Skip to content

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

Which statement about the Kaplan-Meier estimate of the survival function is correct?

The Kaplan-Meier estimator is a step function that falls only at observed death times, each time by the fraction of deaths to the number at risk, while censored lives simply leave the risk set afterwards.

  1. AIt is a smooth curve that changes at every censoring time
  2. BIt is a step function that drops only at observed death times, with each drop based on deaths divided by the number at riskCorrect
  3. CIt requires every life to be observed until death
  4. DIt ignores lives censored before the first death
  5. It is a step function that drops at censoring times only

Explanation

Kaplan-Meier is the product of (1 - d_i/n_i) over death times. It changes only at deaths, while censored lives leave the risk set without causing a drop. Censored lives therefore still contribute to n_i until they leave.

Did you get it right without looking?

One question tells you little. A timed set on Estimation procedures for lifetime distributions shows your real accuracy, how long you take and where you lose marks.

Practise Estimation procedures for lifetime distributionsFree diagnostic mock

More Estimation procedures for lifetime distributions questions