Some small violations may have little practical effect on the analysis, while other violations may render the survival test results uselessly incorrect or uninterpretable. In particular, small sample sizes may increase the effect of assumption violations. Heavy censoring or crossing hazard or survival functions may also affect the reliability of the survival tests.
Implicit factors can also affect censoring times, by affecting the probability that a subject will be withdrawn from the study or lost to follow-up. For example, younger subjects may tend to move away (and be lost to follow-up) more frequently than older subjects, so that age (an implicit factor) is correlated with censoring. If the sample under study contains many younger people, the results of the study may be substantially biased because of the different patterns of censoring. This violates the assumption that the censored values and the noncensored values all come from the same survival distribution.
Stratification can be used to control for an implicit factor. For example, age groups (such as under 50, 51-60, 61-70 and 71 or older) can be used as strata to control for age. This is similar to using blocking in analysis of variance. The goal is to have each group/stratum combination's subjects have the same survival distribution.
If a loss or withdrawal of one subject could tend to increase the probability of loss or withdrawal of other subjects, this would also lead to lack of independence between censoring and the subjects.
The survival tests rely on independence between censoring times and survival times. If independence does not hold, the results may be inaccurate.
An implicit factor not accounted for by stratification may lead to a lack of independence between censoring times and observed survival times.
A high censoring rate may also indicate problems with the study: ending too soon (many subjects still alive at the end of the study), or a pattern in the censoring (many subjects withdrawn at the same time, younger patients being lost to follow-up sooner than older ones, etc.)
The survival tests perform better when the censoring is not too heavy, and, in particular, when the pattern of censoring is similar across the different groups.
A Kaplan-Meier plot, plots of the life table survival
functions, plots of the life table hazard functions
for each sample will demonstrate whether the
survival functions or hazard functions cross
(are non-parallel). If the functions do cross
then none of the three tests (Gehan-Breslow,
Mantel-Cox, or Tarone-Ware) will be particularly
good at detecting differences between the
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