At each distinct event time , let events occur among people in the risk set. The Kaplan–Meier estimator iscensorings remove people from later risk sets but create no factor.
Left truncation, or delayed entry, means that an individual is observed only after surviving to an entry time. A registry assembled from patients alive when a clinic opens is a practical example. Adapt Kaplan–Meier by admitting each person to the risk set only at their entry time.
Period survival analysis is useful when recent prognosis is desired but complete long-term follow-up of a recent diagnosis cohort is unavailable. For a chosen calendar year, intersect every patient's observed follow-up with that year. Express the surviving pieces on the time-since-diagnosis scale, treat the beginning of the calendar window as delayed entry and its end as right censoring, and apply Kaplan–Meier with those entry and exit times.
Take the 2017 calendar window to be on the supplied month scale. Intersecting each follow-up interval with this window and translating to time since diagnosis gives:
- patient 1: delayed entry at duration 10 and censoring at 22;
- patient 3: delayed entry at 8 and death at 15;
- patient 4: delayed entry at 4 and censoring at 7;
- patient 5: delayed entry at 2 and censoring at 14;
- patient 6: entry at 0 and censoring at 9;
- patient 7: entry at 0 and death at 6;
- patient 8: entry at 0 and censoring at 6;
- patient 9: entry at 0 and censoring at 4.
Patient 2 died before the period and patient 10 entered after it, so neither contributes. At duration 6, patients 4, 5, 6, 7, and 8 are at risk, giving factor . At duration 15, patients 1 and 3 are at risk, giving factor . Therefore the period Kaplan–Meier estimator isover the range supported by the period data.
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