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IAI Actuarial Core Principles · Actuarial Statistics · Purpose and function of data analysis

An actuary studies claim settlement times for 200 health claims using a database extracted on 31 March. For 30 claims, the settlement had not occurred by that date, and the database shows only that the time to settlement exceeds the elapsed time. Which treatment is most appropriate?

The 30 open claims are right-censored: all that is known is that settlement time exceeds the time elapsed. They should be retained and analysed with censoring-aware methods. Deleting them or treating elapsed times as exact would bias settlement times downwards.

  1. ADelete the 30 claims, since their times are unknown
  2. BSet their settlement times equal to the elapsed times and treat them as exact
  3. CTreat them as right-censored observations and use methods that allow for censoringCorrect
  4. DTreat them as left-truncated observations
  5. Replace their times with the mean of the 170 settled claims

Explanation

We know only that the true time exceeds the elapsed time, which is right censoring. Deleting them or treating elapsed times as exact biases settlement times downwards because the longest delays are lost. Mean imputation ignores the information that times exceed the elapsed values, and truncation concerns observations excluded entirely.

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