Possible alternatives if your data violate Kaplan-Meier assumptions
If the populations from which
data for a Kaplan-Meier estimation were sampled
violate one or more of
the Kaplan-Meier assumptions, the results of the analysis may be
incorrect or misleading.
For example, if the assumption of
independence
of censoring times is violated, then the estimates
for survival may be biased and unreliable.
If there are factors
unaccounted for in the analysis that affect
survival and/or censoring times, then the
Kaplan-Meier method may not give useful estimates
for survival.
In such cases, stratification
of the data or
using a parametric method
may provide a better analysis.
Stratification involves dividing a sample into
subsamples based on one or more characteristics
of the population. For example, a sample may
be stratified by gender. This gives multiple
subsamples, each of which can be analyzed
separately.
If the survival function is different for
the different strata, then the characteristic
used for stratification may be an
implicit factor,
and the separate analysis
for each individual subsample may be more
informative than an analysis of the entire sample.
Stratification may also reveal
correlations between censoring and strata.
A potential drawback with stratification is that one or
more of the subsamples may be small in size, leading to
problems
with the reliability of the estimates.
Also, the results for each subsample are generalizable
to only a part of the sample population.
If a specific survival distribution can be assumed
based on previous knowledge, then that assumption can
be used to make survival estimates.
A specific functional (parametric) form for the survival
distribution function, such as the Weibull distribution
or the exponential distribution,
or the Cox proportional hazards model,
can be fitted to individual data, if a particular
distribution makes sense a priori.
(If the exponential model is appropriate, the
graph of the log of the survival function
[or the cumulative hazard function, which is
-log(survival function)], against
time should look like a straight line passing
through the origin. If the Weibull distribution
is appropriate, a graph of the log of the log of
the survival function [or the log of the cumulative
hazard function] against the log of time should
look like a straight line.)
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it or give you a refund.
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