Examining Kaplan-Meier results to detect assumption
violations
A typical Kaplan-Meier step function plot will have short horizontal runs (the
steps) at the beginning, when there are many subjects and relatively short times
between deaths, and longer steps in later stages of the experiment, when there
are fewer subjects and the wait between noncensored survival times becomes
longer.
If there are relatively few or no tied or censored values, the vertical drops
(the risers) for the steps will all be about the same in height. If a vertical
drop is particularly long, there may be tied
values or many
censored values in a particular interval.
The individual observations can be examined for signs of lack
of independence or lack
of uniformity in the censoring. When examining Kaplan-Meier results, you
should keep these potential problems in mind, along with the possibility of implicit
factors not surfaced in the data.
The problems detectable from the Kaplan-Meier results themselves are often
related to problems due to lack of data.
You should be alert to the possibility of systematic patterns in the
censoring, For example, if there are many values censored earlier in the
experiment rather than later, there may have been a change of conditions
during the experiment. (For example, one physician may have withdrawn referred
patients early on while other doctors did not.) If there was a relatively
large number of censored values in a short span of time, then the censorings
may be related. (For example, a physician transfers to another hospital, and
all referred patients suddenly leave the study.)
A common problem with a survival analysis experiment studying medical
treatments is that patients who do not do well one or more of the treatments
must be withdrawn from the study, so that sicker patients may be more likely
to have censored survival times.
If there are many censored values, the Kaplan-Meier table estimates become
less reliable, and the estimated variances may be considerably smaller than
the actual variances.
If many subjects are censored at approximately the same time, the
possibility of a common cause should be considered. This would violate the
assumption of independence
of censoring and survival times.
If many subjects are left alive at the end of the study, the study may
simply not have continued long enough to give reliable estimates. If the last
observation is censored, the Kaplan-Meier estimate of survival can not reach
0.
Kaplan-Meier's product-limit estimator for survival assumes that the
intervals between deaths are small enough that it is unlikely that there will
be tied survival values. If there are many such tied values, then the survival
estimates may be less reliable. Also, tied survival values may point to the
presence of implicit
factors in the data.
Small sample sizes tend to lead to wide intervals (the times between
successive noncensored survival times), raising the question of whether the
assumption of a constant survival probability within each interval is
appropriate. High
censoring rates also reduce the effective sample size for subsequent
intervals. If the final interval(s) of a study contain only a few subjects,
the Kaplan-Meier estimates for those intervals are not reliable, and should
not be given much weight.
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