AI Glossary / Governance, ethics and safety / Intermediate
Risk set
Definition
A risk set is the collection of study subjects or units that are being observed and are eligible to experience a specified event at a particular time. In a standard time-to-first-event analysis, it includes those who have entered observation and have not yet had the event or been censored before that time. The risk set changes as observation proceeds.
What it means
The word risk here does not mean that every member is considered high risk. It means that the unit belongs in the relevant comparison at that moment. A machine that already failed is no longer eligible for its first failure, while one whose monitoring has ended cannot contribute later observed follow-up. Risk sets provide the changing denominators needed for survival analysis. This differs from a risk register, which lists organizational concerns, and from a risk group, which classifies people or items by a predicted score.
How it works
Choose the event, time origin, and observation rules. At each event time, determine who is under observation and still eligible just before the event occurs. Record events and censoring consistently, and account for delayed entry when units begin observation later. Kaplan - Meier estimation uses event counts relative to the number at risk to update survival estimates. Cox-model calculations also use risk sets when comparing the unit experiencing an event with eligible units at that time. Recurrent-event and multistate analyses require more specialized definitions because a unit's eligibility can change or resume.
Three practical examples
- A maintenance study tracks which devices remain under observation and have not yet experienced their first failure at each failure time.
- A service study examines time until a user's first return visit, updating the risk set as follow-up ends or the visit occurs.
- An AI survival model uses event-time data to predict time until equipment replacement, with careful distinction between observed replacements and records whose observation ended. These examples require a clear event definition before any denominator is calculated.
Think of it this way
Think of a race official tracking who is still on the course before each finish. Someone who has finished is no longer eligible to be the next first-time finisher, and someone whose tracking stopped cannot simply be assumed to remain observed. The analogy is limited because survival studies may allow delayed entry, censoring, or multiple types of transition, so the statistical rules can be more complex than a single race.
Worked example
Suppose five fictional devices, A through E, begin observation at time 0. A fails at time 2. B is last observed without failure at time 3 and is then right-censored. C fails at time 4. D and E remain observed beyond time 4. Just before time 2, the risk set contains all five devices; the first Kaplan - Meier survival factor is 1 - 1/5 = 4/5. Just before time 4, A has failed and B has been censored, so the risk set contains C, D, and E. The next factor is 1 - 1/3 = 2/3. The survival estimate immediately after time 4 is (4/5)×(2/3) = 8/15, approximately 53.3%. B's censoring removes later observation; it is not counted as a failure or as proof of indefinite survival.
Illustrative case study
Fictional case: Harbor Equipment initially divides every observed failure by the original fleet size, even after some devices leave monitoring. An analyst reconstructs entry, event, and censoring times and explains the changing risk sets. The team also investigates why monitoring ended, because departures linked to impending failures could undermine a simple analysis. This invented case illustrates both correct denominator construction and the need to examine censoring assumptions. Rebuilding the risk set alone does not guarantee an unbiased survival estimate.
Common misconceptions and mistakes
The risk set is not always the original sample and not simply the people who eventually experience the event. Censored units contribute while they are observed and eligible, then stop contributing later follow-up under the specified rules. Censoring is not equivalent to a negative outcome. The order of events and censoring at the same recorded time can matter, so the method's convention should be understood. Delayed-entry units should not be counted before they enter observation. A changing risk set is expected and should not be confused with arbitrary deletion of inconvenient records.
Business use
When using AI for time-to-event prediction, preserve the timestamps and event-status information needed to construct risk sets. Define what counts as entry, failure, withdrawal, and end of observation. Audit missing or inconsistent times and report how many units remain under observation at important horizons. Assess whether censoring assumptions are plausible for the intended analysis. Avoid evaluating long-term predictions as if all units had complete follow-up. In complex settings with competing or recurrent events, use a method and risk-set definition that matches the actual process.
People also ask
Does being in the risk set mean someone has a high predicted risk?
No. It means they are eligible and observed for the event comparison at that time.
Does censoring mean the event never happened?
No. It means the available observation does not establish the later event time.
Can a unit enter a risk set after the study starts?
Yes, in delayed-entry designs, using appropriate methods and timing rules.
Check your understanding
A device leaves monitoring before the next observed failure elsewhere. Should it remain in the later observed risk set as if monitoring continued?
Answer: No. Its contribution ends according to the censoring or observation rules. That does not imply that it failed or remained failure-free forever.
Related terms
- Survival analysis
- Censoring
- Cox model
- delayed entry
- Kaplan–Meier estimator
- hazard
- event time
- competing risks
- number at risk
Learn next
Draw timelines for five units with different event and censoring times. List the risk set just before each event. Then add a late-entering unit and explain when it can first contribute to the comparison.
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Sources
Frank Harrell, Glossary of Statistical Terms, risk set: https://hbiostat.org/glossary/ R survival package, survival-curve documentation: https://stat.ethz.ch/R-manual/R-devel/library/survival/help/survfit.html R survival package, time-based observation intervals: https://www.stat.ethz.ch/R-manual/R-devel/library/survival/html/tmerge.html NIST, censoring in reliability studies: https://www.itl.nist.gov/div898/handbook/apr/section1/apr131.htm
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