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

A pension scheme includes only members who were alive and aged at least 60 when it began in 2015, and follows them until death or 2024. Members who died before reaching the scheme's start date are absent from the data. What is the effect on the lifetime data of a person joining at age 65?

The lifetime is left truncated at 65. The member is observed only because they survived to that age, so the likelihood contribution must be conditioned on survival to 65, dividing by S(65).

  1. AThe lifetime is right truncated at 65
  2. BThe lifetime is left truncated at 65, so likelihood is conditional on survival to 65Correct
  3. CThe lifetime is left censored at 65, so the death is known to be before 65
  4. DThe lifetime is interval censored from 60 to 65
  5. The lifetime is unaffected because entry age does not alter the likelihood

Explanation

Only people who survived to entry are observed, so the data are left truncated at the entry age. The likelihood contribution must be conditional on survival to entry, such as f(x)/S(65) for a death or S(x)/S(65) for a censoring. Ignoring this biases estimated mortality downward.

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