Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 46 / 4 / b

Use time since enrolment, and assume the cohorts share a common survival distribution with independent administrative censoring. The PDF starts cohort A in 2006, not the corrupted 2000 date in the TeX aid. During the first follow-up year the pooled sample begins with 200 subjects and has $28+31=59$ deaths, with no earlier censoring. By part (a),At one year, the 69 remaining cohort-B subjects are administratively censored. Cohort A supplies 72 subjects at risk for the second follow-up year, with 24 deaths and 48 survivors. ThereforeThe given grouped totals suffice because there is no censoring inside either follow-up interval; no assumption about the ordering or ties of its deaths is needed.

Cohort A alone would give ${\hat{F}}_A(2)=48/100=0.48$. But two-year survival is the product of first-year survival and conditional survival through the second year. Cohort B contributes a full year's information to the first factor even though it has no second-year follow-up. Omitting it discards useful early deaths and survivors. The pooled estimate $0.47$ combines the first-year information from both cohorts with the conditional second-year information from cohort A.

Thus lack of two-year follow-up is handled by censoring, not by removing the entire short-follow-up cohort. This is cohort pooling under administrative censoring. The criticism assumes comparable time-since-entry survival distributions: if enrolment cohort or calendar period genuinely changes the hazard, naive pooling is not justified. One should model or stratify that effect, and an estimand specifically restricted to cohort A may appropriately use its own survival distribution.