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

In a Cox model fitted by partial likelihood, which statement about the baseline hazard h0(t) is correct?

β is estimated without specifying the form of the baseline hazard, because h0(t) cancels in every term of the partial likelihood. This is why the Cox model is semi-parametric, and the estimate depends only on the ordering of events and the risk sets.

  1. AThe estimate of β is obtained without specifying the form of h0(t)Correct
  2. Bh0(t) must be specified as a Weibull form before β can be estimated
  3. Ch0(t) must be estimated first and then substituted into the likelihood
  4. DThe partial likelihood depends on the actual lengths of the survival times, not only their order
  5. h0(t) must be constant between death times for estimation to work

Explanation

In each term of the partial likelihood the h0(t) factor cancels between numerator and denominator. So β can be estimated without any assumption on h0(t), which makes the model semi-parametric. The likelihood depends only on the ordering of events and the risk sets, not on exact time values.

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