Why Define Causes as First Events?
In many studies, more than one type of event matters, but the first event ends observation for the endpoint being studied. For example, after a patient dies, a later disease relapse cannot be observed. A useful description of the data must therefore say not only which events count, but also how to classify a participant whose follow-up ends with one event before another could be observed. The key is to define the endpoint in terms of the first qualifying event.
This definition is operational: it describes what is recorded under a stated follow-up and event-classification rule. It does not require imagining when each of several mutually preventing events would have happened if the others had not occurred. That distinction keeps the observed first-event classification separate from claims about unobserved event times.
Define the Endpoint Before Classifying Follow-Up
A complete endpoint definition names the time origin, the qualifying event types, how event times are determined, and what ends observation. Suppose \(T\) is the time from the origin to the first qualifying event in the course of follow-up, and \(C\) is the time at which observation is censored. If no qualifying event ever occurs, set \(T=\infty\). The observed time is \(Y=\min(T,C)\), and the event indicator is \(\Delta=I(T\leq C)\), subject to a stated convention for an event tied with censoring.
When \(\Delta=1\), record \(J\), the type of the event at time \(T\). When \(\Delta=0\), no first-event cause was observed by the end of follow-up, so \(J\) is undefined in the observed record. It is not an additional cause, and it does not imply that the participant will never experience an event. Crucially, this definition uses the one actual first event under the endpoint rule; it does not define separate hypothetical event times for each cause.
The classification itself does not require a probability model or an assumption that censoring is independent of event risk. Such assumptions may be needed for particular statistical analyses, but they are not needed to decide which event was first in an adequately recorded history. Classification does require consistent event definitions and adequate information to determine event order and type.
Worked Example: Relapse and Death
Consider a hypothetical study that starts follow-up at randomization and records either (1) disease relapse or (2) death before a recorded relapse. The endpoint is the first of these events. A participant relapses at month 14 and dies at month 20.
The relapse occurred first, so \(T=14\) months and \(J=1\), where cause 1 denotes relapse. The later death is not a second first-event cause: the endpoint has already been reached. If instead the participant dies at month 14 with no prior relapse, the recorded first-event cause is \(J=2\), death before relapse. These two cause labels cannot both describe the same participant’s first event.
If a third participant is lost to follow-up at month 14 without either event, then \(C=14\) months and \(\Delta=0\). The record says that no first event was observed before censoring; it does not assign a relapse or death cause.
Why First-Event Causes Are Mutually Exclusive
The exclusivity follows from the ordering rule, not from a claim that only one type of event could ever occur in a person’s life. If two distinct event types occur at different times, only the earlier one can be the first qualifying event. If they occur at the same recorded time, the endpoint needs an explicit rule before a single cause label can be assigned.
This expression refers to the minimum over qualifying events that actually occur under the endpoint definition. It does not take a minimum over event types that were not observed, nor does it require defining an event-specific time for an event prevented by an earlier event. If no qualifying event occurs during the relevant course, \(T=\infty\), and there is no cause label \(J\).
When event times are distinct, the minimum is unique, so exactly one type receives the first-event label. When a tie is possible, the data and protocol must determine what “first” means. A prespecified adjudication rule might use finer time records or clinical review. If neither event can reasonably be selected as first, a distinct simultaneous-event category may be appropriate; it must be defined as part of the endpoint rather than silently assigned to one cause.
Worked Example: Classifying a Hypothetical Follow-Up Table
A hypothetical study follows participants from enrollment for up to 24 months. Its qualifying first events are hospitalization for condition A (cause 1) and death before such a hospitalization (cause 2). A participant is censored at loss to follow-up or at month 24 if neither event has occurred. Assume event times are known to the nearest day and that no ties occur in these records.
| Participant | Recorded history | Observed time \(Y\) | \(\Delta\) | First-event cause \(J\) |
|---|---|---|---|---|
| A | Condition A hospitalization at month 8 | 8 months | 1 | 1 |
| B | Death at month 11, no earlier hospitalization | 11 months | 1 | 2 |
| C | Lost at month 6, no event recorded | 6 months | 0 | Undefined |
| D | No event through month 24 | 24 months | 0 | Undefined |
| E | Hospitalized at month 9, died at month 15 | 9 months | 1 | 1 |
For participant A, the first event is the condition A hospitalization: \(Y=\min(8,C)=8\) months, \(\Delta=1\), and \(J=1\). For participant B, death occurs first, so \(Y=11\) months, \(\Delta=1\), and \(J=2\). Participant C contributes an observed follow-up time of 6 months but no event indicator or cause: \(Y=6\), \(\Delta=0\), and \(J\) is undefined. Participant D also has \(\Delta=0\); reaching the administrative end of follow-up is not itself a qualifying event. Participant E is assigned cause 1 because hospitalization preceded death. The later death does not alter the first-event classification.
The endpoint rules justify every classification: the event types are explicit, the origin and maximum follow-up are specified, and the example states that recorded event times are not tied. If a record did contain an unresolved tie, assigning either cause without a rule would not be justified.
Competing Events, Censoring, and Other Summaries
A competing event is a qualifying event type that can occur first and thereby prevents observation of another event type as the first event. Death before relapse is a familiar example when relapse is the endpoint of interest. By contrast, loss to follow-up is generally censoring: it ends observation but is not itself a clinical event type in the endpoint. Administrative study end is likewise not a cause unless the study explicitly defines it as a substantive event, which is unusual.
This distinction matters because an unobserved event after a competing event is not the same as an event known to have occurred later. If death precedes a possible relapse, the record establishes death as the first event. It does not establish whether the person would have relapsed later in a hypothetical world without death. The first-event data alone do not answer that counterfactual question.
A composite endpoint takes a different approach: it combines several event types into one outcome, such as “relapse or death.” It can simplify the outcome definition but does not retain which component occurred unless component information is also reported. A multi-state description can represent transitions and later events when these are observed and relevant; a first-event classification instead stops at the earliest qualifying event. These approaches answer different questions, so the choice should follow the scientific endpoint rather than convenience.
Worked Example: Tied Events and a Prespecified Rule
Suppose a hypothetical registry records both an organ failure and death for one participant on the same calendar date. The study’s endpoint includes organ failure (cause 1) and death before organ failure (cause 2). Daily records do not establish which occurred first.
The data as stated do not support assigning cause 1 or cause 2: the ordering needed to distinguish them is unknown. If the protocol prespecified that clinical adjudicators use source records to determine sequence, the adjudication result can determine the cause. If sequence remains indeterminate, the study could record a distinct simultaneous/indeterminate category, provided that category was defined and its use is reported. It would be incorrect to choose cause 1 merely because organ failure is the primary scientific interest.
The classification is valid only if the rule is applied consistently to all such records. A tie rule chosen after inspecting which assignment favors a preferred result can make comparisons biased and difficult to interpret.
Diagnostics, Limitations, and Common Mistakes
Before analyzing first-event data, inspect whether the endpoint can be applied reproducibly. Check that the origin is clear, event definitions do not overlap unintentionally, and records contain enough timing detail to order events. Review the frequencies of each cause, censoring, and unresolved or adjudicated ties. If different sites use different definitions or timing precision, apparent cause differences may reflect recording practice rather than differences in event occurrence.
- Mistake: treating censoring as a competing cause. A participant lost to follow-up without an event has no observed first-event cause. Record the censoring time and event indicator; do not create a clinical cause label.
- Mistake: assigning multiple first causes. Later events can be recorded in a richer event history, but they are not additional first-event labels. Apply the endpoint’s ordering rule.
- Mistake: treating an unobserved event as if it occurred. An event prevented from being observed by an earlier event has no observed time or first-event label. Do not infer its occurrence or timing from the competing event alone.
- Mistake: assuming a recorded timestamp resolves a tie. Dates rounded to a day may conceal the true order. Check the resolution of the timing data and use a prespecified rule for unresolved cases.
- Mistake: calling the cause label an explanation. \(J\) classifies the type of first event under the endpoint definition. It does not, by itself, establish why the event occurred or a causal effect of treatment.
The first-event framework is limited to the question it defines. It discards the order and timing of later events from the first-event outcome, and its cause labels depend on event definitions and ascertainment. Those features are not defects when the first event is the scientific target, but they should be explicit when interpreting results.
Check Your Understanding
Answer each question using the first-event rules. Solutions follow the questions.
- A participant has event type 2 at month 5 and event type 1 at month 9. Which event is the first-event cause, and why?
- A participant is lost at month 7 without an observed qualifying event. Is loss a competing cause? State the observed event indicator and cause status.
- Why should separate hypothetical times for every event type not be required to define an observed first-event cause?
- Two qualifying events are recorded on the same date, with no information about their order. What must be resolved before assigning one cause label?
- Explain one difference between a composite endpoint and a first-event cause classification.
Solutions. (1) Cause 2 is first because its event occurred at month 5, before the event of type 1 at month 9. The later event does not change the first-event label. (2) No. Loss to follow-up is censoring here, so \(\Delta=0\) and no cause is observed; \(J\) is undefined. (3) The classification uses the earliest event that actually occurs under the endpoint definition. A competing event may prevent another event from being observed, so assigning that unobserved event a separate hypothetical time would add information the record does not provide. (4) A prespecified tie rule must establish which event was first, or the endpoint must define a joint or indeterminate category for unresolved ties. The record alone does not justify choosing one cause. (5) A composite endpoint combines component events into one outcome, whereas a cause classification retains which type was the first qualifying event. A composite may therefore lose component identity unless it is separately reported.