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Which one (if any) of the below sentences correctly describe the interpretation of the median of a Kaplan-Meier product limit estimate of survival when the time-frame is the age of the study participants?

a) "The median age of males at the time of death was 14,732 days and the median age of females was 16,328".

b) "The age at which half of the study participants had expired was 14,732 and 16,328 days for males and females respectively".

c) "The median survival was 14,732 days and 16,328 days for males and females respectively."

I created an example below. I am fully aware that it makes no sense to analyse this particular data in this fashion and it is only included for illustrative purposes.

library(survival)
lung$age_start <- lung$age * 365
lung$age_stop <- lung$age_start + lung$time
sf <- survfit(Surv(age_start, age_stop, status) ~ sex, data = lung)

#       records n.max n.start events median 0.95LCL 0.95UCL
# sex=1     138    11       0    112  14732      NA      NA
# sex=2      90     8       0     53  16328   16227      NA
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Interpretation of Kaplan-Meier when age is the timescale of interest is not straightforward, as delayed entries are commonly introduced. The median age at the event is not interpreted as the age by which 50% of the study population has experienced the event of interest. It may occur, for example, that by age a, less than 50% of participants have actually entered the study. An intuitive way of taking into account the presence of delayed entries, simplifying the interpretation of the percentiles of attained age, is to condition each individual survival experience on his/her baseline age.

All three interpretations you provide are correct if you condition on the age at baseline of the participants.

You may find this paper of mine of interest, there is a section where we discuss how the interpretation of survival percentiles differs when changing time scale: Bellavia, A., Discacciati, A., Bottai, M., Wolk, A. and Orsini, N., 2015. Using Laplace Regression to model and predict percentiles of age at death when age is the primary time scale. American journal of epidemiology, 182(3), pp.271-277.

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  • $\begingroup$ An excellent response and interesting article. To clarify, would I be correct in thinking that in the special case wherein all individuals enter the study at the same age (i.e. a birth-cohort) the usual interpretation of medians apply, as I write them above? $\endgroup$ Jul 24, 2017 at 10:29
  • $\begingroup$ Exactly, that is a special case where the interpretation is simplifed $\endgroup$
    – andbel
    Aug 11, 2017 at 15:57

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