevalence Calculator - Demonstration analyses - 14
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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
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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
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
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Summarise measures of association from a 2x2 table
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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!