Possible alternatives if your data violate survival test assumptions
If the populations from which
data for a survival test were sampled
violate one or more of
the survival test 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
survival test may not give useful results.
In such cases, stratification
of the data or
using a parametric method
may provide a better analysis.
Although the Mantel-Cox, Gehan-Breslow, and Tarone-Ware
are similar tests, they are not identical. In some
situations,
one of the tests may be preferable to the others.
There are also other nonparametric tests for comparing survival functions.
The best cures for some problems--running an experiment
longer or doing more aggressive follow-up to avoid
a large proportion of censored values, or
using a large enough sample size to lessen the
problems of
small sample sizes--are outside the scope of
statistical analysis per se.
Alternative procedures:
Stratification: Dividing
the sample into homogeneous subsamples
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. The Gehan-Breslow,
Mantel-Cox, and Tarone-Ware tests can all
be used with stratified data.
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 test results.
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 use a survival tests geared to that
particular function.
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.
A Kaplan-Meier or
life table plot of the
survival function may provide a clue.
(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.)
The Mantel-Cox, Gehan-Breslow, and Tarone-Ware tests are quite
similar, but differ in the weight they assign each survival value.
The Gehan-Breslow test gives more weight to earlier failures (deaths),
while the Mantel-Cox test gives equal weight to all failures.
The Tarone-Ware tests falls in between.
The Mantel-Cox test is more powerful
with data following exponential
or Weibull survival distributions, and in situations with random but
equal censoring. It is sensitive to differences in the right tails
of survival distributions (i.e., at later times), and in detecting
non-parallel hazard functions (i.e., lack of proportional hazards).
The Gehan-Breslow test is more powerful with data from a lognormal
survival distribution, but may have low power if there is heavy
censoring.
The Tarone-Ware test, with its intermediate weighting scheme,
is designed to have good power across a wide range of survival
functions, although it may not be the most powerful of the
three tests in a particular situation.
If there are no censored observations (all subjects are followed
until failure/death), then no special survival tests are needed.
If there is no censoring, a two-sample data set
can be analyzed using a Mann-Whitney rank sum test,
and a multi-sample data set
can be analyzed using a Kruskal-Wallis test.
Stratified data with no censoring can be analyzed by using
stratification as blocking and performing a Friedman's test
or a two-sample paired signed-rank test.
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