 Solution

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.