This paper introduces a novel nonparametric approach for testing the equality of two of more survival distributions when the group membership information are not available for the right censored individuals. Although such data structures arise in practice very often, this problem has received less than satisfactory treatment in the nonparametric testing literature. Currently there is no nonparametric test for this hypothesis in its full generality in the presence of right censored data. We propose to use the imputed group membership for the censored observations leading to fractional weights that can be used with a two sample censored data test. We obtain an asymptotic linear representation of our test statistic and propose two resampling alternatives which might be easier to use in practice. We study a class of weighted log-rank tests obtained this way through simulation. We illustrate our testing methodology using two real data sets.
A Novel Approach to Testing Equality of Survival Distributions When the Group Memberships are Censored