Applying Competing Risks Analysis in Veterinary Research

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

Key Takeaways

• Standard survival analysis (e.g., Kaplan-Meier) is inappropriate when competing events (e.g., death from unrelated causes, culling) prevent observation of the event of interest, leading to biased estimates by assuming censored animals remain at risk.
• Cause-specific hazard models estimate the instantaneous rate of the event of interest among subjects still event-free, answering etiologic questions about factors influencing the biological mechanism of that specific outcome.
• Subdistribution hazard models directly estimate the cumulative incidence function, accounting for competing events and answering prognostic questions about the absolute risk of an event occurring over time, crucial for clinical decision-making.
• The Fine-Gray model is a regression approach for subdistribution hazards, while Gray's test provides a non-parametric comparison of cumulative incidence functions across groups, both essential for robust veterinary research.
• Transparent reporting requires specifying event definitions, censoring conventions, the chosen model type (cause-specific vs. subdistribution), and justifying the selection based on the research question, with cumulative incidence curves often being more informative than hazard ratios alone.
• Common errors include treating death as censoring instead of a competing event, confusing cause-specific and subdistribution hazard ratio interpretations, and failing to account for informative censoring, such as euthanasia due to progressive disease before formal event criteria are met.

Veterinary survival studies frequently encounter a fundamental complication: the event of interest may never be observed because a different event occurs first. A dog enrolled in a study of lymphoma progression may die from renal failure before relapse is documented. A calf followed for respiratory disease may be culled for poor growth. A cat in a vaccine safety trial may develop an unrelated neoplasia. When the occurrence of one event alters the probability of observing another, standard survival analysis that treats all failures as equivalent produces biased estimates. Competing risks analysis provides the formal framework for estimating event-specific probabilities when multiple, mutually exclusive outcomes are possible.

This article explains when competing risks methods are required, how cause-specific and subdistribution hazard models differ, and how to report results transparently. It is written for veterinary researchers designing observational cohorts, clinical trials, or intervention studies across species. The methods described apply equally to companion animal oncology, production animal epidemiology, and laboratory animal carcinogenicity studies. The goal is to equip the reader to choose an appropriate model, interpret its output correctly, and recognize the assumptions that can invalidate conclusions.

At a Glance

The Conceptual Foundation of Competing Risks

Competing risks analysis originated in actuarial science and human demography. A classic formulation decomposes mortality into distinct hazard components that operate simultaneously across the lifespan, with one component dominant during immaturity, a constant hazard during adulthood, and a Gompertzian hazard during senescence. This three-component model, developed for animal survival data, was shown to fit human life tables across mean life spans from 16 to 74 years, demonstrating that competing mortality processes are also a statistical nuisance but a biologically meaningful decomposition of risk.

The same logic applies in veterinary research. An animal under observation is always at risk of multiple events. Death is the ultimate competing event for virtually every other outcome. When death and the event of interest are correlated, as when sicker animals are both more likely to die and more likely to experience disease recurrence, naive censoring of deaths produces biased estimates. The bias arises because censoring assumes the censored animal remains at risk, but a dead animal cannot experience the event of interest.

When Standard Survival Analysis Fails

Standard Kaplan-Meier estimation and Cox proportional hazards regression treat censoring as non-informative. This assumption is violated when the censoring event is death or another outcome correlated with the event of interest. In veterinary oncology, animals that die from their disease are often censored in analyzes of time to metastasis, yet death from disease is itself evidence of aggressive tumor biology. The resulting Kaplan-Meier curve overestimates the true event-free survival because the animals most likely to metastasise have been removed from the risk set.

The magnitude of bias depends on the strength of the correlation between the competing event and the event of interest. When the correlation is weak, the bias may be modest. When the correlation is strong, as in studies of frail or critically ill animals, the bias can reverse the direction of a treatment effect. Researchers should therefore ask a screening question before choosing an analytic approach: could the competing event plausibly be related to the event of interest? If yes, competing risks methods are required.

Cause-Specific Hazards

The cause-specific hazard is the instantaneous rate of the event of interest among animals that have not yet experienced any event. It is estimated by treating competing events as censored, but the interpretation differs from standard survival analysis. The cause-specific hazard answers etiologic questions: what factors increase the rate of the event of interest among animals still at risk? This is the appropriate model when the research question concerns the biological mechanism of a specific outcome.

Cause-specific hazard models are estimated using standard Cox regression with competing events censored. The resulting hazard ratios describe the relative rate of the event of interest conditional on being event-free. These estimates are valid for etiologic inference even when competing events are informative, provided the model is correctly specified. The limitation is that cause-specific hazard ratios do not directly translate into statements about absolute risk, because the cumulative incidence depends on both the cause-specific hazard of the event and the cause-specific hazards of all competing events.

Model Selection: Cause-Specific Versus Subdistribution Hazards

The choice between cause-specific hazard models and subdistribution hazard models depends on the research question. Cause-specific hazards model the instantaneous rate of the event of interest among animals still at risk of any event. Subdistribution hazards model the cumulative incidence function directly, treating competing events as a censoring mechanism while retaining animals in the risk set.

Cause-specific models answer etiologic questions. They estimate the effect of a covariate on the biological process leading to the event of interest, independent of other events. Subdistribution models answer prognostic questions. They estimate the effect of a covariate on the absolute risk of an event occurring over time, given that competing events can remove animals from observation.

A practical example clarifies the distinction. Consider a study of tumor recurrence after surgical excision in dogs. Death from unrelated causes is a competing event. A cause-specific hazard model would estimate how tumor grade affects the rate of recurrence among dogs still alive. A subdistribution hazard model would estimate how tumor grade affects the probability of recurrence by two years, acknowledging that some dogs die before recurrence can occur.

The two approaches can produce different conclusions. A covariate may accelerate recurrence among surviving dogs but have no effect on the cumulative incidence of recurrence because it also increases mortality. Conversely, a covariate may show no effect on the cause-specific hazard yet still influence cumulative incidence through its effect on the competing event.

The subdistribution approach has a specific advantage when the competing event is informative. If animals that die are systematically different from those that remain at risk, standard Kaplan-Meier estimates overestimate the cumulative incidence of the event of interest. The subdistribution model corrects this by retaining competing-event cases in the risk set with appropriate weighting.

Cause-specific models remain preferable when the goal is to understand disease mechanisms. They also handle time-varying covariates more naturally. The subdistribution model assumes that the subdistribution hazard is proportional, an assumption that can be violated when the competing event is common.

Worked Example: Conduit Survival After Truncus Arteriosus Repair

A published study of 107 infants undergoing truncus arteriosus repair compared bovine jugular venous valved conduits with allografts. The investigators used parametric risk-hazard analysis and competing risks techniques to model conduit survival. The competing events were conduit replacement for in-conduit stenosis, replacement for branch pulmonary artery stenosis, and replacement for regurgitation.

The analysis revealed that the propensity-adjusted three-year freedom from replacement for in-conduit stenosis was 96 percent for the jugular venous conduit and 69 percent for the allograft. The risk of intervention for branch pulmonary artery stenosis was similar between conduit types. This distinction mattered clinically. A standard survival analysis treating all conduit replacements as a single outcome would have obscured the differential performance of the two conduits across failure modes.

For veterinary researchers, the lesson is that the event definition must match the clinical question. If a study asks whether a new implant fails faster than a standard implant, the analysis must account for the possibility that animals die with a functioning implant. If the study asks whether the implant causes a specific complication, the analysis must treat other complications as competing events.

Analytical Workflow

The analytical sequence for competing risks data follows a defined structure. First, define the events of interest precisely. Each event must be mutually exclusive and exhaustive. An animal can experience only one event, and the events must cover all possible outcomes.

Second, determine whether the competing events are independent of the event of interest. Independence is rarely testable directly. Sensitivity analyzes comparing cause-specific and subdistribution models provide evidence about the robustness of conclusions to violations of independence assumptions.

Third, fit the appropriate model. For cause-specific hazards, use standard Cox proportional hazards models with censoring at the time of the competing event. For subdistribution hazards, use Fine-Gray models or parametric cumulative incidence functions. Software implementations are available in standard statistical packages.

Fourth, assess model fit. Proportional hazards assumptions should be tested for each covariate. The cumulative incidence function should be plotted against observed cumulative incidence to check calibration.

Fifth, report results transparently. The ARRIVE guidelines for reporting animal research require specification of the statistical methods used. The EQUATOR Network reporting guidelines provide additional structure for observational studies. State which model was used, why it was chosen, and how competing events were defined.

Documentation and Reporting

The methods section of a manuscript should specify the event definitions, the censoring rules, and the model type. A common error is reporting cause-specific hazard ratios while interpreting them as subdistribution effects. The two quantities answer different questions and should not be conflated.

When reporting results, present the cumulative incidence function for each event type. A table showing the cumulative incidence of each event at specified time points is more informative than a single hazard ratio. Confidence intervals should accompany all estimates.

The choice of model should be justified in the methods section. If both cause-specific and subdistribution models are fitted, report both and explain any discrepancies. This practice strengthens the manuscript and helps readers interpret the findings correctly.

Species and Context Considerations

The correct analytical approach varies with the study population. In production animal studies, culling for economic reasons is a common competing event that may be related to the disease under study. In companion animal oncology, euthanasia is a competing event that is almost never independent of disease status. In wildlife studies, capture and relocation create competing events that differ from natural mortality.

The MSD Veterinary Manual provides species-specific context for understanding disease natural history, which informs event definitions. The WOAH terrestrial animal health standards describe surveillance and disease control frameworks that may define outcomes in regulatory studies.

For studies with small sample sizes, parametric models may be preferable to semiparametric approaches. The three-component mortality model described by Siler demonstrates that parametric competing risks models can fit survival data across widely varying life spans, from 16 to 74 years. This approach has direct application to veterinary studies where the age structure of the population varies substantially.

Radiation carcinogenesis studies in experimental animals illustrate the necessity of competing risks methods. As noted in the review of radiation carcinogenesis, specific approaches must correct for competing risks when analyzing tumor data in animals. These include actuarial estimates, non-parametric models, and analytical models. The choice among these depends on the study design and the number of events observed.

When the competing event is rare, standard survival analysis may produce similar results to competing risks analysis. When the competing event is common, the differences become material. A rule of thumb is to consider competing risks methods when the cumulative incidence of the competing event exceeds 10 percent at the time horizon of interest.

Recognized Complications and Failure Modes

Competing risks models fail in characteriztic ways, and early detection depends on inspecting diagnostics instead of waiting for implausible output. The most common failure is misspecification of the event set. When a competing event is defined too broadly, such as grouping all non-disease deaths into a single category, the cause-specific hazard for the event of interest becomes biased if the grouped events have heterogeneous relationships with covariates. Conversely, defining too many competing events fragments the risk sets and produces unstable estimates, particularly in small veterinary cohorts.

A second failure mode is violation of the proportional hazards assumption within either the cause-specific or subdistribution framework. Unlike standard Cox models, where the assumption applies to a single hazard, competing risks models require assessment for each event type separately. Schoenfeld residuals or scaled score processes should be examined for every cause-specific model. When the subdistribution hazard is used, the assumption applies to the cumulative incidence function, and tests based on weighted residuals are appropriate.

Informative censoring presents a subtler problem. If animals are censored because they are removed from the study for reasons related to the event of interest, such as euthanasia for progressive disease that has not yet met the event definition, the estimates become biased. This situation is common in veterinary oncology, where owners elect euthanasia for quality-of-life decline before formal recurrence criteria are met. Sensitivity analyzes that reclassify such cases as competing events or as events of interest should be reported.

Convergence failures and boundary estimates occur more often with subdistribution models in small samples. When the cumulative incidence approaches zero or one within a stratum, the weighted estimating equations may produce extreme coefficients with large standard errors. Inspecting the influence diagnostics and the effective sample size per event type identifies this problem before interpretation.

Common Errors and Corrective Actions

Less experienced analysts frequently confuse the interpretation of cause-specific and subdistribution hazard ratios. A cause-specific hazard ratio describes the instantaneous rate of the event among animals still at risk, whereas a subdistribution hazard ratio describes the effect on the cumulative incidence scale. Reporting one when the other was fitted misleads clinical readers. The corrective action is to state explicitly which model was used and to interpret the coefficients on that model's scale.

Another recurrent error is treating death as a censoring event instead of a competing event. This mistake inflates the estimated cumulative incidence of the event of interest because animals that die are assumed to remain at risk indefinitely. The correction is to recognize that standard Kaplan-Meier methods are inappropriate when competing events exist, as documented in methodological guidance for animal tumor data that requires specific approaches correcting for competing risks, including actuarial and non-parametric models.

A third error involves the handling of frailty or clustering. Veterinary studies frequently enrol littermates, herdmates, or multiple animals from the same household. Ignoring this clustering underestimates standard errors. Shared frailty models or cluster-robust variance estimators should be applied when the design includes such dependencies.

Limitations of Current Evidence

The evidence base for competing risks methods in veterinary research remains thinner than in human medicine. Most methodological development has occurred in human epidemiology, and direct transfer to veterinary settings requires careful consideration of species-specific differences in mortality patterns. The classic three-component mortality model, which partitions risk into immaturity, adult, and senescence hazards, was developed using animal survival data and fits human life tables across a wide range of life spans. This historical link suggests the conceptual framework transfers, but species differences in lifespan, reproductive strategy, and management-related mortality mean that parameter estimates from one species should not be extrapolated to another.

Expert opinion still differs on whether cause-specific or subdistribution hazards should be the primary analysis in veterinary studies. Proponents of cause-specific models argue that they answer etiologic questions about the biological effect of exposures on specific event pathways. Proponents of subdistribution models argue that clinical decision-making requires estimates of absolute risk, which the cumulative incidence function provides directly. The choice depends on the research question, and both should be reported when they diverge materially.

Reporting quality remains inconsistent. The ARRIVE guidelines specify the minimum information required for transparent animal research reporting, and the EQUATOR Network provides a library of reporting standards that includes study-type specific checklists. Veterinary journals increasingly require adherence to these standards, but compliance is variable, particularly for statistical methods sections.

Escalation and Referral

Referral to a biostatistician is warranted when the study involves multiple event types with complex interdependencies, when the proportional hazards assumption fails and time-varying coefficients are needed, or when the cohort is small relative to the number of events. Statistical consultation should occur at the design stage, not after data collection, because sample size calculations for competing risks models differ from those for standard survival analysis.

Laboratory involvement may be required when competing events are defined by diagnostic thresholds that vary between institutions. Standardizing histopathology, imaging, or clinical pathology criteria across sites prevents misclassification of events. Regulatory reporting obligations arise when the study involves notifiable diseases, adverse events related to licensed products, or animals used in regulated research settings. The World Organization for Animal Health terrestrial animal health standards define surveillance and reporting obligations for listed diseases WOAH terrestrial animal health standards, and national authorities may impose additional requirements. Professional practice resources from organizations such as the AVMA can clarify local expectations for adverse event reporting in clinical research AVMA professional practice resources.

Troubleshooting Table

Frequently Asked Questions

How do I justify a competing risks approach to a reviewer who expects standard Kaplan-Meier analysis?

Explain that Kaplan-Meier treats competing events as censored observations, which assumes the censored event is independent of the outcome of interest. When death prevents disease recurrence, that assumption fails and estimates become biased. Cite the methodological precedent in human clinical research, such as the competing risks framework used to evaluate conduit performance after infant cardiac repair, where death and conduit replacement were analyzed as mutually exclusive events. State plainly that standard analysis overestimates cumulative incidence when competing events are frequent. Offer to provide the cause-specific and subdistribution hazard estimates alongside the Kaplan-Meier curves so reviewers can compare the magnitude of the discrepancy directly.

What sample size is needed for a competing risks analysis in a veterinary cohort?

There is no universal threshold, but the limiting factor is the number of events in the least common category, not total enrollment. A useful rule is to ensure at least 10 events per predictor variable in the cause-specific hazard model for the rarest competing event. For a study of tumor recurrence versus death from other causes, if only 8 animals die from unrelated disease, you can fit at most one predictor reliably. Consider combining rare competing events into a single category if clinically defensible. Pilot data from institutional records can estimate event proportions. When events are scarce, report the analysis as exploratory and present cumulative incidence curves without multivariable adjustment.

How do I handle competing risks in a multi-center study where follow-up protocols differ between sites?

Site-specific follow-up intensity can create differential ascertainment of competing events. A site that performs more frequent diagnostic imaging will detect recurrence earlier, while a site with less intensive follow-up may record death as the first event more often. Fit cause-specific models with site as a stratification factor instead of a covariate, which allows baseline hazards to vary without estimating site effects. Alternatively, include site as a random effect in a frailty model if the number of sites is adequate. Document the follow-up schedule at each site in the supplementary materials. If ascertainment differences are severe, consider a sensitivity analysis restricted to sites with identical protocols.

Can competing risks analysis be applied to non-fatal outcomes such as culling or euthanasia in production animals?

Yes, and this is a common veterinary application. In production settings, culling for poor production, culling for disease, and natural death are distinct competing events with different management implications. A subdistribution hazard model is often more interpretable here because producers want to know the cumulative incidence of each culling reason over time. The cause-specific hazard approach answers aetiological questions, such as whether a management intervention reduces culling specifically for lameness. For production species, consult species-specific reporting standards and consider how regional production systems affect event definitions, since culling criteria vary substantially between jurisdictions and production types.

What should I do when the proportional hazards assumption is violated for one competing event?

First, test the assumption using scaled Schoenfeld residuals for each cause-specific model separately. If violation is limited to one event type, options include time-varying coefficients, splitting the time axis at the point where the hazard ratio changes direction, or using an additive hazards model. For subdistribution models, the Fine-Gray approach is less flexible for time-varying effects, so consider reporting both cause-specific and subdistribution results when the assumption fails. A practical alternative is to restrict the analysis window to the period where the assumption holds, provided this is clinically justified and stated in advance. Report the violation explicitly instead of ignoring it, and show the time-varying effect graphically.

How should I report competing risks results in a manuscript to satisfy reporting guidelines?

Follow the reporting standards endorsed by the EQUATOR Network, which catalogues guidelines for observational and experimental studies. State the number of events for each competing outcome separately, report cumulative incidence curves instead of Kaplan-Meier curves for the primary outcome, and present both cause-specific hazard ratios and subdistribution hazard ratios when both were estimated. Describe how competing events were defined and adjudicated, including whether death from the disease of interest was treated as the event or as a competing risk. For animal studies, confirm that the manuscript complies with the ARRIVE guidelines, which specify the minimum information needed for transparent reporting of animal research. Include a flow diagram showing how animals moved from enrollment to each event type.

Related Clinical & Scientific Guides

• Conducting Systematic Reviews of Veterinary Diagnostic Test Accuracy
• Bias in Veterinary Research: Types, Sources, and Mitigation
• Cluster Randomized Trials in Veterinary Research: Design and Analysis

References and Further Reading

• Parameters of mortality in human populations with widely varying life spans.. 1983.
• Jugular venous valved conduit (Contegra) matches allograft performance in infant truncus arteriosus repair.. 2008.
• Prospective Associations of Diet Quality With Incident Frailty in Older Adults: The Health, Aging, and Body Composition Study.. 2019.
• Radiation carcinogenesis in experimental animals and its implications for radiation protection.. 1985.
• Tecovirimat for the Treatment of Mpox.. 2026.
• Integrating ecological uncertainty and farm-scale economics when planning restoration. 2008.
• ARRIVE Guidelines 2.0 for Reporting Animal Research. PLOS Biology, 2020.
• EQUATOR Network Reporting Guidelines. EQUATOR Network.
• MSD Veterinary Manual, Professional Edition. MSD Veterinary Manual.

Related Articles

• Cluster Randomized Trials in Veterinary Research: Design and Analysis
• Using Mixed Methods in Veterinary Research
• Conducting Qualitative Research in Veterinary Settings
• How to Write a Research Protocol for Veterinary Studies
• The ARRIVE Guidelines for Animal Research: Implementation and Compliance

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.