How Do Competing Events Affect Prognostic Study Design?

What Happens When Another Event Makes Your Outcome Impossible?

You are studying the probability of hospital readmission after discharge. Some patients are readmitted, while others die before readmission can occur. Should the patients who die simply be removed from the analysis?

Or consider a study of academic withdrawal. Some students withdraw, while others complete the program. Once a student has completed the qualification, withdrawal from that same program may no longer be possible.

These situations involve competing events. They matter because the probability of the outcome of interest depends not only on how frequently that outcome occurs, but also on how frequently other events prevent it from occurring.

Ignoring competing events can produce prognostic estimates that do not represent the real-world probabilities researchers intend to describe.

Identify Competing Events Before Choosing the Outcome Estimator

How Competing Events Change Prognostic Estimation and Interpretation

What Is a Competing Event?

A competing event is an event whose occurrence prevents the outcome of interest from occurring afterward in the form defined by the study.

For example, death before a first hospital readmission prevents subsequent readmission. Death before disease recurrence similarly prevents later recurrence from being observed in the living patient.

In educational research, program completion may compete with withdrawal when the outcome concerns withdrawal before completion.

The definition depends on the outcome and the states included in the research question.

An event is not competing merely because it occurs before the outcome or is associated with outcome risk. It must prevent the specified event from subsequently occurring under the study's event definition.

Why Must Competing Events Be Defined Relative to Time Zero?

A competing event must occur after the defined starting point and before the outcome of interest.

For example, death after hospital discharge may compete with readmission. Death during the initial hospitalization, however, occurs before entry into a cohort defined by discharge alive.

The latter concerns eligibility for the discharge-based population rather than a competing event within that cohort.

Researchers should therefore establish the starting point for prognosis before classifying events.

The same real-world event can have different analytical roles depending on the chosen starting population and outcome.

How Are Competing Events Different From Censoring?

Right-censoring occurs when the event of interest has not been observed by the end of an individual's available follow-up.

For example, a patient may remain event-free when administrative observation ends, or may leave the study before the outcome is known.

A competing event is different because it establishes that the defined outcome can no longer occur afterward.

For instance, a patient who dies before readmission is not simply someone whose future readmission status is unobserved. Subsequent readmission is impossible.

This distinction matters because conventional survival estimators often rely on assumptions that do not support treating competing events as ordinary censoring when estimating real-world cumulative incidence.

How Do Common Event Types Compare?

Researchers should establish event definitions according to the substantive process rather than assigning categories based only on convenient database codes.

Why Can Kaplan-Meier Estimation Be Misleading?

The Kaplan-Meier estimator is commonly used to estimate survival or event-free probabilities under suitable censoring assumptions.

When competing events occur, researchers sometimes censor participants at the time of the competing event and calculate one minus the Kaplan-Meier survival estimate.

This quantity generally does not equal the actual cumulative probability of the event of interest in the presence of competing events.

It can overestimate the real-world event probability because it effectively removes competing events from the risk calculation in a way that does not represent their prevention of the event.

The resulting estimate may still have an interpretation in relation to a hypothetical or net-risk quantity under additional assumptions, but it should not automatically be labeled the observed-world cumulative incidence.

Researchers should distinguish these estimands explicitly.

What Is the Cumulative Incidence Function?

The cumulative incidence function, or CIF, estimates the probability that a specified event type occurs by a given time in the presence of competing events.

It accounts for the fact that participants who experience competing events can no longer experience the event of interest.

For example, the cumulative incidence of readmission by 90 days describes the probability of readmission before death or other relevant competing events within that period.

Unlike one minus the Kaplan-Meier estimator obtained by censoring competing events, the CIF represents the observed-world event probability under the relevant assumptions.

For mutually exclusive first-event types, their cumulative incidences at a given time sum to the probability of experiencing any of those events by that time.

How Is Cumulative Incidence Related to Event-Specific Hazards?

The cumulative incidence of an event depends on its cause-specific hazard and on survival free of all event types.

This relationship explains why a prognostic analysis focused on absolute event probability cannot generally ignore the occurrence of competing events.

What Is a Cause-Specific Hazard?

The cause-specific hazard describes the instantaneous rate of a particular event among individuals who have not yet experienced any of the mutually exclusive first-event types.

For example, the cause-specific hazard of readmission concerns patients who remain alive and have not yet been readmitted.

Cause-specific Cox regression can examine associations between prognostic factors and that hazard, subject to the model's assumptions.

When fitting a cause-specific hazard model, competing events are commonly handled as censoring for the event-specific hazard analysis.

However, this analytical treatment does not imply that competing events are noninformative censoring for estimating the actual cumulative incidence through one minus Kaplan-Meier.

The distinction between a cause-specific hazard and an absolute event probability is essential.

What Is the Fine-Gray Subdistribution Hazard Model?

The Fine-Gray model examines associations with the subdistribution hazard, a quantity mathematically linked to the cumulative incidence function.

It uses a modified risk-set construction that retains the influence of individuals who have experienced competing events.

The resulting subdistribution hazard ratio describes a relationship with the subdistribution hazard, not the ordinary instantaneous event rate among people currently free of all events.

Consequently, a subdistribution hazard ratio should not automatically be interpreted as a risk ratio or a cause-specific hazard ratio.

Fine-Gray regression can be useful for investigating cumulative-incidence-related associations, but it does not eliminate the need to estimate and report absolute risks.

How Do Cause-Specific and Fine-Gray Models Differ?

Neither model is universally superior. The choice depends on the estimand and the scientific question.

For prediction of absolute cumulative incidence, modeling all relevant cause-specific hazards and combining them appropriately is another defensible strategy.

Can a Competing Event Reduce the Observed Risk of the Main Outcome?

Yes. This is one of the most important interpretive features of competing risks.

Suppose a population has a high mortality rate. Fewer individuals may remain alive long enough to experience a nonfatal complication.

The cumulative incidence of that complication may therefore be lower than in a population with better survival, even if the underlying event-specific hazard is similar.

This does not necessarily mean that the first population has a more favorable clinical course.

Researchers should interpret the event of interest alongside the competing-event probability and the overall clinical context.

A lower cumulative incidence of a nonfatal event can sometimes reflect more frequent death rather than better health.

How Do Competing Events Affect Prognostic Factor Interpretation?

A prognostic factor may be associated with both the event of interest and competing events.

For example, older age may be associated with both readmission and mortality. The relationship between age and the cumulative incidence of readmission may therefore differ from its relationship with the cause-specific readmission hazard.

Researchers should not interpret these different associations as contradictory without considering the underlying event processes.

The choice of model should follow whether the objective is to examine event-specific associations or predict the actual probability of experiencing the outcome.

The distinction between prognostic factor and prediction-model research is especially relevant when competing events are present.

How Should Competing Events Be Handled in Prediction Models?

A prediction model intended to estimate the real-world probability of an event should account for competing events that affect that probability.

For example, a model predicting five-year recurrence in patients at risk of death should distinguish recurrence probability from a hypothetical probability calculated as though death could not prevent recurrence.

Appropriate approaches may include cause-specific hazard models combined to estimate cumulative incidence, direct cumulative incidence modeling, or other suitable competing-risk prediction methods.

Validation should evaluate predicted probabilities against appropriate observed cumulative incidence estimates.

Calibration and discrimination measures should reflect the event type, horizon, and competing-risk structure.

Standard binary prediction methods may be inadequate when they ignore varying follow-up or competing events.

When Are Multistate Models More Appropriate?

Some research questions involve more than one possible transition between states.

For example, a patient may move from hospitalization to discharge, then readmission, and eventually death. A student may progress from enrollment to interruption, reenrollment, completion, or withdrawal.

These processes may not be adequately represented by a single first-event competing-risk analysis.

Multistate models can describe transitions among defined states, including recurrent or intermediate events where appropriate.

However, they require clear state definitions, suitable longitudinal information, and assumptions about transition processes.

Researchers should select a multistate approach when the transitions themselves are central to the question rather than automatically increasing model complexity.

How Do Competing Events Affect Follow-Up Planning?

Competing events should be anticipated when determining follow-up duration and sample size.

If many participants experience a competing event early, fewer may remain at risk of the outcome of interest.

This can reduce the number of target events available for analysis and affect the precision of cumulative incidence estimates.

Researchers should therefore consider expected rates of both the outcome of interest and competing events.

Extending follow-up may increase the number of observed events, but it may also increase the importance of competing outcomes.

Planning follow-up duration in prognostic studies should reflect the full event structure rather than only the target outcome.

How Should Competing Events Be Reported?

Researchers should define the event of interest, competing events, time zero, and follow-up horizon.

They should report the number of each event type and distinguish these events from censoring and loss to follow-up.

For absolute-risk questions, cumulative incidence estimates with appropriate uncertainty should be presented at meaningful time points.

When regression models are used, researchers should specify whether the reported hazard ratios are cause-specific or subdistribution hazard ratios.

Figures should label the estimand clearly rather than describing every curve as a survival probability.

Transparent reporting is necessary because different competing-risk methods can produce quantities with different interpretations.

Why Death Before Readmission Cannot Simply Be Ignored

The example is intentionally simple. The exact numerical difference between a Kaplan-Meier-based estimate and cumulative incidence cannot be reconstructed from aggregate first-event counts alone when event timing and censoring matter.

Actual competing-risk analyses require appropriate event dates, follow-up information, and assumptions concerning censoring.

Common Misconceptions About Competing Events

How to Choose an Appropriate Competing-Risk Strategy

Begin by defining the outcome of interest and identifying events that would prevent it from occurring.

Then determine whether the objective is to estimate actual cumulative event probability, examine a factor's association with an event-specific hazard, or predict transitions among several states.

The study protocol should define each event type, its date, how simultaneous or ambiguous events will be classified, and the outcome horizon.

For prediction research, performance evaluation should correspond to the cumulative incidence or other estimand the model is intended to predict.

The appropriate analysis is the one that represents the actual event process and supports the scientific interpretation researchers intend to make.

Before Analyzing Prognostic Outcomes With Competing Events

Frequently Asked Questions About Competing Events in Prognostic Research

Competing Events Change the Probability of What Can Happen Next

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