Measures of Association in Veterinary Epidemiology: Risk and Odds Ratios

By Dr. Zubair Khalid, DVM, MS, PhD · 2026-08-11

Key Takeaways

• The Risk Ratio (RR) quantifies the relative increase or decrease in disease incidence between exposed and unexposed animal groups, directly interpretable as "how many times more likely" disease is in the exposed group. It is calculated using cumulative incidence from cohort studies or randomized trials and is preferred for common outcomes due to its direct interpretation.
• The Odds Ratio (OR) compares the odds of exposure among diseased animals to the odds of exposure among non-diseased animals, or vice versa, and is the primary measure in case-control studies where incidence cannot be directly calculated. While it approximates the RR when the outcome is rare (incidence < 10%), it overestimates the RR for common outcomes, leading to potential misinterpretation of effect magnitude.
• Incidence Rate Ratios (IRR) are crucial for dynamic populations with varying follow-up times, such as in production animal systems with continuous entry and exit. They compare disease occurrence per unit of animal-time at risk, providing a more accurate measure of risk in these complex scenarios than cumulative incidence.
• Study design dictates the appropriate measure: case-control studies are limited to ORs, while cohort studies and randomized trials can yield both RR and OR. When both are calculable from cohort data, the RR is generally preferred for clear communication of relative risk, though ORs remain valuable for multivariable analyses using logistic regression.
• Misclassification of exposure or outcome, particularly with diagnostic tests lacking perfect sensitivity or specificity (e.g., ELISA for seroprevalence), can bias association measures. Non-differential misclassification biases towards the null, while differential misclassification can bias in either direction, necessitating careful validation of diagnostic criteria.
• Effect measure modification, where the strength of association differs across strata of a third variable (e.g., age at first exposure influencing BVDV persistence risk), requires reporting stratum-specific measures rather than a single pooled estimate to accurately reflect biological differences.

Veterinary researchers routinely quantify the strength of association between an exposure and a health outcome. The risk ratio and the odds ratio are the two most frequently reported measures for binary outcomes in observational and experimental studies of animal health. This article explains how each measure is calculated, when each is appropriate, and how to interpret the results in the context of veterinary study designs. It serves veterinary researchers, graduate students in epidemiology, and clinicians who appraise the literature to inform practice decisions.

The central question addressed is straightforward: does the occurrence of disease differ between exposed and unexposed animals, and by how much? Answering that question requires a measure that accounts for the underlying study design, the frequency of the outcome, and the structure of the data. Confusion between risk ratios and odds ratios produces misinterpreted findings, particularly when the outcome is common. This article provides the conceptual foundation and computational framework needed to select, calculate, and report these measures correctly.

At a Glance

Conceptual Foundations of Association Measures

Association measures compare disease occurrence between two groups defined by exposure status. The fundamental comparison is between the incidence of disease in exposed animals and the incidence in unexposed animals. Incidence itself can be expressed as cumulative incidence, the proportion of animals developing disease over a defined period, or as an incidence rate, the number of new cases per animal-time at risk. The choice between these expressions determines which association measure can be calculated and how it should be interpreted.

The risk ratio uses cumulative incidence. It answers the question: how many times more likely is disease in exposed animals compared with unexposed animals over the study period? The odds ratio answers a different question: what are the odds of exposure among diseased animals relative to the odds of exposure among nondiseased animals? In a case-control study, the odds ratio is the only valid measure of association because the study design fixes the number of cases and controls instead of following animals forward in time. The conceptual distinction matters because the two measures converge only under specific conditions, and applying the wrong interpretation leads to clinical misjudgment.

The Risk Ratio

Calculation from Cohort Data

The risk ratio is calculated from a cohort or randomized trial in which animals are followed forward from exposure status to disease outcome. The formula is:

RR = (a / (a + b)) / (c / (c + d))

where a is the number of exposed animals that develop disease, b is the number of exposed animals that remain disease-free, c is the number of unexposed animals that develop disease, and d is the number of unexposed animals that remain disease-free. The numerator is the cumulative incidence in the exposed group, and the denominator is the cumulative incidence in the unexposed group.

A risk ratio of 1.0 indicates no association. Values above 1.0 indicate increased risk among the exposed, and values below 1.0 indicate a protective effect. The confidence interval around the risk ratio communicates the precision of the estimate. When the confidence interval excludes 1.0, the association is statistically significant at the chosen alpha level. The width of the interval reflects sample size and the number of outcome events, not the magnitude of the point estimate itself.

Incidence Rate Ratios

When animals are followed for different lengths of time, cumulative incidence becomes misleading because it does not account for varying follow-up periods. The incidence rate ratio compares incidence rates expressed as cases per animal-time at risk. This measure is preferred in production animal studies where animals enter and leave the population at different times, such as dairy herds with rolling culling or feedlots with staggered placement dates. The incidence rate ratio retains the direct interpretation of relative risk while properly handling time at risk. Veterinary researchers should report which denominator was used, since cumulative incidence and incidence rates answer different questions about disease occurrence.

The Odds Ratio

Calculation from Case-Control Data

The odds ratio is calculated from the exposure distribution among cases and controls:

OR = (a × d) / (b × c)

where a is the number of cases exposed, b is the number of controls exposed, c is the number of cases unexposed, and d is the number of controls unexposed. The odds ratio can also be calculated from cohort data using the same formula, but its interpretation differs by design.

In a case-control study, the odds ratio estimates the odds of exposure among cases divided by the odds of exposure among controls. This is the only association measure available when the total number of diseased animals is fixed by design and incidence cannot be calculated. The odds ratio from a case-control study approximates the risk ratio when the disease is rare, conventionally defined as an incidence below 10 percent in the source population. When the outcome is common, the odds ratio overestimates the risk ratio, sometimes substantially. The magnitude of overestimation increases with both the baseline incidence and the strength of the association.

Odds Ratios from Cohort and Cross-Sectional Studies

Odds ratios are also produced by logistic regression, which makes them ubiquitous in the veterinary literature even when cohort data are available. Logistic regression accommodates multiple predictors, continuous exposures, and confounder adjustment, which explains its popularity. The resulting odds ratio, however, retains the same interpretive limitation: it is a ratio of odds, not a ratio of risks. Researchers reporting odds ratios from cohort data should state whether the outcome was rare enough for the odds ratio to approximate the risk ratio. When the outcome is common, the odds ratio will exaggerate the apparent association, and the risk ratio should be reported instead.

Choosing Between Risk and Odds Ratios

Outcome Frequency as the Deciding Factor

The rarity of the outcome determines whether the odds ratio can be interpreted as an approximation of relative risk. For outcomes with incidence below 10 percent, the odds ratio and risk ratio are numerically similar and the distinction is clinically unimportant. For outcomes with incidence above that threshold, the odds ratio diverges from the risk ratio and should not be described as relative risk. Common outcomes in veterinary medicine, such as mastitis in dairy herds, lameness in feedlot cattle, or respiratory disease in group-housed pigs, frequently exceed this threshold. Reporting an odds ratio as a risk ratio for these conditions misrepresents the magnitude of the association.

Study Design Constraints

The study design sometimes dictates the available measure. Case-control studies, which are efficient for rare diseases or diseases with long latent periods, can only produce odds ratios. Cohort studies and randomized trials can produce either measure. When both are available, the risk ratio is generally preferred for communication because its interpretation is direct and clinically meaningful. The odds ratio remains valuable in multivariable analysis, where logistic regression provides a flexible framework for confounder control that is not easily matched by alternative regression approaches.

Reporting Conventions

Veterinary journals increasingly require authors to report effect measures with confidence intervals and to specify the study design that generated them. The CDC principles of epidemiology in public health practice describe the standard framework for calculating and interpreting these measures across health research. Authors should state whether the reported measure is a risk ratio or an odds ratio, identify the denominator used for incidence calculations, and avoid describing odds ratios as relative risks unless the rare disease assumption is explicitly justified.

Applied Interpretation in Veterinary Studies

The Worked Example: Enzootic Pneumonia in Feedlot Calves

A prospective cohort study follows 1,200 recently arrived feedlot calves through a 60 day receiving period. At arrival, 400 calves are classified as high risk based on transport distance, auction market origin, and commingling. The remaining 800 are classified as low risk. During the observation period, 96 high risk calves and 64 low risk calves develop undifferentiated bovine respiratory disease requiring parenteral antimicrobial therapy.

The risk in the high risk group is 96 divided by 400, or 0.24. The risk in the low risk group is 64 divided by 800, or 0.08. The risk ratio is 0.24 divided by 0.08, which equals 3.0. High risk classification is associated with a threefold higher cumulative incidence of respiratory disease over the receiving period.

The odds of disease in the high risk group are 96 divided by 304, or 0.316. The odds in the low risk group are 64 divided by 736, or 0.087. The odds ratio is 0.316 divided by 0.087, which equals 3.63. Because the outcome is not rare, the odds ratio overstates the risk ratio by roughly 20 percent.

The 95 percent confidence interval for the risk ratio can be calculated on the log scale. The standard error of the log risk ratio is the square root of the sum of the reciprocals of the four cell counts. For this example, the standard error is approximately 0.145, producing a 95 percent confidence interval from 2.26 to 3.98. The interval excludes 1.0, so the association is statistically significant at the conventional alpha level.

If the same data were analyzed with a logistic regression model adjusting for arrival weight, body condition score, and serum haptoglobin concentration, the adjusted odds ratio would be reported. The unadjusted odds ratio of 3.63 serves as the baseline for comparison. The adjusted estimate would likely move toward the null if the covariates explain part of the association.

Comparing Risk and Odds Ratios in Practice

The choice between the two measures is not always under the analyst's control. A case-control study with incident case selection cannot produce a risk ratio because the total population at risk is unknown. The odds ratio is the only valid measure of association available from that design. A prospective cohort with complete follow-up can produce either measure, and the risk ratio is usually preferred for direct communication to producers and regulatory bodies.

Effect Measure Modification and Stratified Reporting

A single summary measure can mislead when the association differs across strata of a third variable. Consider a study of bovine viral diarrhea virus persistence and subsequent pneumonia risk in calves. The risk ratio may differ by age at first exposure, with younger calves showing a stronger association. Reporting only the pooled estimate obscures this difference.

Stratified analysis examines the risk ratio within each level of the potential modifier. If the stratum-specific estimates differ meaningfully, the pooled estimate is not an adequate summary. The correct response is to report stratum-specific risk ratios with their confidence intervals and to describe the modification explicitly. If the stratum-specific estimates are similar, the pooled estimate adjusted for the stratifying variable is appropriate.

The distinction between effect measure modification and confounding is central to this decision. Confounding produces a distorted pooled estimate that can be corrected by adjustment. Effect measure modification reflects a genuine biological difference in the magnitude of association across subgroups. The two can coexist, and the analytic approach must address both. Stratified tables and interaction terms in regression models serve complementary roles in this assessment.

Species and Production System Considerations

The correct measure and its interpretation depend on the production context. In dairy herds with year-round calving, the population at risk changes continuously. A risk ratio calculated over a fixed calendar period misclassifies animals that enter or leave the herd during the interval. An incidence rate ratio using animal-time at risk is more appropriate for such dynamic populations.

In swine production with all-in all-out batch flow, the cohort is well defined and the risk ratio is straightforward. The same disease investigated in a continuous-flow finishing barn requires careful definition of the follow-up period and handling of censoring. The choice of measure should follow the structure of the population, not the preference of the analyst.

Wildlife and free-ranging populations present additional challenges. The denominator for a risk calculation may be unknown, and case-control designs are often the only feasible approach. The odds ratio from such studies must be interpreted with attention to the case definition and the sampling frame. The WOAH animal health surveillance standards provide guidance on case definitions and data collection that directly affect the validity of these measures.

Companion animal practice frequently relies on hospital-based case-control studies. Referral bias can distort the exposure distribution in both cases and controls. The odds ratio remains valid as a measure of association, but its generalizability to the broader patient population depends on the referral patterns of the participating hospitals. The AVMA practice resources offer guidance on clinical data collection that supports sound epidemiologic analysis in practice settings.

Reporting Standards and Documentation

Published reports should state the measure used, the exact calculation method, and the confidence interval. A risk ratio without a defined follow-up period is uninterpretable. An odds ratio from a case-control study should specify how controls were selected and matched. The CDC principles of epidemiology describe standard reporting conventions that apply across species.

The distinction between statistical significance and clinical importance deserves explicit attention. A large study may produce a statistically significant risk ratio of 1.1 that has no practical impact on herd health decisions. A small study may produce a risk ratio of 4.0 with a wide confidence interval that includes values of no clinical importance. Both findings should be reported with their uncertainty, and the interpretation should separate statistical evidence from biological plausibility and practical consequence.

For regulatory submissions and notifiable disease investigations, the reporting format may be prescribed by the relevant authority. The WOAH terrestrial animal health code specifies surveillance and reporting requirements that affect how association measures are documented and communicated. Compliance with these standards requires attention to the case definitions, population denominators, and time frames used in the analysis.

Common Errors in Calculation and Interpretation

Misclassification of the exposure or outcome is the most frequent source of error in computing association measures. A calf classified as pneumonic when it has only transient fever inflates the risk in the exposed group and biases the risk ratio toward the null. Detection depends on a priori case definitions with explicit clinical criteria, applied identically across exposure groups. The CDC principles of epidemiology in public health practice emphasize standardized outcome definitions as the foundation of valid comparison.

A second common error is computing an odds ratio when the study design yields incidence data and a risk ratio is the more interpretable measure. This occurs when investigators default to logistic regression because it is the familiar tool. The corrective action is to state the design before analysis: cohort studies permit direct estimation of risk, whereas case-control studies do not. When the outcome is rare, the odds ratio approximates the risk ratio, but this approximation fails as outcome frequency rises above roughly 10 percent.

Students frequently confuse the reference category when constructing two-by-two tables. The odds ratio is invariant to which factor level is coded as exposed, provided the table is oriented consistently, but the risk ratio is not. Reversing the exposure coding transforms the risk ratio into its reciprocal only when the outcome coding is also reversed. A simple check is to recalculate with the table transposed and confirm the point estimate and confidence interval are unchanged.

Failure Modes and Troubleshooting

Zero-cell problems deserve particular attention. When no events occur in the exposed group, the risk ratio is undefined and the odds ratio is zero. The standard response is to report the exact confidence interval or to use a penalised estimation approach, and to state clearly which method was applied. The MSD Veterinary Manual notes that sparse data are common in production animal studies where herd-level interventions reduce incidence to near zero.

Limitations of the Evidence Base

Veterinary epidemiology frequently relies on observational data because randomised trials are impractical for many production diseases. Observational estimates carry residual confounding that adjustment cannot fully remove. The Women's Health Initiative randomised trials demonstrated this directly: observational studies had suggested cardioprotective effects of hormone therapy that the trials did not confirm. Veterinary researchers should expect similar discrepancies when observational and experimental evidence are compared.

Expert opinion still differs on the threshold at which the odds ratio ceases to approximate the risk ratio. Some authorities accept the approximation up to 20 percent outcome frequency, while others recommend the risk ratio whenever incidence exceeds 10 percent. The choice matters most in vaccine efficacy trials and outbreak investigations where outcomes are common. Reporting both measures when feasible resolves the ambiguity.

Another contested area is the handling of clustered data. Animals within a herd are not independent, and ignoring clustering produces confidence intervals that are too narrow. Multilevel models or generalized estimating equations are appropriate, but they require assumptions about correlation structure that are difficult to verify. The WOAH animal health surveillance standards recognize herd-level reporting as the unit of interest for many notifiable diseases, which implies that cluster-level analysis is often the correct approach.

Referral and Escalation

Most association analyzes do not require specialist consultation. Escalation is warranted when the study involves regulatory endpoints, when the analysis informs trade decisions, or when the results will be used to set policy. The WOAH terrestrial animal health code specifies reporting requirements for notifiable diseases, and analyzes supporting such reports should be reviewed by an epidemiologist familiar with international standards.

Laboratory involvement is indicated when diagnostic test performance affects exposure classification. If the test has imperfect sensitivity or specificity, the association measure will be biased, and the direction of bias depends on whether misclassification is differential or non-differential. A veterinary diagnostic laboratory can provide test validation data that permit quantitative bias analysis.

Referral to a veterinary epidemiologist is appropriate when the study involves complex sampling designs, when multiple correlated exposures are examined, or when the analysis requires advanced methods such as propensity scoring or instrumental variables. The AVMA practice resources list epidemiological consultation as a resource for practitioners undertaking herd-level investigations. Early consultation is preferable to post hoc correction, because design decisions made before data collection have greater influence on validity than any analytic adjustment applied afterward.

Frequently Asked Questions

When Should I Report a Risk Ratio Instead of an Odds Ratio in a Grant Proposal or Manuscript?

Report the risk ratio whenever the study design provides a true denominator of animals at risk over a defined period, such as a prospective cohort or a clinical trial. Veterinary journals and funding bodies increasingly expect risk ratios for these designs because they communicate the probability of disease directly. Reserve the odds ratio for case-control studies, for analyzes adjusted through logistic regression, or when the outcome is rare enough that the odds ratio approximates the risk ratio. If you report an odds ratio from a cohort study, justify the choice in the methods section. The CDC principles of epidemiology provide the standard framework for matching the measure to the design.

How Do I Calculate an Odds Ratio When My Case-Control Study Used Matching?

For matched case-control designs, the crude odds ratio from a standard 2 by 2 table is biased. Use conditional logistic regression or the McNemar odds ratio, which accounts for the matched sets. The McNemar approach uses only the discordant pairs, where the case was exposed and the control was not, or vice versa. The ratio of these discordant pairs gives the matched odds ratio. Ignoring the matching structure inflates the estimate and narrows the confidence interval. This same principle applies to veterinary studies that match on herd, pen, or calving season. The WOAH animal health surveillance standards emphasize that analysis must respect the sampling design.

What Should I Do When the Outcome Is Common but I Have Only Case-Control Data?

You cannot calculate a valid risk ratio from case-control data because the sampling fractions for cases and controls are fixed by the investigator. The odds ratio remains the correct measure, but you must interpret it as an odds ratio, not as a proxy for risk. When the outcome exceeds roughly 10 percent, the odds ratio overstates the risk ratio, and the degree of overstatement grows with outcome frequency. Report the odds ratio with its confidence interval and state plainly that the absolute risk cannot be estimated from this design. If absolute risk is needed for clinical decision making, a cohort study or a representative cross-sectional survey is required. The MSD Veterinary Manual provides species-specific guidance on designing follow-up studies for common production diseases.

How Do I Explain the Difference Between Risk and Odds to a Producer or Practice Owner?

Use a concrete example from their operation. If 20 of 100 calves develop pneumonia, the risk is 20 percent, meaning one in five calves. The odds are 20 divided by 80, or 0.25, meaning for every calf that develops pneumonia, four do not. Most producers understand risk immediately because it matches how they experience disease. Explain that the odds ratio compares the odds between two groups, and that it is a research tool used when we cannot follow a full population over time. Avoid saying the odds ratio is a "chance" or "probability." The AVMA practice resources offer communication frameworks for translating epidemiological concepts into management decisions.

What Are the Minimum Cell Counts Needed for a Stable Odds Ratio Estimate?

There is no universal threshold, but sparse data produce unstable estimates with wide confidence intervals. A common rule of thumb is that each cell in the 2 by 2 table should contain at least five observations for the normal approximation to the confidence interval to hold. When any cell is zero, the odds ratio is undefined or infinite, and you should add 0.5 to each cell as a continuity correction, or better, use exact logistic regression. In veterinary field data, sparse cells are common when studying rare diseases or small herds. Report the exact confidence interval when counts are low. The WOAH terrestrial animal health code notes that surveillance data from small populations require cautious interpretation.

How Should I Handle Confounding When My Sample Size Is Too Small for Multivariable Adjustment?

Stratified analysis is the practical alternative. Calculate the odds ratio or risk ratio within strata of the suspected confounder, such as age group, herd, or vaccination status. If the stratum-specific estimates are similar to each other but differ from the crude estimate, confounding is present, and the adjusted estimate is the Mantel-Haenszel weighted average. If the stratum-specific estimates differ from each other, effect modification is present, and you should report the estimates separately. With small strata, confidence intervals widen considerably, and you must acknowledge the loss of precision. The CDC epidemiology course provides worked examples of Mantel-Haenszel methods that transfer directly to veterinary data.

Related Clinical & Scientific Guides

• Evaluating Veterinary Surveillance System Attributes
• Network Analysis for Infectious Disease Spread in Animal Populations
• Randomized Controlled Trials in Veterinary Field Settings

References and Further Reading

• Association among serum perfluoroalkyl chemicals, glucose homeostasis, and metabolic syndrome in adolescents and adults.. 2009.
• Estrogen plus progestin and risk of venous thrombosis.. 2004.
• Use of hormone replacement therapy and risk of venous thromboembolism: nested case-control studies using the QResearch and CPRD databases.. 2019.
• Association of Menopausal Hormone Therapy With Breast Cancer Incidence and Mortality During Long-term Follow-up of the Women's Health Initiative Randomized Clinical Trials.. 2020.
• Dietary intake of total, animal, and vegetable protein and risk of type 2 diabetes in the European Prospective Investigation into Cancer and Nutrition (EPIC)-NL study.. 2010.
• Dietary inflammatory index and anthropometric measures of obesity in a population sample at high cardiovascular risk from the PREDIMED (PREvención con DIeta MEDiterránea) trial.. 2015.
• WOAH Animal Health Surveillance Standards. WOAH.
• CDC Principles of Epidemiology in Public Health Practice. CDC.
• MSD Veterinary Manual, Professional Edition. MSD Veterinary Manual.

Related Articles

• Basic Reproductive Ratio (R0) in Veterinary Epidemiology
• Likelihood Ratios in Veterinary Diagnostic Testing
• Using Simulation Models in Veterinary Epidemiology
• Risk-Based Surveillance in Animal Health
• Effect Modification and Interaction in Veterinary Epidemiology

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.