Competing Risks in Survival Analysis

By Dr. Zubair Khalid, DVM, MS, PhD · 2026-08-22

Key Takeaways

• Competing risks arise when subjects can experience multiple mutually exclusive event types, and standard survival analysis methods (Kaplan-Meier, Cox) overestimate event probabilities by treating competing events as censoring.
• The Cumulative Incidence Function (CIF) is the primary descriptive tool, estimating the probability of a specific event occurring by a given time, accounting for the possibility of competing events precluding it.
• For regression analysis focused on predicting the absolute risk of a specific event, the Fine-Gray subdistribution hazard model is indicated, modeling the hazard of the event within the context of competing risks.
• The cause-specific hazard model remains appropriate when the research question targets the etiologic effect of a covariate on the instantaneous rate of a particular event, independent of competing events.
• Misinterpreting subdistribution hazard ratios as cause-specific hazard ratios is a common error; the former reflects the impact on cumulative incidence, while the latter reflects the impact on the event rate among those still at risk.
• A practical workflow involves clearly defining mutually exclusive event types, estimating CIFs, fitting the Fine-Gray model for prediction, and assessing the proportional subdistribution hazards assumption.

Quick Answer

• Competing risks occur when study subjects can experience multiple mutually exclusive event types, and standard Kaplan-Meier or Cox methods overestimate event probabilities.
• Use the cumulative incidence function (CIF) for descriptive analysis and the Fine-Gray subdistribution hazard model for regression when the primary interest is predicting the absolute risk of a specific event.
• The cause-specific hazard model remains appropriate when the research question targets the etiologic effect of a covariate on the rate of a particular event, not the cumulative probability.

Understanding Competing Risks in Time-to-Event Data

Survival analysis in biological and medical research typically focuses on the time until an event of interest occurs. Standard approaches such as the Kaplan-Meier estimator and the Cox proportional hazards model assume that censoring is independent and that the event of interest is the only possible outcome. In practice, study participants may experience multiple distinct events, and the occurrence of one event can preclude the occurrence of another. This situation is known as competing risks.

Consider a study of disease progression in a cohort of patients. The primary event of interest may be recurrence of the disease. However, some patients may die from unrelated causes before recurrence can be observed. Death from an unrelated cause is a competing event because it prevents the recurrence from ever being observed. If the analysis treats death from unrelated causes as ordinary censoring, the estimated probability of recurrence will be inflated because patients who die are incorrectly assumed to remain at risk for recurrence.

The presence of competing risks requires a different analytical framework. The cumulative incidence function (CIF) provides an estimate of the probability of a specific event occurring over time while accounting for the fact that competing events can occur first. The Fine-Gray subdistribution hazard model extends this framework to allow regression analysis of the CIF. Understanding when to use these methods and how to interpret their results is essential for producing valid conclusions from time-to-event data.

Core Principles of Competing Risks Analysis

The Definition of Competing Risks

Competing risks arise when each subject in a study can experience one of several distinct event types, and the occurrence of one event type prevents the occurrence of all other event types. The events are mutually exclusive and exhaustive in the sense that each subject eventually experiences exactly one event type or is censored. The presence of competing risks means that the standard assumption of independent censoring is violated when the competing event is treated as a censoring event.

The key distinction is between censoring and competing events. Censoring occurs when the event of interest has not been observed by the end of the follow-up period, or when the subject is lost to follow-up. In the case of censoring, the subject remains at risk for the event of interest. A competing event is different because the subject is no longer at risk for the event of interest after the competing event occurs. Treating a competing event as censoring introduces bias because it assumes that the subject would have experienced the event of interest at the same rate as subjects who remain at risk.

The Cumulative Incidence Function

The cumulative incidence function (CIF) is the fundamental quantity for describing the probability of a specific event in the presence of competing risks. The CIF for event type k at time t represents the probability that event k occurs before time t and before any competing event occurs. This is distinct from the complement of the Kaplan-Meier estimator, which estimates the probability of event k occurring in a hypothetical world where competing events do not exist.

The CIF is calculated by considering both the hazard of the event of interest and the survival probability from all events combined. The hazard of event k at time t is the instantaneous rate of event k among subjects who have not yet experienced any event. The overall survival function is the probability of being event-free at time t. The CIF for event k is the integral of the hazard of event k multiplied by the overall survival function. This formulation ensures that the CIF accounts for the fact that subjects who experience a competing event are no longer at risk for event k.

The CIF has several important properties. The CIF for each event type is a nondecreasing function of time. The sum of the CIFs for all event types plus the overall survival function equals one at any time point. The CIF for a specific event type approaches the probability of that event occurring as time approaches infinity, but this probability is less than one because competing events can occur first.

The Subdistribution Hazard

The subdistribution hazard is a quantity that is derived from the CIF. The subdistribution hazard for event type k at time t is defined as the probability of event k occurring at time t given that the subject has not yet experienced event k. This definition differs from the cause-specific hazard, which conditions on the subject being event-free from all event types.

The subdistribution hazard is useful because it has a direct relationship with the CIF. The CIF for event type k can be expressed as one minus the exponential of the negative integral of the subdistribution hazard. This relationship allows the subdistribution hazard to be modeled using a proportional hazards structure, which is the basis of the Fine-Gray model.

The interpretation of the subdistribution hazard is subtle. It represents the risk of event k among subjects who have not yet experienced event k, including subjects who have already experienced a competing event. This is a hypothetical construct because subjects who have experienced a competing event are no longer at risk in the real world. However, this construct is useful for predicting the absolute risk of event k over time.

The Fine-Gray Model

Model Specification

The Fine-Gray model, also known as the subdistribution hazard model, was introduced to allow regression analysis of the CIF. The model specifies that the subdistribution hazard for event type k depends on covariates through a proportional hazards structure. The model can be written as the subdistribution hazard at time t for a subject with covariate vector X equals the baseline subdistribution hazard multiplied by the exponential of the linear predictor.

The regression coefficients in the Fine-Gray model are interpreted as the log subdistribution hazard ratios. A positive coefficient indicates that the covariate is associated with an increased subdistribution hazard, which corresponds to an increased cumulative incidence of the event of interest. The subdistribution hazard ratio is a measure of the association between the covariate and the absolute risk of the event.

The Fine-Gray model is estimated using a weighted partial likelihood approach. Subjects who experience a competing event are retained in the risk set with time-dependent weights. This weighting scheme ensures that the estimated coefficients are consistent for the subdistribution hazard parameters. The weights are based on the inverse of the probability of being censored, which is estimated from the data.

Comparison with the Cause-Specific Hazard Model

The cause-specific hazard model is the alternative regression approach for competing risks data. The cause-specific hazard for event type k is the rate of event k among subjects who are event-free. The cause-specific hazard model specifies a proportional hazards structure for this rate. The regression coefficients are interpreted as the log cause-specific hazard ratios.

The choice between the Fine-Gray model and the cause-specific hazard model depends on the research question. The cause-specific hazard model is appropriate when the interest is in the biological mechanism of the event. The cause-specific hazard ratio describes how a covariate affects the rate of the event among subjects who are at risk. The Fine-Gray model is appropriate when the interest is in the absolute risk of the event. The subdistribution hazard ratio describes how a covariate affects the cumulative probability of the event over time.

The two models can produce different conclusions. A covariate may have a positive effect on the cause-specific hazard but a negative effect on the subdistribution hazard. This can occur when the covariate also increases the risk of a competing event. The cause-specific hazard ratio captures the direct effect on the event rate, while the subdistribution hazard ratio captures the net effect on the cumulative probability.

Assumptions and Limitations

The Fine-Gray model relies on several assumptions. The proportional subdistribution hazards assumption requires that the subdistribution hazard ratio is constant over time. This assumption can be tested using methods similar to those used for the Cox model, such as examining Schoenfeld residuals or including time-by-covariate interactions.

The model also assumes that censoring is independent of the event process. This is a standard assumption in survival analysis. The weighted estimation approach requires that the censoring distribution is correctly specified. If the censoring distribution depends on covariates, the model should include those covariates in the censoring model.

The Fine-Gray model has a limitation in that the subdistribution hazard does not have a direct biological interpretation. The subdistribution hazard conditions on a hypothetical population that includes subjects who have already experienced competing events. This makes the subdistribution hazard ratio difficult to interpret in terms of the underlying disease process. The cause-specific hazard ratio is more interpretable for etiologic questions.

Practical Workflow for Competing Risks Analysis

Step 1: Define the Event Types

The first step in a competing risks analysis is to define the event types clearly. The event types must be mutually exclusive and exhaustive. Each subject should be assigned to exactly one event type or censored. The definitions should be based on the research question and should be specified before the analysis begins.

The event types should be clinically or biologically meaningful. For example, in a study of cancer treatment, the event types might be disease recurrence and death from any cause. In a study of cardiovascular disease, the event types might be myocardial infarction, stroke, and death from other causes. The definitions should be documented in the analysis plan.

Step 2: Estimate the Cumulative Incidence Functions

The next step is to estimate the CIF for each event type. The CIF can be estimated nonparametrically using the Aalen-Johansen estimator. This estimator is the competing risks analog of the Kaplan-Meier estimator. The CIF for each event type is calculated at each observed event time, and the estimates are typically displayed as step functions.

The CIF estimates should be plotted for each event type. The plots show the cumulative probability of each event type over time. The plots can be used to describe the absolute risk of each event in the study population. The CIF estimates can also be compared between groups defined by categorical covariates.

Step 3: Fit the Fine-Gray Model

The Fine-Gray model is fitted to assess the association between covariates and the cumulative incidence of the event of interest. The model is fitted using a weighted Cox proportional hazards approach. The output includes the regression coefficients, the subdistribution hazard ratios, and the confidence intervals.

The model should be fitted for the event of interest. If there are multiple event types, a separate model should be fitted for each event type. The model for each event type treats the other event types as competing events. The results for each event type should be reported separately.

Step 4: Assess the Proportional Hazards Assumption

The proportional hazards assumption should be assessed for the Fine-Gray model. This can be done by examining the scaled Schoenfeld residuals or by including time-by-covariate interactions in the model. If the assumption is violated, the model can be extended to include time-varying effects.

The assessment of the proportional hazards assumption is important because the interpretation of the subdistribution hazard ratio depends on the assumption. If the assumption is violated, the subdistribution hazard ratio is not constant across time, and the model results are not valid.

Step 5: Report the Results

The results of the competing risks analysis should be reported in a transparent manner. The report should include the CIF estimates for each event type, the subdistribution hazard ratios from the Fine-Gray model, and the confidence intervals. The report should also describe the methods used to handle competing risks and the assumptions that were made.

The reporting should follow the relevant reporting guidelines. The EQUATOR Network provides a collection of reporting guidelines for health research. The use of reporting guidelines ensures that the analysis is reported in a complete and transparent manner. The guidelines can be accessed through the EQUATOR Network website.

At a Glance

Practical Implementation in R

Data Preparation

The analysis of competing risks data in R requires the data to be in a specific format. The data should include a time variable, an event variable, and the covariates of interest. The event variable should be coded as 0 for censored, 1 for the event of interest, and 2 for the competing event. The event variable can be coded as a factor or as a numeric variable.

The data should be checked for completeness and consistency. The time variable should be positive and the event variable should be coded correctly. The data should be sorted by the time variable for the analysis.

Fitting the Fine-Gray Model

The Fine-Gray model can be fitted in R using the crr function from the cmprsk package. The function requires the time variable, the event variable, and the covariate matrix. The function returns the regression coefficients, the subdistribution hazard ratios, and the standard errors.

The crr function uses the weighted approach to estimate the subdistribution hazard. The function requires the specification of the censoring distribution. The default is to use the Kaplan-Meier estimator for the censoring distribution. The function can also be used to fit a model with time-varying effects.

Estimating the Cumulative Incidence Function

The cumulative incidence function can be estimated in R using the cuminc function from the cmprsk package. The function requires the time variable and the event variable. The function returns the CIF estimates for each event type at each time point.

The cuminc function can also be used to compare the CIFs between groups. The function can be used to test for differences in the CIFs between groups using a Gray's test. The Gray's test is a nonparametric test for comparing the CIFs between groups.

Example Code

The following code demonstrates how to fit a Fine-Gray model in R. The code assumes that the data is in a data frame called dat with columns time, event, and cov1.

library(cmprsk)
fit <- crr(dat$time, dat$event, cov1 = dat$cov1)
summary(fit)

The crr function returns the model fit. The summary function provides the regression coefficients, the standard errors, and the p-values. The subdistribution hazard ratios can be obtained by exponentiating the coefficients.

The cumulative incidence function can be estimated using the following code.

cif <- cuminc(dat$time, dat$event)
plot(cif)

The cuminc function returns the CIF estimates. The plot function creates a plot of the CIFs for each event type.

Options and Tradeoffs in Model Selection

When to Use the Fine-Gray Model

The Fine-Gray model is the appropriate choice when the research question is about the absolute risk of a specific event in the presence of competing risks. This is the case when the goal is to predict the probability of an event for an individual patient or to compare the risk of an event between groups. The Fine-Gray model provides a direct estimate of the cumulative incidence function, which is the quantity of interest for clinical decision-making.

The Fine-Gray model is also appropriate when the goal is to identify risk factors for the cumulative incidence of an event. The subdistribution hazard ratio provides a measure of the association between a covariate and the cumulative probability of the event. This is useful for identifying patients at high risk of the event.

Choosing the Cause-Specific Hazard Model

The cause-specific hazard model is the appropriate choice when the research question is about the biological mechanism of the event. The cause-specific hazard ratio provides a measure of the association between a covariate and the rate of the event among subjects who are at risk. This is useful for understanding the underlying disease process.

The cause-specific hazard model is also appropriate when the goal is to estimate the effect of a covariate on the event rate in the presence of competing events. The cause-specific hazard model provides an estimate of the direct effect of the covariate on the event rate, independent of the competing events.

The Tradeoff Between the Two Models

The two models answer different questions and can produce different results. The choice between the two models should be based on the research question. The Fine-Gray model is more appropriate for clinical decision-making and risk prediction. The cause-specific hazard model is more appropriate for etiologic research.

The two models can be used together to provide a complete picture of the data. The cause-specific hazard model can be used to understand the mechanism of the event, and the Fine-Gray model can be used to estimate the absolute risk. The results of the two models should be reported together when both are fitted.

Observations and Measurements in Competing Risks Analysis

Data Quality Checks

The quality of the data is important for the validity of the competing risks analysis. The data should be checked for errors in the time and event variables. The time variable should be measured consistently across all subjects. The event variable should be coded correctly and consistently.

The data should be checked for missing values. Missing values in the covariates can be handled using multiple imputation or complete-case analysis. The choice of the method for handling missing data should be based on the missing data mechanism.

The Role of the Censoring Distribution

The censoring distribution plays an important role in the Fine-Gray model. The model uses the censoring distribution to compute the weights for the subjects who experience a competing event. The censoring distribution is estimated from the data, and the estimation method can affect the results.

The censoring distribution should be estimated using a model that accounts for the covariates that are associated with censoring. If the censoring is dependent on the covariates, the censoring model should include those covariates. The censoring model should be checked for the proportional hazards assumption.

The Effect of the Competing Event

The competing event has a direct effect on the cumulative incidence of the event of interest. The cumulative incidence of the event of interest is reduced by the presence of the competing event. The magnitude of the reduction depends on the rate of the competing event.

The competing event can also affect the subdistribution hazard ratio. The subdistribution hazard ratio is a measure of the effect of a covariate on the cumulative incidence of the event of interest. The effect of the covariate on the cumulative incidence can be different from the effect on the cause-specific hazard. This is because the covariate can also affect the competing event.

Records and Documentation

The Analysis Plan

The competing risks analysis should be documented in an analysis plan. The analysis plan should specify the research question, the event types, the covariates, the models to be fitted, and the methods for handling the censoring. The analysis plan should be written before the analysis is conducted.

The analysis plan should be updated if the analysis is changed. The changes should be documented and the reasons for the changes should be explained. The analysis plan should be made available to the reviewers of the study.

The Analysis Code

The analysis code should be documented and made available for reproducibility. The code should be well-commented and should be run in a reproducible manner. The code should be stored in a version control system.

The analysis code should be reviewed by a second person to check for errors. The code should be tested on a small subset of the data before running the full analysis. The code should be run in a clean environment to ensure that the results are reproducible.

The Results

The results of the analysis should be documented in a clear and complete manner. The results should include the CIF estimates, the subdistribution hazard ratios, and the confidence intervals. The results should be presented in tables and figures.

The results should be interpreted in the context of the research question. The interpretation should be based on the statistical results and the biological or clinical context. The limitations of the analysis should be discussed.

Common Failure Patterns in Competing Risks Analysis

Treating Competing Events as Censoring

The most common failure in competing risks analysis is treating competing events as censoring. This approach produces biased estimates of the cumulative incidence of the event of interest. The bias occurs because subjects who experience a competing event are incorrectly treated as being at risk for the event of interest.

The bias can be substantial when the competing event is common. The cumulative incidence of the event of interest is overestimated when the competing event is treated as censoring. The overestimation is larger when the competing event is more common.

Using the Kaplan-Meier Estimator

The Kaplan-Meier estimator is not appropriate for estimating the cumulative incidence of an event in the presence of competing risks. The Kaplan-Meier estimator estimates the probability of the event in a hypothetical world where the competing events do not exist. This is not the quantity of interest for clinical decision-making.

The Kaplan-Meier estimator produces estimates that are larger than the cumulative incidence function. The difference between the two estimates is larger when the competing event is more common. The Kaplan-Meier estimator should not be used for estimating the cumulative incidence of an event in the presence of competing risks.

Misinterpreting the Subdistribution Hazard Ratio

The subdistribution hazard ratio is often misinterpreted as a cause-specific hazard ratio. The subdistribution hazard ratio is a measure of the effect of a covariate on the cumulative incidence of the event. The cause-specific hazard ratio is a measure of the effect of a covariate on the rate of the event among subjects who are at risk.

The two ratios can be different. A covariate can have a positive effect on the cause-specific hazard and a negative effect on the subdistribution hazard. The interpretation of the subdistribution hazard ratio should be in terms of the cumulative incidence, not the cause-specific hazard.

Ignoring the Proportional Hazards Assumption

The proportional hazards assumption is important for the validity of the Fine-Gray model. The assumption should be tested and the model should be adjusted if the assumption is violated. The violation of the assumption can lead to biased estimates of the subdistribution hazard ratio.

The proportional hazards assumption can be tested using the scaled Schoenfeld residuals or by including time-by-covariate interactions. The model can be adjusted by including time-varying effects for the covariates that violate the assumption.

Quality and Welfare Controls in Research

Reproducibility

Reproducibility is a key aspect of the quality of the research. The analysis should be reproducible by other researchers. The data and the code should be made available for the reproducibility of the analysis. The data should be documented and the code should be commented.

The reproducibility of the analysis can be improved by using a version control system for the code and the data. The analysis should be run in a clean environment to ensure that the results are reproducible. The results should be reported in a way that allows other researchers to reproduce the analysis.

Data Management

The data management is an important aspect of the research quality. The data should be managed in a way that ensures the integrity of the data. The data should be stored in a secure location and the access to the data should be controlled.

The NIH Data Management and Sharing Policy provides expectations for the data management and sharing of the research data. The policy is available on the NIH website. The policy requires that the data be managed and shared in a way that is consistent with the research.

Reporting Guidelines

The reporting of the research should follow the relevant reporting guidelines. The EQUATOR Network provides a collection of reporting guidelines for health research. The guidelines are available on the EQUATOR Network website. The guidelines ensure that the research is reported in a complete and transparent manner.

The reporting guidelines should be used in the preparation of the manuscript. The guidelines should be followed for the reporting of the methods and the results. The guidelines should be cited in the manuscript.

Safety and Regulatory Context

The Use of the Fine-Gray Model in Regulatory Submissions

The Fine-Gray model is used in the analysis of clinical trials and observational studies. The model is used to estimate the cumulative incidence of an event in the presence of competing risks. The model is used in the regulatory submissions for the approval of the drugs and the devices.

The regulatory agencies require that the analysis of the competing risks data be conducted in a valid manner. The analysis should be conducted using the appropriate methods. The analysis should be reported in a transparent manner.

The Use of the Fine-Gray Model in the NIH-Funded Research

The NIH-funded research is expected to be conducted in a rigorous manner. The analysis of the competing risks data should be conducted using the appropriate methods. The analysis should be reported in a transparent manner.

The NIH provides the funding for the research. The NIH Grants and Funding website provides the information about the NIH grant policy and the application process. The website is available at the NIH website.

The Use of the Fine-Gray Model in the Publication

The publication of the research should be conducted in an ethical manner. The publication should be conducted in accordance with the publication ethics. The Committee on Publication Ethics provides the core practices for the publication ethics. The core practices are available on the COPE website.

The publication should be conducted in a transparent manner. The authors should be listed in the appropriate manner. The data should be shared in accordance with the data sharing policy.

Professional Escalation Criteria

When to Consult a Biostatistician

The competing risks analysis is a complex statistical method. The analysis should be conducted by a researcher with the appropriate statistical expertise. The researcher should consult a biostatistician if the analysis is complex or if the researcher is not familiar with the methods.

The biostatistician can provide the guidance on the choice of the model and the interpretation of the results. The biostatistician can also provide the guidance on the handling of the assumptions and the limitations of the analysis.

When to Seek Additional Expertise

The competing risks analysis can be complex when the data has a complex structure. The data can have a complex structure when the data is from a multi-center study or when the data has a complex censoring pattern. The analysis of the complex data should be conducted by a researcher with the appropriate expertise.

The researcher should seek the additional expertise if the analysis is complex. The additional expertise can be provided by a biostatistician or a data scientist. The additional expertise can be provided by the collaboration with the other researchers.

When to Escalate the Issue

The researcher should escalate the issue if the analysis is not valid. The analysis is not valid if the assumptions are not met or if the data is not appropriate. The researcher should escalate the issue to the supervisor or the research team.

The researcher should escalate the issue if the results are not interpretable. The results are not interpretable if the model is not appropriate or if the data is not appropriate. The researcher should escalate the issue to the supervisor or the research team.

Decision Framework for Selecting Between Competing Risks Models

Choosing between the Fine-Gray model and the cause-specific hazard model requires a structured decision process that goes beyond the research question alone. The following framework integrates the study objective, the anticipated event rates, the covariate effects, and the intended use of the results. This framework is designed to be applied before data analysis begins and should be documented in the analysis plan.

Step 1: Classify the Primary Research Objective

The first decision point requires classifying the study objective into one of three categories. The first category is etiologic inference, where the goal is to understand the biological or mechanistic effect of a covariate on the rate of a specific event. The second category is absolute risk prediction, where the goal is to estimate the probability of an event for clinical decision-making or patient counseling. The third category is a combined objective, where both etiologic and predictive questions are of interest.

For the first category, the cause-specific hazard model is the appropriate choice. For the second category, the Fine-Gray model is the appropriate choice. For the third category, both models should be fitted and reported together, with the interpretation of each model matched to its corresponding research question.

Step 2: Assess the Expected Competing Event Rate

The magnitude of the competing event rate influences the practical importance of the model choice. When the competing event is rare, the difference between the cause-specific hazard model and the Fine-Gray model is typically small. When the competing event is common, the difference can be substantial.

A practical assessment can be made by estimating the cumulative incidence of the competing event using the Aalen-Johansen estimator. If the cumulative incidence of the competing event exceeds 10 percent at the median follow-up time, the choice of model is likely to have a meaningful impact on the conclusions. If the competing event rate is below this threshold, the two models may produce similar results, but the model choice should still be based on the research question.

Step 3: Examine the Direction of Covariate Effects

The direction of the covariate effects on the event of interest and the competing event determines whether the two models will produce divergent conclusions. A covariate that increases the rate of the event of interest but also increases the rate of the competing event can produce a positive cause-specific hazard ratio and a negative subdistribution hazard ratio.

To assess this possibility, fit both models and compare the direction and magnitude of the coefficients. If the coefficients have opposite signs or if the confidence intervals do not overlap, the interpretation of the results depends critically on the model choice. This situation should be reported explicitly, and the interpretation should be tied to the research question.

Step 4: Consider the Intended Use of the Results

The intended use of the results determines the model that should be emphasized in the reporting. If the results will be used for clinical decision-making, patient counseling, or risk stratification, the Fine-Gray model and the cumulative incidence function are the appropriate quantities. If the results will be used to inform the design of future studies or to understand the biological mechanism, the cause-specific hazard model is the appropriate choice.

When both models are fitted, the report should present the results of both models in a way that makes the distinction clear. The report should state which model is the primary analysis and which is the secondary analysis, and the interpretation should follow this designation.

Step 5: Validate the Model Choice with Sensitivity Analysis

A sensitivity analysis should be conducted to assess the robustness of the conclusions to the model choice. The sensitivity analysis should fit both models and compare the conclusions. If the conclusions are the same under both models, the results are robust to the model choice. If the conclusions differ, the report should discuss the reasons for the difference and the implications for the interpretation.

The sensitivity analysis should also include an assessment of the proportional hazards assumption for both models. The assessment should be conducted using the scaled Schoenfeld residuals or time-by-covariate interactions. The results of the sensitivity analysis should be reported in the supplementary materials.

Step 6: Record the Decision in the Analysis Plan

The decision framework should be applied before the analysis is conducted, and the decision should be recorded in the analysis plan. The analysis plan should document the research question, the classification of the objective, the expected competing event rate, the direction of the covariate effects, and the intended use of the results. The analysis plan should also document the sensitivity analysis that will be conducted.

The analysis plan should be made available to the reviewers of the study. The plan should be updated if the analysis is changed, and the changes should be documented with the reasons for the changes.

Common Failure Patterns in the Decision Process

A common failure is to choose the model based on the statistical significance of the results instead of the research question. This approach can produce results that are not aligned with the study objective. The model choice should be made before the analysis is conducted and should not be changed based on the results.

Another common failure is to report only one model without documenting the decision process. The report should include the rationale for the model choice and the results of the sensitivity analysis. The report should also include the cumulative incidence estimates for all event types, beyond the event of interest.

A third failure is to interpret the subdistribution hazard ratio as a cause-specific hazard ratio. The interpretation should be tied to the model that was fitted. The subdistribution hazard ratio should be interpreted in terms of the cumulative incidence, and the cause-specific hazard ratio should be interpreted in terms of the event rate among event-free subjects.

Practical Implementation Steps

The decision framework can be implemented in a structured manner using the following steps. First, write the research question in a single sentence and classify it into one of the three categories. Second, estimate the cumulative incidence of the competing event using the Aalen-Johansen estimator. Third, fit both models and compare the direction and magnitude of the coefficients. Fourth, document the intended use of the results and the primary audience. Fifth, conduct the sensitivity analysis and record the results. Sixth, document the decision and the sensitivity analysis in the analysis plan.

The implementation steps should be completed before the final analysis is run. The decision should be recorded in the analysis plan and the code should be documented. The results of the sensitivity analysis should be reported in the final manuscript or report.

Frequently Asked Questions

What is the difference between the cause-specific hazard and the subdistribution hazard?

The cause-specific hazard is the rate of the event among subjects who are event-free. The subdistribution hazard is the rate of the event among subjects who have not yet experienced the event of interest, including subjects who have experienced a competing event. The cause-specific hazard is used for the etiologic research, and the subdistribution hazard is used for the prediction of the absolute risk.

When should I use the Fine-Gray model instead of the cause-specific hazard model?

The Fine-Gray model should be used when the research question is about the absolute risk of the event in the presence of competing risks. The cause-specific hazard model should be used when the research question is about the biological mechanism of the event. The choice of the model should be based on the research question.

How do I interpret the subdistribution hazard ratio?

The subdistribution hazard ratio is a measure of the effect of a covariate on the cumulative incidence of the event. A subdistribution hazard ratio greater than 1 indicates that the covariate is associated with a higher cumulative incidence of the event. A subdistribution hazard ratio less than 1 indicates that the covariate is associated with a lower cumulative incidence of the event.

What is the cumulative incidence function?

The cumulative incidence function is the probability of a specific event occurring before a given time in the presence of competing risks. The cumulative incidence function is the quantity of interest for the prediction of the absolute risk of the event.

How do I estimate the cumulative incidence function in R?

The cumulative incidence function can be estimated in R using the cuminc function from the cmprsk package. The function requires the time variable and the event variable. The function returns the cumulative incidence function estimates for each event type.

What is the difference between the Kaplan-Meier estimator and the cumulative incidence function?

The Kaplan-Meier estimator estimates the probability of the event in a hypothetical world where the competing events do not exist. The cumulative incidence function estimates the probability of the event in the presence of competing risks. The cumulative incidence function is the appropriate estimator for the absolute risk of the event.

How do I test the proportional hazards assumption in the Fine-Gray model?

The proportional hazards assumption can be tested using the scaled Schoenfeld residuals or by including time-by-covariate interactions in the model. The assumption is violated if the residuals show a pattern over time or if the interaction is significant.

What should I report when I use the Fine-Gray model?

The report should include the cumulative incidence function estimates for each event type, the subdistribution hazard ratios from the Fine-Gray model, and the confidence intervals. The report should also describe the assumptions and the limitations of the analysis.

Using the Evidence

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References and Further Reading

• Research Methods Resources. National Library of Medicine.
• EQUATOR Network. EQUATOR Network.
• Core Practices. Committee on Publication Ethics.
• NIH Grants and Funding. National Institutes of Health.
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This article is educational and does not replace validated analysis plans, institutional policy, clinical interpretation, or specialist review.