"Nonparametric comparison of two survival time distributions in the
presence of dependent censoring"

A. G. DiRIENZO 
Department of Biostatistics, Harvard School of Public Health, 
Boston, Massachusetts 02115, U.S.A.

When the distribution of time to censoring is independent of
randomized treatment group, the logrank test of the null
hypothesis, that treatment-specific survival time distributions 
are equal, is asymptotically valid.  We introduce a test of the
null for use when the distribution of time to censoring depends 
on treatment group and further on survival time.  This test does not 
make any assumptions regarding independence of censoring time and 
survival time distributions.  Asymptotic validity of this test only
requires a consistent estimate of the conditional probability that 
the survival event is observed given both treatment group and that 
the survival event occurred before the time of analysis.  However, 
by not making unverifiable assumptions about the data generating 
process,  for each treatment group, all that can be identified 
from the observed data is the interval within which the corresponding 
sample mean estimate of this probability must lie.  Over this rectangle 
in the unit square the proposed test can be calculated, and a rejection 
region identified.  A decision on the null that considers uncertainty 
because of censoring that may depend on treatment group and further on 
survival time, can then be directly made.  

We also present a generalized logrank test that can be used when the
distribution of censoring depends on treatment group and survival time.
Introduction of this test enables conditions to be provided under which 
the ordinary logrank test is asymptotically valid.  However, this 
generalized test may not be well suited for data analysis because of 
the complexity of required sensitivity analyzes.  A simulation study 
and an example using a recent AIDS clinical trial are provided.