Time intervals in K-M or N-A estimates

[Lauren]

Hi

I have a question about how to determine the final time interval to use when specifying the Kaplan-Meier / Nelson-Aalen estimate of the survival function.

I understand that if the last observation was a death, then the final time interval will be t >= time of that last death. However, when the last observation is a censor, I've seen inconsistent answers.

For example, in Q10 of CT4 April 2011, the last observation was a censor at duration 87 days. However, the final time interval went from the time of the last death to 92 days, the overall period of investigation from 1 June-31 August (even though no lives were observed past a duration of 87 days).

However, in Q8 of CT4 September 2014, the last observation was a censor at duration 36 days. The final time interval went from the time of the last death to 36 days, even though the overall period of investigation from 1 January - 28 February is 59 days.

Please could someone tell me the correct approach to use? I'm struggling to understand why it's so inconsistent. My understanding tells me it should be the time of last censor since no lives were observed past this time so you can't say what happens to the survival function, but the first approach was used in questions in the notes as well.

 

[Dave Johnson]

Hi Lauren

I agree the approach sometimes appears to be inconsistent. CT4 Apr 11 Q10 has come up before, and my response was that the survival function should only run to 87 days, and in fact if you look at the chart for part (iii) in the Examiners Report you will see that it clearly only runs to 87 days and not 92!

I would use the following convention:

• If there are no surviving lives at the end of the investigation then the survival function should run to infinity (since no new information could change it)
• If there are surviving lives then the survival function should run up to the time of the last censoring but no further

I think the confusion occurs when the times are rebased to (eg) time since surgery/onset of the disease, which means that we will often see the number of lives gradually fall to zero rather than cut off suddenly. However this does not affect the methodology, and so the length of the study will become the longest time that any life was observed for, rather than the calendar difference between the start and end of all observations.

Hope that helps

Dave