Past exam of the mathematics course of the University of Cambridge 2016 iii Paper 207 4 d Solution Created 2026-10-03 Updated 2026-10-06
Assign the seventh individual's event weights , the conditional probabilities obtained from the original Kaplan–Meier estimator. The last three fractional counts areTheir conditional event fractions are , , and , exactly as in the original censored-data calculation. Hence the fractional allocation reproduces the original estimate:This illustrates self-consistency of Kaplan–Meier estimation: distributing the unobserved event according to the current conditional fitted event distribution leaves the fitted distribution unchanged. The first imputation in part (b) was not such a self-consistent allocation.