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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Maximum likelihood estimators for transition intensities

A three-state model has states H (healthy), S (sick) and D (dead) with constant transition intensities. Over the study, the total time spent in state H by all lives was 5,000 years. There were 150 transitions H to S, 50 transitions H to D and 100 transitions S to H. Which is the MLE of the intensity from H to S?

The estimate is 150 transitions from H to S divided by 5,000 years spent in state H, giving 0.03. Only the specific transition count and the waiting time in the originating state are used, not transitions from other states.

  1. A0.010
  2. B0.020
  3. C0.030Correct
  4. D0.040
  5. 0.060

Explanation

The MLE of a transition intensity from state i to j is the number of i-to-j transitions divided by total time spent in state i. Here it is 150/5000 = 0.03. Using 200 transitions out of H would give 0.04, which is the total exit intensity, not the H to S one.

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