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

In a Cox model with a single binary covariate z (1 = smoker, 0 = non-smoker), the estimated coefficient is β̂ = 0.405. Taking e^0.405 ≈ 1.5, which statement is correct?

The smoker's hazard is about 1.5 times the non-smoker's at every duration. The Cox model gives a constant hazard ratio exp(β̂), here e^0.405 ≈ 1.5. It is a multiplicative effect on the hazard, not an additive one and not a statement about survival probabilities.

  1. AAt every duration, a smoker's hazard is about 1.5 times a non-smoker'sCorrect
  2. BA smoker's hazard exceeds a non-smoker's by 0.405 at every duration
  3. CA smoker's survival probability is 1.5 times a non-smoker's at every duration
  4. DA smoker's expected lifetime is 1.5 times a non-smoker's
  5. A smoker's hazard is 40.5% higher than a non-smoker's only at time zero

Explanation

The hazard ratio is exp(β̂) = 1.5, constant over time under proportional hazards. It is a ratio of hazards, not a difference, and not a ratio of survival probabilities or expected lifetimes.

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