Reconcile Risk Sets at Each Survival Event Time

Define who is at risk immediately before each event

A survival calculation uses the participants eligible to experience the event at each relevant time. Record the time origin, event definition, entry rule, and censoring rule before constructing that sequence. The number initially enrolled is not necessarily the denominator at every later event time.

The official survival package documentation describes survival curves through the numbers at risk and events at distinct event times. Aggregating events into broad intervals can discard the timing information needed for that calculation.

Reconcile ordered rows

For each exact-time row, record the starting risk set, events, censorings, and entries that occur after the row. Under the demonstration tool's convention, events occur before same-time censorings and new entries join afterward. The next starting risk set must equal the current start minus events and censorings plus those entries.

This ordering is a stated computational convention, not permission to guess when events occurred. If actual entry or censoring happens between distinct event times, place it consistently in the event-time history. Resolve ties and delayed entry using the study's definitions and the analysis software's documented conventions.

Check a fictional two-row history

Suppose the first row starts with 100 at risk, has five events and ten subsequent censorings, and no new entries. Its conditional survival factor is 1−5/100 = 0.95, and the next risk set is 85.

At the next row, five events occur among 85 at risk, with no censorings or entries. The second factor is 80/85. Their product is approximately 0.894118, with 80 remaining after the row. The survival-risk-set tool reproduces this invented history and checks row consistency.

Review what the product assumes

Use the risk-set worksheet to preserve ordered counts and their source. Confirm that participants do not disappear, reappear, or contribute an event after their recorded exit. Do not substitute total event count divided by baseline enrollment for the product calculation when censoring changes denominators.

The tool is an exact-time arithmetic illustration, not a grouped actuarial life table, full survival analysis, or validation of independent censoring and truncation assumptions. It cannot recover event order from an interval total or estimate a competing-risk cumulative incidence merely by changing labels.

Inspect whether loss to follow-up plausibly relates to future outcomes and whether delayed-entry eligibility is represented correctly. A reconciled table can still support a biased estimate if these assumptions fail.

Finish with the event definition, time scale, ordered risk-set audit, and unresolved timing questions. Keep uncertainty intervals and model diagnostics tied to the intended full analysis. A smooth decreasing survival curve is not enough evidence that its denominators and censoring process were handled correctly.

Source checked on 4 November 2026; fictional risk sets independently recalculated.