Examining survival test results to detect assumption
violations
The individual observations can be examined for signs of lack
of independence or lack
of uniformity in the censoring. When examining survival test results, you
should keep these potential problems in mind, along with the possibility of implicit
factors not surfaced in the data (unless you used stratification
to control for such a factor).
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 (For example, one physician may have withdrawn referred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 were 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must be withdrawn from the study, so that sicker patients may be more likely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 effective sample size becomes
smaller and the survival test results become less reliable.
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 provide a reliable comparison of
survival functions.
Small sample sizes tend to violate the asymptotic estimation assumptions
that the Gehan-Breslow, Mantel-Cox, and Tarone-Ware survival tests rely on. High
censoring rates also reduce the effective sample size for subsequent
intervals.
If the assumptions for the censoring and survival distributions are
correct, then a plot of either the censored or the noncensored values (or both
together) against time should show no particular patterns.
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