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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)

In a three-state illness-death model (healthy H, sick S, dead D) with constant transition intensities, a study observes 400 life-years in state H, with 20 transitions H to S and 8 transitions H to D. What is the maximum likelihood estimate of the total force of exit from state H, and the probability that a healthy life stays healthy for 2 years under it?

The total exit force from the healthy state is (20+8)/400 = 0.07, so the probability of remaining healthy for 2 years is exp(-0.14). Both exit types must be counted, and the duration of two years multiplies the intensity.

  1. A0.070 and exp(-0.14)Correct
  2. B0.070 and exp(-0.07)
  3. C0.050 and exp(-0.10)
  4. D0.020 and exp(-0.04)
  5. 0.070 and 1-0.14

Explanation

Total exit intensity estimate = (20+8)/400 = 0.07. Staying in H for 2 years has probability exp(-0.07*2) = exp(-0.14). exp(-0.07) ignores the 2-year duration; 0.05 omits deaths.

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