Why Follow-Up Time Determines What an Outcome Means
A record with no recorded event is not automatically an event-free outcome. A person may have been observed without an event through the required prediction horizon, or follow-up may have ended before that horizon was reached. Those situations look alike in a simple event/no-event field, but they contain different information. The first supports a negative label for that horizon; the second does not establish whether the event would occur later.
This distinction matters when designing a prediction data set. If a model is intended to predict whether an event occurs within a stated period, each record needs enough follow-up to determine that target—or a clearly recorded event within the period. Otherwise, the label is not yet observable. Timeline-based checks make that difference visible.
For a fixed-horizon target, the intended outcome is \(Y(H)=1\) if the event occurs by time \(H\), and \(Y(H)=0\) if it does not occur by time \(H\). The outcome can be assigned from the observed data if the event is observed by both the horizon and the end of follow-up, or if follow-up reaches the horizon without an event. If follow-up ends before the horizon and no event has been observed, the fixed-horizon outcome remains unknown.
Here \(I(\cdot)\) equals 1 when its condition is true and 0 otherwise, and \(R(H)=1\) means the fixed-horizon label is observable. When \(R(H)=0\), the data do not establish \(Y(H)\). The event time \(T\) need not be known exactly for every record: if no event occurs during follow-up, the data may establish only that \(T>C\).
The endpoint convention must be stated. In the examples below, an event recorded at or before the last follow-up time counts as observed, and an event at exactly the horizon counts as occurring by the horizon. A real data specification should define how dates recorded only to the day are handled when event and follow-up dates coincide.
Reading a Timeline
A useful timeline marks the index, the horizon, any observed event, and the last date on which event status is known. The decision is then made in order: Was an event observed by the horizon? If not, did observation continue through the horizon? If neither condition holds, the horizon outcome is immature rather than negative.
State the index time, event definition, and horizon. “Event within 90 days of enrollment” is more precise than “eventually has an event.”
Record the last observable time \(C\) and, if applicable, the observed event time \(T\), both measured from the same index.
An observed event by \(H\) gives a positive label. No event by \(H\) gives a negative label only when observation reaches \(H\). Otherwise, mark the fixed-horizon label unknown.
Worked Timeline Examples
Worked Example: A Record With Complete Follow-Up
A hypothetical benefit administrator wants to predict whether a participant will submit a qualifying claim within 6 months after enrollment. The index is enrollment, month 0; the event is the first qualifying claim; and the horizon is \(H=6\) months. Participant A has no claim recorded, and the administrator can verify claim status through month 6. Determine the label.
Method. Compare the last observable follow-up time with the horizon. Here, \(C=6\) and \(H=6\), so observation reaches the full target window. No event is observed by month 6.
Participant A has an observable negative label for the 6-month target. The conclusion is limited to that target: the record does not establish that the participant will never submit a claim.
Common mistake avoided: Calling the record “no claim ever.” The data support “no qualifying claim within 6 months,” because that is the period observed and the period being predicted.
Worked Example: An Immature Label at the Data Extract Date
A hypothetical service program defines an adverse event as a return visit within 90 days after an initial appointment. The program extracts data 60 days after Client B’s appointment. No return visit is recorded by the extract date. Classify the 90-day outcome.
Method. Measure follow-up from the appointment. The target horizon is \(H=90\) days, but the last observable time is \(C=60\) days. There is no observed event by day 60, and observation does not cover the remaining 30 days.
The 90-day outcome is immature and cannot be labeled negative. The data establish only that no return visit was observed in the first 60 days. Client B could still have a return visit during days 61 through 90.
Common mistake avoided: Coding every record without a recorded event as 0. For this target, that would incorrectly treat 60 days of observation as if it covered 90 days.
Worked Example: An Event Before Follow-Up Ends
A hypothetical equipment warranty program predicts whether a covered failure occurs within 12 months of activation. The event is a verified covered failure. For Unit C, follow-up ends at month 7 because the data source stops supplying records; a verified failure is recorded at month 5. Determine whether the 12-month label is observable.
Method. Check whether the event was observed by the horizon and while follow-up was still available. The event time is \(T=5\), the end of follow-up is \(C=7\), and the horizon is \(H=12\).
Unit C has an observable positive label. Follow-up ending at month 7 does not erase the already observed event at month 5. If no failure had been observed by month 7, however, the 12-month label would be unknown because the remaining 5 months were not observed.
Common mistake avoided: Dropping every record whose follow-up ends before the horizon. A record with an observed event by the horizon already supplies a positive label; it does not need event-free observation through month 12.
Why the Label Rule Works
The fixed-horizon target depends on whether \(T\le H\). The observed record does not necessarily reveal the full event time \(T\), so the label is usable only when the observed information determines which side of the horizon \(T\) falls on. If an event is observed at \(T\le C\) and \(T\le H\), then \(T\le H\) is known, so the label is 1. If there is no observed event but \(C\ge H\), the event did not occur during the observed interval from the index through \(H\), so \(T>H\) and the label is 0. If instead \(C<H\) with no observed event, the observation establishes only \(T>C\); that fact allows both \(C<T\le H\) and \(T>H\). Since either a positive or a negative horizon outcome remains possible, the label cannot be determined.
This is a statement about what the timeline identifies, not a claim that the event is impossible after censoring. A censored record can still contain valuable information about how long the person or unit was observed without the event. For a fixed-horizon binary target, though, that partial observation does not by itself settle the outcome.
Consequences for Data Design
A data extract made on one calendar date creates a particular risk for a fixed-horizon target. Records with recent index dates may not yet have completed the outcome window, while older records may have. If all no-event records are coded negative, the data set mixes observed negatives with immature outcomes. The apparent event rate can then be misleading.
For example, suppose a cohort has 100 records with a 90-day target. By the extract date, 80 have complete 90-day observation, and 20 have only 45 days. Of the 80 mature records, 12 have an event within 90 days and 68 do not. The event proportion among records with observable labels is \(12/80=0.15\), or 15%. If the 20 immature records are incorrectly coded as negative, the apparent proportion becomes \(12/100=0.12\), or 12%. The difference arises solely from using unknown outcomes as if they were known negatives; it does not show that the underlying risk changed.
This calculation does not establish that the 15% mature-record proportion is automatically representative of every record. Whether records with complete follow-up differ from those without it is a separate data-design concern. The immediate requirement is to label records honestly: distinguish positive, negative, and unknown outcomes before deciding how the modeling analysis will handle unknown labels.
The same timeline logic applies to claims, renewals, repeat visits, defaults, and other events measured after an index date. A record may be right-censored because the study or data extract ended, or because observation for that entity ended earlier. The reason is relevant to understanding the data, but it does not change the basic rule: absence of an observed event before an early end of follow-up is not proof of absence through a later horizon.
Common Mistakes and an Audit Checklist
- Using “no recorded event” as a negative label. First check whether the full horizon was observable.
- Confusing the event-free period with the prediction horizon. Being event-free through day 45 does not establish a 90-day negative outcome.
- Discarding a known positive event. An event observed before follow-up ends and within the horizon determines a positive label, even if later follow-up is unavailable.
- Calling a censored record a non-event forever. Censoring marks the boundary of observation, not the end of the event’s possible future.
- Leaving the index or endpoint vague. State what starts the clock, the event definition, the horizon, and how boundary dates are treated.
Before accepting a fixed-horizon outcome field, check whether the event and follow-up dates are measured from the same index; whether the horizon is explicit; whether events before the horizon are captured; and whether no-event records have follow-up through the horizon. Keep immature labels distinct rather than silently assigning them 0. These checks are aligned with the SOA Exam PA (Predictive Analytics) syllabus because they connect data design to the validity of the target a predictive model is asked to learn.
Check Your Understanding
For each problem, use the stated event definition, index, horizon, and follow-up end. Apply the endpoint convention used in this tutorial.
- A hypothetical lender predicts whether a borrower misses a payment within 6 months of account opening. Follow-up is complete through month 6, with no missed payment recorded. Is the label positive, negative, or unknown? (Answer: Observable negative.)
- A hypothetical clinic predicts a repeat visit within 30 days of discharge. A patient has no recorded visit by day 18, when the available records end. What is the 30-day label? (Answer: Unknown, or immature; right-censored at day 18.)
- A hypothetical fleet program predicts a vehicle failure within 9 months of service. Follow-up ends at month 5, and a verified failure is recorded at month 4. Is the target label observable, and what is it? (Answer: Yes; observable positive.)
- A hypothetical membership program predicts cancellation within 120 days of enrollment. One member has no cancellation by day 120, and records confirm follow-up through day 120. Another has no cancellation by day 75, when the source stops reporting. Give each member’s label. (Answer: First member, observable negative; second member, unknown/immature.)
- A hypothetical insurer predicts whether a specified claim occurs within 1 year of policy inception. Of 50 records, 35 have complete 1-year follow-up; 7 of those have the claim. The remaining 15 have no observed claim but only 8 months of follow-up. What is the claim proportion among records with observable labels, and what error results from coding all 15 immature records as negative? (Answer: \(7/35=0.2000\), or 20.00%, among observable labels; coding the 15 as negative gives \(7/50=0.1400\), or 14.00%, incorrectly treating unknown outcomes as negatives.)