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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Estimation procedures for lifetime distributions

In the Kaplan-Meier estimator, a life censored at time t, where a death also occurs at the same time t, is normally treated in which way?

The censored life is kept in the risk set at the death time. The usual convention treats censoring as happening just after deaths at the same time, so the life counts in the denominator but not as a death.

  1. AAs having died just before t, so removed from the risk set
  2. BAs being in the risk set at t, since censoring is assumed to occur just after deaths at that timeCorrect
  3. CAs not contributing at all to the data
  4. DAs left truncated at t
  5. As having died at t, adding to the death count

Explanation

Standard convention places censoring just after deaths at the same time, so the censored life remains in the risk set for that death time. This slightly lowers each hazard estimate relative to removing the life earlier.

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