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

A Cox model with a single covariate z (1 = smoker, 0 = non-smoker) gives an estimated β of 0.4055. Using exp(0.4055) = 1.5, which statement is correct?

The smokers' hazard is 1.5 times the non-smokers' hazard at every duration, because exp(0.4055) = 1.5 is the hazard ratio and the proportional hazards assumption keeps it constant over time. Beta itself is the log hazard ratio.

  1. AThe hazard for smokers is 1.5 times that of non-smokers at every durationCorrect
  2. BThe hazard for smokers is 0.4055 times that of non-smokers at every duration
  3. CThe hazard for smokers is 0.5 higher than that of non-smokers at every duration
  4. DSmokers' survival probability is 1.5 times that of non-smokers
  5. The hazard for smokers is 1.5 times that of non-smokers only at duration zero

Explanation

The hazard ratio is exp(β) = 1.5, and under proportional hazards it applies at all durations. The additive reading (0.5 higher) confuses a ratio with a difference. The coefficient itself is a log hazard ratio, not the ratio.

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