An interval censoring model is carefully defined and the range of its applicability is illustrated. A class of rank tests for the two- and $k$-sample problems is proposed. The statistic is based on the exact ranks of the observed responses and resembles the rank statistic in the usual uncensored case. This statistic is shown to be asymptotically equivalent to the efficient scores test statistic under an assumed parametric model. An alternative rank statistic, based on the estimated ranks of the unobserved variables of interest and applicable under a more general interval censoring model, is also proposed.
"Rank Tests with Interval-Censored Data." Ann. Statist. 16 (4) 1490 - 1502, December, 1988. https://doi.org/10.1214/aos/1176351050