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

In a mortality investigation using the two-state model, a life is observed from age 40 and the observation ends because the life withdraws from the study alive at age 43.5. How should this life be treated in the MLE of μ?

The life adds 3.5 years to the total waiting time and adds nothing to the death count. A censored life was at risk for the time observed, so excluding it would overstate mortality.

  1. AContributes 3.5 to V and 1 to D
  2. BContributes 3.5 to V and nothing to DCorrect
  3. CIs excluded from the data altogether
  4. DContributes 0 to V and 1 to D
  5. Contributes 3.5 to D and nothing to V

Explanation

Withdrawal is censoring, which is non-informative here. The life was exposed to the risk of death for 3.5 years, so that time enters V. Since no death occurred, D is not increased. Excluding the life would discard valid exposure and bias the estimate upward.

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