# Sample Size Calculations for Veterinary Surveys


## Key Takeaways

- Sample size calculations for veterinary surveys are critically dependent on the specific objective: estimating prevalence requires precision-based formulas (e.g., n = Z² × p(1-p) / d²), while substantiating freedom from disease necessitates a detection-based framework to demonstrate prevalence is below a threshold with high confidence.
- Diagnostic test performance (sensitivity and specificity) is a crucial input; imperfect tests necessitate sample size inflation or post-collection adjustment to account for apparent versus true prevalence, with Bayesian approaches offering a robust method to incorporate test uncertainty.
- Cluster sampling, common in veterinary surveys (e.g., sampling animals within herds), requires accounting for the "design effect" to inflate sample size, as within-cluster similarity reduces the effective sample size compared to simple random sampling.
- Finite population corrections are essential when sampling a significant proportion (e.g., >10%) of a small, closed population (e.g., a regional stud or research colony) to avoid overestimating the required sample size.
- Risk-based sampling strategies can optimize resource allocation in repeated surveys by prioritizing sampling in strata with higher perceived risk of infection, potentially reducing overall sample size and cost while maintaining surveillance efficacy.
- Stochastic modeling offers a more advanced approach for complex survey designs, allowing simulation of population structure, sampling schemes, and test performance to provide a realistic assessment of survey outcomes, particularly for national or regional freedom claims.

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Veterinary surveys are used to estimate disease prevalence, substantiate freedom from infection, and support trade certification. Each of these objectives demands a defensible sample size, yet the calculation is often treated as a mechanical step instead of a design decision. This article provides a practical guide to sample size calculations for veterinary surveys, covering simple random sampling, finite population corrections, two-stage cluster designs, and risk-based approaches. It is written for veterinary researchers, epidemiologists, and graduate students who need to plan surveys that will withstand peer review and regulatory scrutiny.

The central question is straightforward: how many animals, herds, or clusters must be sampled so that the survey result answers the research question with acceptable precision and confidence? The answer depends on the survey objective, the expected prevalence, the diagnostic test performance, the population structure, and the acceptable error. This article explains the statistical logic behind each of these inputs, provides worked decision frameworks, and identifies common failure modes. Clinical trial sample size and diagnostic test evaluation are excluded, the focus is exclusively on observational surveys of animal populations.

## At a Glance

| Parameter | Definition | Typical Source or Default |
|---|---|---|
| Expected prevalence | Anticipated proportion of positive animals or herds | Prior surveys, expert opinion, literature |
| Desired precision | Half-width of the confidence interval around the prevalence estimate | 5% for common diseases, 2% for rare conditions |
| Confidence level | Probability that the true value lies within the stated interval | 95% (z = 1.96) |
| Design effect | Inflation factor for cluster sampling relative to simple random sampling | 2 to 5 for livestock herds, estimated from intracluster correlation |
| Population size | Total number of eligible animals or herds | Census data, movement records, holding registries |
| Test sensitivity and specificity | Probability of correct classification of truly positive and truly negative subjects | Assay validation studies, manufacturer data |
| Threshold prevalence | Maximum acceptable prevalence for disease freedom claims | WOAH standards or national policy |
| Power | Probability of detecting prevalence above the threshold when it exists | 80% or 90% |

## The Statistical Foundation of Survey Sample Size

### The Precision-Based Formula for Prevalence Estimation

For a simple random sample from a large population, the required sample size for estimating a proportion is derived from the normal approximation to the binomial distribution. The formula is n = Z² × p(1 - p) / d², where Z is the standard normal deviate for the chosen confidence level, p is the expected prevalence, and d is the desired absolute precision. The variance term p(1 - p) reaches its maximum at p = 0.5, which is why surveys targeting unknown prevalence often use 50% as a conservative planning value. This approach is described in standard epidemiologic teaching materials such as the [CDC principles of epidemiology in public health practice](https://www.cdc.gov/csels/dsepd/ss1978/index.html).

When the population is finite, the sample size can be reduced using the finite population correction. The corrected sample size is n_adj = n / (1 + (n - 1) / N), where N is the population size. The correction becomes negligible when N is large relative to n, but it matters for small herds, closed flocks, or regional populations of limited size. For example, sampling 50 of 100 herds requires a smaller sample than sampling 50 of 10,000 herds to achieve the same precision.

### The Freedom-from-Disease Framework

Surveys designed to substantiate freedom from infection use a different logic. The objective is not to estimate prevalence but to demonstrate that prevalence is below a specified threshold. The null hypothesis is that prevalence exceeds the threshold, and the survey seeks to reject this hypothesis with high confidence. The required sample size depends on the threshold prevalence, the desired confidence level, and the diagnostic test performance. When the test is imperfect, the effective sensitivity of the survey is reduced, and sample sizes must increase accordingly. Bayesian approaches that incorporate prior distributions for test sensitivity and specificity have been developed specifically for this purpose, allowing the calculation to account for uncertainty in test performance [Johnson et al., sample size calculations for surveys to substantiate freedom of populations from infectious agents](https://pubmed.ncbi.nlm.nih.gov/15032786/).

The same Bayesian framework extends to hierarchical designs where clusters such as herds or villages are sampled first and animals within clusters are sampled second. In this setting, the sample size is a combination of the number of clusters and the number of subjects per cluster, and the calculation must account for variability in prevalence among infected clusters [Branscum et al., sample size calculations for disease freedom and prevalence estimation surveys](https://pubmed.ncbi.nlm.nih.gov/16287201/). A region may contain many herds with zero prevalence and a smaller number of heavily infected herds, the survey design must be able to detect this pattern instead of assuming uniform prevalence.

## Diagnostic Test Performance as a Design Input

### Sensitivity, Specificity, and Apparent Prevalence

The sample size calculation for a prevalence survey should be based on the true prevalence, not the apparent prevalence produced by the diagnostic test. If the test has imperfect sensitivity or specificity, the number of positive results observed will be biased, and the precision of the estimate will be degraded. The relationship between true prevalence, test performance, and apparent prevalence is p_apparent = p × Se + (1 - p) × (1 - Sp), where Se is sensitivity and Sp is specificity. When planning a survey, the researcher must decide whether to inflate the sample size to compensate for imperfect test performance or to adjust the analysis after data collection. The former is safer, because the latter can produce confidence intervals that are too narrow if the adjustment is not applied correctly.

### Herd-Level versus Animal-Level Testing

Many veterinary surveys test animals but make inferences about herds or regions. The herd is the epidemiological unit of interest, and the sampling scheme must reflect this. Herd-level sensitivity depends on the number of animals tested per herd, the within-herd prevalence, and the animal-level test sensitivity. A stochastic modeling approach can be used to evaluate the properties of alternative herd-level sampling schemes before the survey is conducted, allowing the planner to compare the expected evidence generated by different combinations of herds sampled and animals per herd [Audigé et al., stochastic modeling as a tool for planning animal-health surveys and interpreting screening-test results](https://pubmed.ncbi.nlm.nih.gov/11267684/). This is particularly valuable when the survey is intended to support a claim of freedom from infection at a national or regional level, because the consequences of a false freedom claim are severe.

## Population Structure and Sampling Frames

### Defining the Eligible Population

The sampling frame must match the target population. For livestock, the frame is often derived from holding registries, movement records, or census data. The quality of the frame determines the representativeness of the sample, and errors in the frame produce selection bias that no sample size calculation can correct. Methods for classifying holdings from movement data, including rule-based epidemiological approaches and machine learning cluster analysis, have been developed to improve the accuracy of sampling frames for livestock populations [Smith et al., determining pig holding type from British movement data](https://pubmed.ncbi.nlm.nih.gov/32302777/). A survey that draws its sample from an incomplete or inaccurate frame will produce estimates that do not generalize to the intended population, regardless of how carefully the sample size was computed.

### Cluster Sampling and the Design Effect

When animals are sampled in groups, the effective sample size is smaller than the number of animals sampled because animals within a cluster are more similar to each other than to animals in other clusters. The design effect is the ratio of the variance under cluster sampling to the variance under simple random sampling, and it must be estimated before the survey is planned. A common approach is to use a design effect of 2 for infectious diseases with moderate clustering and higher values for diseases with strong herd-level aggregation. The required sample size under cluster sampling is the simple random sample size multiplied by the design effect. This inflation can be substantial, and it is a frequent source of underpowered surveys when ignored.

## Choosing a Sampling Strategy in Practice

The choice between simple random sampling and a more complex design depends on the population structure, the survey objective, and the resources available. For a prevalence survey in a homogeneous population with a complete sampling frame, simple random sampling is adequate. When animals are grouped into herds, flocks, or flocks, cluster sampling becomes necessary, and the design effect must be incorporated into the sample size calculation.

The design effect is the ratio of the variance of the estimate under the actual sampling design to the variance under simple random sampling of the same number of individuals. A design effect of 2 means that twice as many animals are needed to achieve the same precision as simple random sampling. Typical design effects for veterinary surveys range from 1.5 to 4, depending on the degree of clustering of the infection and the herd size distribution. If no prior data exist, a design effect of 2 is a conservative starting point for many production animal pathogens.

The number of clusters and the number of animals per cluster are not interchangeable. Increasing the number of clusters reduces the design effect more efficiently than increasing the number of animals per cluster, because the between-cluster variance dominates the total variance for most infectious agents. A common error is to sample many animals from few herds, which yields precise estimates within herds but poor precision at the population level.

## Sample Size Formulas and Worked Examples

The table below summarizes the standard formulas for the two main survey objectives. These formulas assume binomial sampling, which is appropriate when the population is large relative to the sample size. For finite populations where the sample exceeds roughly 10% of the population, a finite population correction should be applied.

| Objective | Formula | Parameters | Typical Use |
|-----------|---------|------------|-------------|
| Prevalence estimation | n = Z² × p(1-p) / d² | Z = confidence level Z-value, p = expected prevalence, d = desired absolute precision | Estimating the proportion of herds or animals infected |
| Disease detection (freedom) | n = [1 - (1 - α)^(1/N)] × [N - (N-1) × (1 - p)] | α = desired confidence, N = population size, p = minimum detectable prevalence | Demonstrating freedom from infection with a specified confidence |

For prevalence estimation, the formula n = Z² × p(1-p) / d² gives the required sample size. For example, to estimate a prevalence of 20% with 5% absolute precision at the 95% confidence level, Z = 1.96, p = 0.2, and d = 0.05. The calculation is n = (1.96)² × 0.2 × 0.8 / (0.05)² = 245.8, rounded up to 246 animals.

When the expected prevalence is unknown, use p = 0.5, which maximizes the product p(1-p) and therefore the sample size. This is the most conservative choice and is appropriate when no prior information exists. For rare diseases with expected prevalence below 5%, the precision-based formula becomes unstable and the detection-based approach is preferred.

For disease detection, the formula accounts for the probability of selecting at least one positive animal when the prevalence is at or above the threshold. With a population of 1,000 animals, a desired confidence of 95%, and a minimum detectable prevalence of 1%, the calculation is n = [1 - (1 - 0.95)^(1/1000)] × [1000 - 999 × 0.99] = 299 animals. This means that if 299 animals are tested and all are negative, the surveyor can be 95% confident that the true prevalence is below 1%.

Software packages such as R, Epitools, and WinBUGS implement these formulas directly. The Bayesian approaches described by Johnson and colleagues provide user-friendly programs for sample size calculation and analysis of survey data, available through the University of California Davis diagnostic test evaluation website. These programs allow specification of prior distributions for test sensitivity and specificity, which is essential when imperfect tests are used.

## Risk-Based Sampling for Repeated Surveys

When a region conducts surveillance repeatedly over time, the sample size for each new survey can be reduced by incorporating information from previous surveys. The risk-based approach assigns different sampling probabilities to different strata based on their perceived risk of infection. High-risk groups, such as herds with recent animal movements or those in high-density areas, are sampled more intensively than low-risk groups.

Schwermer and colleagues demonstrated that risk-based sample size calculations can reduce the sample size and costs for repeated surveys by one-third compared to traditional random sampling. The method requires calculating the loss of confidence due to disease import between surveys and the time value of historical testing information. The order of surveys matters, and a separate process must incorporate the time value of information from all conducted surveys.

This approach is particularly relevant for documenting freedom from non-highly contagious diseases in support of international trade. The [WOAH terrestrial animal health standards](https://www.woah.org/en/what-we-do/standards/codes-and-manuals/terrestrial-code-online-access/) require that disease freedom be documented through statistically valid surveillance, and risk-based sampling provides a cost-effective means of meeting this requirement while maintaining confidence levels.

## Stochastic Modeling for Complex Survey Designs

For large national or regional surveys, deterministic formulas may be insufficient because they cannot capture the full complexity of the sampling process. Stochastic simulation models allow the survey planner to model the population structure, the sampling scheme, and the diagnostic test performance simultaneously.

Audigé and colleagues developed a stochastic simulation model for planning animal-health surveys and interpreting screening-test results in the context of substantiating freedom from infection at a national or regional level. The model uses a Bayesian approach to derive the post-survey probability of freedom from infection from the pre-survey probability of freedom and the likelihood ratio associated with screening-test results. Applied to two consecutive surveys for infectious bovine rhinotracheitis in Switzerland, the model showed that the survey of 1999 provided less evidence than that of 1998 to support a status of freedom from infection, despite similar herd-level sampling schemes.

The key advantage of stochastic modeling is the ability to evaluate alternative sampling strategies before committing resources. The planner can simulate different combinations of herds sampled and animals per herd, different test protocols, and different assumptions about within-herd prevalence, then compare the resulting probabilities of freedom. This approach is computationally intensive but provides a more realistic assessment of survey performance than a single formula.

## Species-Specific Considerations

The correct sampling strategy varies by species and production system. In dairy cattle, the sampling frame is typically the herd register, and within-herd sampling often targets specific age groups because prevalence varies by age. In poultry, the flock is the natural sampling unit, and pooled samples such as boot swabs or dust samples are commonly used, which changes the interpretation of test results. In wildlife, the sampling frame is rarely complete, and convenience sampling from harvested or captured animals may be the only feasible option, which introduces selection bias that must be acknowledged in the interpretation.

The [CDC principles of epidemiology](https://www.cdc.gov/csels/dsepd/ss1978/index.html) emphasize that the validity of any survey depends on the representativeness of the sample. In production animal systems, the availability of movement data can improve the accuracy of the sampling frame. Smith and colleagues demonstrated that British pig movement data could be used to identify the location of pig holdings and estimate herd size, which in turn allows more accurate sample size calculations for prevalence or freedom from disease. When movement data are available, they should be used to construct the sampling frame instead of relying on outdated registers.

For companion animal surveys, the sampling frame is often the clinic population, which is not representative of the general pet population. This limitation should be stated explicitly in the survey report, and the sample size calculation should account for the expected degree of selection bias. In all cases, the survey protocol should document the sampling frame, the sampling method, the sample size calculation, and the assumptions made about test performance and population structure.

## Common Errors and Their Correction

The most frequent error in veterinary survey planning is applying a precision-based formula intended for prevalence estimation to a freedom-from-disease objective. The two frameworks answer different questions. A prevalence survey asks how precisely an unknown proportion is estimated. A freedom survey asks whether the true prevalence exceeds a specified threshold with acceptable confidence. Confusing the two produces sample sizes that are either wasteful or insufficient. Before any calculation, state the survey objective in writing and select the corresponding formula family.

A second recurring error is ignoring the finite population correction when the sampling fraction exceeds roughly 5 percent of the eligible population. In large national herds the correction is negligible, but in small closed populations, such as a regional stud or a single research colony, omitting it inflates the sample size unnecessarily. The correction factor is (N - n) / (N - 1), applied to the variance term.

A third error concerns diagnostic test performance. Designers frequently assume perfect sensitivity and specificity, then interpret the observed test-positive proportion as true prevalence. This assumption is rarely defensible. The [CDC principles of epidemiology](https://www.cdc.gov/csels/dsepd/ss1978/index.html) emphasize that screening test results must be interpreted in light of test accuracy and disease likelihood. When tests are imperfect, the sample size must be inflated and the analysis should estimate true prevalence from apparent prevalence using known or prior distributions for sensitivity and specificity. Bayesian approaches that incorporate test accuracy uncertainty are described in the [sample size framework of Branscum, Johnson, and Gardner](https://pubmed.ncbi.nlm.nih.gov/16287201/).

A fourth error is treating clusters as if they were independent individuals. Analyzing cluster-sampled data with formulas for simple random sampling understates the variance and produces confidence intervals that are too narrow. The design effect must be estimated from prior work or pilot data and applied at the planning stage.

## Recognized Failure Modes

| Observation | Likely cause | Discriminating check |
|---|---|---|
| Calculated sample size exceeds the entire eligible population | Finite population correction omitted or wrong prevalence assumption | Recalculate with the correction, verify the assumed prevalence against regional data |
| Survey declares freedom but a subsequent outbreak occurs | Threshold prevalence set too high, or test sensitivity overestimated | Review the design prevalence against [WOAH surveillance standards](https://www.woah.org/en/what-we-do/animal-health-and-welfare/disease-data-collection/), audit test performance assumptions |
| Confidence intervals from the completed survey are wider than planned | Design effect underestimated or clustering ignored | Compare observed versus assumed variance, check intracluster correlation |
| Sample size changes drastically between consecutive surveys | Risk-based methods applied without accounting for time since last survey | Apply the consecutive-survey adjustment described by [Schwermer and colleagues](https://pubmed.ncbi.nlm.nih.gov/19762100/) |
| Post-survey probability of freedom is lower than expected despite adequate sample size | Prior probability of freedom was set too high | Re-examine the prior, consider stochastic simulation as outlined by [Audigé and co-authors](https://pubmed.ncbi.nlm.nih.gov/11267684/) |

Early detection of these failures requires a pilot analysis. Run the planned calculation with pessimistic and optimiztic inputs for prevalence, test accuracy, and design effect. If the sample size varies by more than a factor of two across plausible inputs, the survey design is fragile and the inputs need refinement before data collection begins.

## Limitations of Current Evidence

The evidence base for veterinary survey sample size is strongest for simple random sampling and for freedom-from-disease surveys in production animal populations. Several gaps remain. First, methods for estimating cluster-level prevalence when clusters vary in size and when some clusters have zero prevalence are relatively recent and require specialised software. Second, risk-based approaches for consecutive surveys depend on assumptions about disease introduction risk and the time value of historical testing information, assumptions that are difficult to validate in most settings. Third, guidance for companion animal and wildlife populations is less developed than for livestock, partly because sampling frames are harder to construct.

Expert opinion still differs on the choice between frequentist and Bayesian frameworks. Frequentist methods are simpler to explain and audit. Bayesian methods accommodate prior information and test uncertainty more naturally, and they produce direct probability statements about freedom status. The [Bayesian approach of Johnson and colleagues](https://pubmed.ncbi.nlm.nih.gov/15032786/) for disease freedom surveys illustrates the additional flexibility but also the additional computational burden. For regulatory submissions, confirm which framework the receiving authority expects before finalising the design.

## When to Seek Specialist Input

Referral to a veterinary epidemiologist or biostatistician is warranted when the survey involves multiple stages of sampling, when diagnostic test performance is uncertain and materially affects the result, when the population structure is poorly characterized, or when the survey outcome will support an official health status claim. Laboratory input is needed early when test sensitivity and specificity must be estimated locally instead of taken from the literature. Regulatory reporting obligations apply when survey results inform notifiable disease status or international trade documentation, the [WOAH terrestrial animal health code](https://www.woah.org/en/what-we-do/standards/codes-and-manuals/terrestrial-code-online-access/) specifies the surveillance evidence required for such claims. Engaging these specialists at the design stage is more efficient than correcting an underpowered survey after data collection has begun.

## Frequently Asked Questions

### How do I adjust my sample size when the budget only allows testing fewer animals than the formula requires?

Reduce the target precision or confidence level instead of silently accepting a smaller sample. For prevalence surveys, widening the confidence interval from 5% to 7.5% can cut the required sample size by roughly one third. For freedom surveys, lowering the design prevalence or accepting a lower confidence level changes the interpretation of a negative result. Document any deviation from the calculated sample size in the study report, because the confidence attached to a negative finding is directly tied to the number of animals tested. If resources are fixed, consider pooling samples or using risk-based approaches that concentrate testing in higher-risk subpopulations, as described in [risk-based sample size methods for consecutive surveys](https://pubmed.ncbi.nlm.nih.gov/19762100/).

### What sample size do I need when the diagnostic test is imperfect?

Imperfect tests inflate the required sample size because apparent prevalence differs from true prevalence. When sensitivity and specificity are below 100%, the number of test-positive animals expected under a given true prevalence changes, and the survey must be sized to detect that shifted signal. Bayesian approaches allow prior distributions for sensitivity and specificity to be incorporated directly into sample size calculations, as developed in [sample size methods for disease freedom and prevalence estimation surveys](https://pubmed.ncbi.nlm.nih.gov/16287201/). If the test has low sensitivity, more animals are needed to achieve the same confidence of detecting infection. If specificity is imperfect, false positives become a concern in low-prevalence populations, and confirmatory testing protocols should be planned alongside the sample size calculation.

### How does the sample size change if I am surveying a wildlife population instead of a domestic herd?

Wildlife surveys introduce two complications: the population size is often unknown, and the sampling frame is incomplete. When the population size is uncertain, use the infinite population formula, which is conservative and does not require a finite population correction. Cluster sampling is frequently necessary because animals are encountered in groups, and the design effect can be substantial when within-group prevalence is heterogeneous. The [stochastic modeling approach for planning animal-health surveys](https://pubmed.ncbi.nlm.nih.gov/11267684/) is particularly useful here, as it can accommodate variable detection probabilities and imperfect sampling frames. Consider whether the target is a free-ranging population or a managed collection, because the latter may permit individual identification and a more reliable sampling frame.

### What records should I keep to document that my sample size calculation was appropriate?

Retain the formula or software used, all input values, and the version of the population estimate that informed the calculation. Record the source of the prevalence or design prevalence assumption, the test sensitivity and specificity values, and the confidence level and precision targets. Note any departures from the original plan, including the number of animals actually sampled, refusals, and animals that could not be tested. This documentation supports the interpretation of negative results and is essential when survey findings are used to substantiate disease freedom for trade purposes. The [WOAH animal health surveillance standards](https://www.woah.org/en/what-we-do/animal-health-and-welfare/disease-data-collection/) describe the reporting expectations for surveillance activities that support official health status claims.

### How do I explain the sample size to a producer or practice owner who wants a smaller survey?

Frame the sample size as the price of a reliable answer. A survey that is too small will not detect infection even when it is present, and a negative result from an undersized survey provides false reassurance. Explain that the confidence level and design prevalence are choices, not fixed constants, and that lowering either one reduces the sample size but also weakens the conclusion. Use a concrete example: detecting a 5% prevalence with 95% confidence requires far more animals than detecting a 20% prevalence with 90% confidence. The [CDC principles of epidemiology](https://www.cdc.gov/csels/dsepd/ss1978/index.html) provide a useful framework for explaining how sample size relates to the precision of an estimate in plain terms.

### When should I use a Bayesian approach instead of a frequentist sample size calculation?

Use a Bayesian approach when prior information is available and trustworthy, such as historical surveillance data, expert opinion on likely prevalence, or published test performance estimates. Bayesian methods are particularly valuable for freedom surveys, where the posterior probability of freedom can be updated across repeated surveys, and for cluster-level prevalence estimation where variability between herds or regions is expected. The [Bayesian sample size framework for disease freedom surveys](https://pubmed.ncbi.nlm.nih.gov/15032786/) explicitly incorporates prior distributions for test sensitivity and specificity and can accommodate finite population sampling. If no defensible prior information exists, a frequentist calculation with conservative assumptions is simpler and less open to criticism. Bayesian approaches also require specialised software and statistical expertise, so consider whether the added complexity is justified by the study objectives.

## Related Clinical & Scientific Guides

* [Evaluating Veterinary Surveillance System Attributes](/knowledge/veterinary-medicine/veterinary-epidemiology/evaluating-veterinary-surveillance-system-attributes)
* [Network Analysis for Infectious Disease Spread in Animal Populations](/knowledge/veterinary-medicine/veterinary-epidemiology/network-analysis-infectious-disease-spread-animal-populations)
* [Randomized Controlled Trials in Veterinary Field Settings](/knowledge/veterinary-medicine/veterinary-epidemiology/randomized-controlled-trials-veterinary-field-settings)


## References and Further Reading

- [Sample size calculations for surveys to substantiate freedom of populations from infectious agents.](https://pubmed.ncbi.nlm.nih.gov/15032786/). 2004.
- [Sample size determination for semiparametric analysis of current status data.](https://pubmed.ncbi.nlm.nih.gov/29488447/). 2019.
- [Sample size calculations for disease freedom and prevalence estimation surveys.](https://pubmed.ncbi.nlm.nih.gov/16287201/). 2006.
- [Risk-based sample size calculation for consecutive surveys to document freedom from animal diseases.](https://pubmed.ncbi.nlm.nih.gov/19762100/). 2009.
- [Stochastic modeling as a tool for planning animal-health surveys and interpreting screening-test results.](https://pubmed.ncbi.nlm.nih.gov/11267684/). 2001.
- [Determining pig holding type from British movement data using analytical and machine learning approaches.](https://pubmed.ncbi.nlm.nih.gov/32302777/). 2020.
- [WOAH Animal Health Surveillance Standards](https://www.woah.org/en/what-we-do/animal-health-and-welfare/disease-data-collection/). WOAH.
- [CDC Principles of Epidemiology in Public Health Practice](https://www.cdc.gov/csels/dsepd/ss1978/index.html). CDC.
- [MSD Veterinary Manual, Professional Edition](https://www.msdvetmanual.com/). MSD Veterinary Manual.

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> This article is educational professional reference material for veterinary audiences. It is not a substitute for veterinary diagnosis, individual clinical judgment, current product labeling, or applicable regulatory requirements.