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

In the Cox proportional hazards model h(t; z) = h0(t) exp(β'z), which feature of the model is left unspecified when β is estimated by partial likelihood?

The baseline hazard h0(t) is left unspecified. In the partial likelihood it cancels from each ratio of hazards across the risk set, so β can be estimated without choosing any parametric form for the baseline. The linear predictor and proportional hazards remain assumptions.

  1. AThe baseline hazard h0(t)Correct
  2. BThe covariate vector z
  3. CThe linear form of β'z
  4. DThe exponential link applied to β'z
  5. The proportionality of hazards between individuals

Explanation

The Cox model is semi-parametric. The partial likelihood is built from ratios of exp(β'z) over the risk set, so h0(t) cancels and need not be specified. The other features, such as the linear predictor, the exponential link and proportionality, are still assumed.

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