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

When maximising the Cox partial likelihood in the presence of tied death times, which statement is correct about the methods of handling ties?

Breslow's approximation uses the full risk set at the tied death time as the denominator for every tied death. It is a simple approximation to the exact partial likelihood. Ties occur in practice through rounding and need handling; they are not dropped.

  1. ATies only matter if the baseline hazard is parametric
  2. BBreslow's approximation uses the full risk set at the tied time for every tied deathCorrect
  3. CBreslow's approximation removes tied individuals from the risk set one at a time
  4. DTies never arise in continuous-time models, so no adjustment is needed
  5. Ties are resolved by dropping all tied lives from the data

Explanation

Breslow's approximation treats all tied deaths as sharing the same risk set, and uses the full risk set at that time in each denominator. It does not remove tied lives one at a time. Ties do occur in real data because of rounding, and dropping tied lives would discard information.

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