Occasionally, investigators collect auxiliary marks at the time of failure in a clinical study. Because the failure event may be censored at the end of the follow-up period, these marked endpoints are subject to induced censoring. We propose two new families of two-sample tests for the null hypothesis of no difference in mark-scale distribution that allows for arbitrary associations between mark and time. One family of proposed tests is a nonparametric extension of an existing semi-parametric linear test of the same null hypothesis while a second family of tests is based on novel marked rank processes. Simulation studies indicate that the proposed tests have the desired size and possess adequate statistical power to reject the null hypothesis under a simple change of location in the marginal mark distribution. When the marginal mark distribution has heavy tails, the proposed rank-based tests can be nearly twice as powerful as linear tests.
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