Accuracy

Alpha and Beta parameters

Asymptotic confidence limits

Bayesian method

Beta distribution

Bias

Bias/AP

Bias/TP

Bias/MSE

Binomial distribution

Confidence & Probability limits

Confidence level

Design Prevalence

Discard

Exact confidence limits

False negatives (FN)

Gibbs sampler

Herd-Sensitivity

Herd-Specificity

Alpha and Beta parameters

Asymptotic confidence limits

Bayesian method

Beta distribution

Bias

Bias/AP

Bias/TP

Bias/MSE

Binomial distribution

Confidence & Probability limits

Confidence level

Design Prevalence

Discard

Exact confidence limits

False negatives (FN)

Gibbs sampler

Herd-Sensitivity

Herd-Specificity

Iterations

Lower Confidence (Probability) limits

LR for negative (LRN)

LR for positive (LRP)

Maximum

Mean

Mean Prevalence

Minimum Prevalence

Maximum Prevalence

Mean Bias

Mean CI width

Mean Standard Error

Mean square error (MSE)

Median

Mode

Minimum

Negative predictive value (NPV)

Lower Confidence (Probability) limits

LR for negative (LRN)

LR for positive (LRP)

Maximum

Mean

Mean Prevalence

Minimum Prevalence

Maximum Prevalence

Mean Bias

Mean CI width

Mean Standard Error

Mean square error (MSE)

Median

Mode

Minimum

Negative predictive value (NPV)

Pooled prevalence

Pooled testing

Pool size

Positive predictive value (PPV)

Posterior probability distribution

Precision

Prevalence

Prior prevalence

Prior sensitivity

Prior specificity

Proportion valid

Random error

Repeatability

Sample size for Se and Sp estimation

Sensitivity (Se)

Specificity (Sp)

Standard deviation (SD)

Pooled testing

Pool size

Positive predictive value (PPV)

Posterior probability distribution

Precision

Prevalence

Prior prevalence

Prior sensitivity

Prior specificity

Proportion valid

Random error

Repeatability

Sample size for Se and Sp estimation

Sensitivity (Se)

Specificity (Sp)

Standard deviation (SD)

The degree to which a measurement, or an estimate based on measurements, represents the true value of the attribute that is being measured. (See also Precision and Validity which are the two components of "Accuracy")

Back to topTwo parameters used to define the Beta probability distribution. The mean value of the distribution can be calculated as alpha/(alpha+beta) and the mode is (alpha-1)/(alpha+beta-2).

Back to topConfidence limits calculated using large-sample theory and assuming a normal approximation of the sampling distribution. Asymptotic confidence limits are symmetrical and may be less than zero or greater than unity if the true proportion is close to these values.

Back to topA statistical method based on Bayes' theorem. Used to calculate the conditional probability of an event given assumed prior knowledge. Prior estimates of probability are updated based on new data. A common application of Bayesian methods is the calculation of the predictive value of a test based on assumed values for prevalence and test sensitivity and specificity and test result.

Back to topBeta distributions are a type of probability distribution that is commonly used to describe uncertainty about the true value of a proportion, such as sensitivity, specificity or prevalence. They are appropriate distributions to express uncertainty about the prior values for prevalence, sensitivity or specificity in the Gibbs sampler ( Joseph et al., 1995; Vose, 2000). When used for this purpose, the Beta distribution can be defined by the two parameters, alpha and beta (written as Beta(alpha, beta)), with alpha = x + 1 and beta = n - x + 1, where x is the number of positive events out of n trials. As n increases, the degree of uncertainty (the width of the distribution) about the estimated proportion (x/n) decreases.

Back to topAny effect at any stage of an investigation tending to produce results that depart systematically from the true values i.e. a systematic error. (See also Random Error)

Back to topThe binomial distribution - Binomial(n, p) - is a probability distribution of the number of successes that occur in *n* independent trials, where the probability of success at any trial is *p*, and the trials are independent (*p* remains constant). The mean of the distribution is *np*.

Confidence limits are the upper and lower end-points of an interval around a parameter estimate, such that if an experiment was repeated an infinite number of times, in the specified percentage (usually 95% or 99%) of trials the interval generated would contain the true value of the parameter. Confidence limits may be calculated using asymptotic (normal approximation) or exact methods.

Probabilty (or credibility) limits are the upper and lower end-points of the interval that has a specified probability (eg 95% or 99%) of containing the true value of a population parameter, such as a mean or proportion. Usually applied instead of confidence limits when Bayesian methods are used.

Back to topThe probability of accepting the null hypothesis when it is true - for example the probability that test results will detect disease when the true prevalence is greater than or equal to the specified design prevalence.

Back to topA fixed value for prevalence used for testing the null hypothesis that the population is infected at a prevalence equal to or greater than the design prevalence. If all samples tested are negative, the null hypothesis is rejected and the prevalence is assumed to be less than the design prevalence (or 0). Alternatively, the assumed value for the true prevalence used in simulating sampling for estimation of prevalence.

Back to topThis is the number of initial iterations from the Gibbs sampler that are discarded to allow for convergence of the model on the true value(s) for the parameter(s) of interest.

Back to topConfidence limits calculated using an appropriate probability distribution (usually the binomial distribution) to arrive at an exact value. Exact confidence limits are asymmetrical and cannot be less than zero or greater than unity.

Back to topThe number of individuals with the characteristic of interest (e.g. truly infected) that have a negative test result.

Back to topA Gibbs sampler is a Bayesian method which uses Markov Chain Monte Carlo simulation to derive posterior probability distributions that best fit given prior distributions and experimental data. The gibbs sampler is run for many thousand iterations to allow the posterior parameter estimates to converge on the true values.

Back to topThe probability that an infected herd will give a positive result to a particular testing protocol, given that it is infected at a prevalence equal to or greater than the design prevalence.

The probability that an uninfected herd will give a negative result to a particular testing protocol.

The total number of times the Gibbs sampler model is repeated to generate probability distributions for the parameter(s) of interest. For simulations to estimate bias, it is the number of model runs (simulations) used to estimate the mean prevalence and bias.

Back to topThe lower limit of the specified confidence or probability interval.

Back to topThe odds of a negative test result in diseased vs disease free individuals and can be calculated as (1-Sensitivity)/Specificity.

Back to topThe odds of a positive test result in diseased vs disease free individuals and can be calculated as Sensitivity/(1-Specificity).

Back to topThe maximum value of the posterior probability distribution for the parameter of interest.

Back to topThe arithmetic mean value of the posterior probability distribution for the parameter of interest.

Back to topThe arithmetic mean of the estimated prevalence across all iterations for each strategy.

Back to topThe minimum value of the estimated prevalence across all iterations for each strategy.

Back to topThe maximum value of the estimated prevalence across all iterations for each strategy.

Back to topThe arithmetic mean of the difference between the estimated prevalence and the assumed (design) prevalence across all iterations for each strategy (or the difference between the mean prevalence and the assumed (design) prevalence.

Back to topThe arithmetic mean of the difference between the upper and lower confidence limits across all iterations for each strategy. 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.

Back to topThe arithmetic mean of the standard errors of the prevalence estimates across all iterations for each strategy. *Mean standard error is not available for variable pool size simulations*.

The mean variance (the mean of the squares of the standard errors) plus the square of the mean bias. *Mean square error is not available for variable pool size simulations*.

Bias as a proportion of the apparent prevalence = The mean bias divided by the mean (apparent) prevalence.

Back to topBias as a proportion of the true prevalence = The mean bias divided by the assumed (design) true prevalence.

Back to topBias as a proportion of the mean square error = The square of the mean bias divided by the mean square error. *Bias/MSE is not available for variable pool size simulations*.

The mid-point value of the posterior probability distribution for the parameter of interest, which is the value where 50% of values are higher and 50% are lower.

Back to topThe maximum value of the posterior probability distribution for the parameter of interest.

Back to topThe probability that a test-negative individual is truly free of infection.

Back to topThe proportion of individuals that have the characteristic of interest (e.g. infected or diseased), estimated from the testing of pooled samples.

Back to topTesting undertaken on aggregated (pooled) samples, where each sample tested is representative of a number of individuals.

Back to topThe number of individuals represented in each pool subjected to pooled testing.

Back to topThe probability that a test-positive individual is truly infected.

Back to topA probability distribution generated by the Gibbs sampler for the parameter of interest (prevalence, sensitivity, specificity, etc). This is derived as the relative frequency distribution of values for the parameter of interest generated from multiple iterations of the model, after discarding a specified number of iterations to allow for convergence of the model.

Back to topThe inverse of the variance of a parameter estimate - a measure of the repeatability or consistency of the estimate. The quality of being sharply defined or stated, ie. lack of random error. Refers to the ability of a test or measuring device to give consistent results when applied repeatedly. See also validity. A good test is both precise and valid which are the two components of accuracy.

Back to topThe proportion of individuals that have the characteristic of interest (e.g. infected or diseased).

Back to topThe assumed prevalence of infection before taking into account any additional data that may be available for analysis. Prior prevalence is expressed as a Beta probability distribution for Bayesian analyses and can be estimated from pre-existing data or based on expert opinion using the estimated mode and 5% or 95% probability limit. The alpha and beta parameters for the distribution can be calculated using the *Beta distribution utility* provided.

The assumed sensitivity of the screening test used before taking into account any additional data that may be available for analysis. Prior sensitivity is expressed as a Beta probability distribution for Bayesian analyses and can be estimated from pre-existing data or based on expert opinion using the estimated mode and 5% or 95% probability limit. The alpha and beta parameters for the distribution can be calculated using the *Beta distribution utility* provided.

The assumed specificity of the screening test used before taking into account any additional data that may be available for analysis. Prior specificity is expressed as a Beta probability distribution for Bayesian analyses and can be estimated from pre-existing data or based on expert opinion using the estimated mode and 5% or 95% probability limit. The alpha and beta parameters for the distribution can be calculated using the *Beta distribution utility* provided.

The proportion of iterations in which the confidence interval for the estimated prevalence contains the true (design) prevalence value.

Back to topThe ability of a test to give consistent results in repeated tests. See also precision .

Back to topThe number of individuals used in previous trials to estimate the sensitivity or specificity of the test being used. The larger the sample size the more precise the estimate and hence the less uncertainty in the resulting estimates of sensitivity, specificity and prevalence.

Back to topThe estimated sensitivity (synonym: True Positive Rate) of a diagnostic test is the estimated (or assumed) proportion of animals with the disease (or infection) of interest which test positive. It is a measure of the probability that a diseased individual will be correctly identified by the test. Sometimes called "population sensitivity" to distinguish from "analytical sensitivity".

For pooled testing, sensitivity is estimated at the pool level, so that in this context, sensitivity is the probability that a pool which includes samples from one or more infected individuals will test positive. Pool-level sensitivity is therefore affected by both prevalence and pool size. The higher the prevalence, the more infected individuals that will be represented in individual pools and the more likely a pool is to test positive and therefore the higher the sensitivity. This is in contrast to individual-level sensitivity, which is independent of prevalence. Conversely, the larger the pool size, the greater the dilution of any positive individual samples, potentially reducing sensitivity.

Back to topThe estimated specificity (synonym: True Negative Rate) of a diagnostic test is the estimated (or assumed) proportion of animals without the disease (or infection) of interest which test negative. It is a measure of the probability that an individual without the disease of interest will be correctly identified by the test. Sometimes called "population specificity" to distinguish from "analytical specificity".

For pooled testing, specificity is estimated at the pool level, so that in this context, specificity is the probability that a pool which does not include samples from any infected individuals will test positive (false positive). Pool-level specificity can therefore be affected by pool size, due to both a possible increase in the number of false-positive individuals in the pool as pool size increases and the effect of dilution on whether these false-positive individuals are also positive in the pooled test.

Back to topThe true sensitivity is the actual proportion of animals without the disease (or infection) of interest which test negative. If the estimated sensitivity differs from the true sensitivity then the resulting prevalence estimates will be biased to a degree depending on the amount of error in the estimate.

Back to topThe true specificity is the actual proportion of animals with the disease (or infection) of interest which test positive. If the estimated specificity differs from the true specificity then the resulting prevalence estimates will be biased to a degree depending on the amount of error in the estimate.

Back to topA standard measure of the variation that exists in a series of values or of a frequency distribution. Calculated as the positive square root of the variance.

Back to topThe standard deviation of a parameter estimate. Commonly used to calculate asymptotic confidence limits.

Back to topThe interpretation of multiple tests where an animal is considered positive if it reacts positively to either or both (or any) of the tests - this increases sensitivity at the expense of specificity.

Back to topThe interpretation of multiple tests where an animal must be positive on both (or all if more than 2) tests to be considered positive - this increases specificity at the expense of sensitivity.

Back to topThe number of alternative pooling strategies evaluated (using simulation) to estimate the precision and bias of the estimated prevalence for each option.

Back to topThe number of individuals with the characteristic of interest (e.g. truly infected) that have a positive test result.

Back to topThe upper limit of the specified confidence or probability interval.

Back to topA standard measure of the variation that exists in a series of values or of a frequency distribution. Estimated as the sum of the squares of the deviations from the mean value for the variable divided by the number of degrees of freedom (*n*-1).

The extent to which a study or test measures what it sets out to measure ie. lack of systematic error or bias. See also precision. A good test is both precise and valid which are the two components of accuracy.

Back to topThe true number of animals with the characteristic of interest (infection or disease) in each of the cells (a=++, b=+-, c=-+, d=--, respectively) of the 2-by-2 table describing the comparison of test results for two tests used concurrently on a sample from the population. Used in the Bayesian estimation of prevalence using two tests - starting values for each cell are required inputs and probability distributions for the true values are produced as outputs from the model.

Back to topThe number of individuals positive to both tests when two tests are applied concurrently to a sample of individuals from a population, as shown by *a* in the table below.

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Test 1: |
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-ve: | c |
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The number of individuals positive to Test 1 and negative to Test 2 when two tests are applied concurrently to a sample of individuals from a population, as shown by *b* in the table below.

Test 2: |
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Test 1: |
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+ve: | a |
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-ve: | c |
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The number of individuals negative to Test 1 and positive to Test 2 when two tests are applied concurrently to a sample of individuals from a population, as shown by *c* in the table below.

Test 2: |
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Test 1: |
+ve | -ve |

+ve: | a |
b |

-ve: | c |
d |

The number of individuals negative to both tests when two tests are applied concurrently to a sample of individuals from a population, as shown by *d* in the table below.

Test 2: |
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Test 1: |
+ve | -ve |

+ve: | a |
b |

-ve: | c |
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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!