Exercise: survival after retirement, suggested answer 1

Graph with 'Probability of survival' on vertical axis, 'Survival time (years)' on horizontal. Two curved lines from survival time = 0, probability = 1.0, going down more and more steeply to time = 20, probablity = 0.38 and probability = 0.30 approximately. Upper line is 'Retired at 65', lower line is 'Retired at 55'.

1. What kind of graph is this? What assumptions are required about the data? Do you think they are plausible?

Suggested answer

This graph shows two Kaplan Meier survival curves, for those who retired at age 65 and those who retired at age 55. The curves are calculated as follows. At each time when there is an event, we calculate the proportion who do not experience an event. We multiply these together for all the times up to the index time to give the proportion who have not experienced the event up to and including this time.

The assumptions required are that observations are independent and that those who are censored are not different from those followed up to death, so that those who are recruited at the end of the study should not differ in their survival probabilities from those at the beginning. The latter is unlikely to be true. People were recruited over a 30 year period, when mortality rates at all ages were falling, so the mortality rates experienced by the earliest recruits may be greater than those experienced be the latest recruits at corresponding ages.

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Last updated: 31 July, 2006.