Under extremely general patterns of patient-arrival, allocation to treatment and loss to follow-up in (randomized) clinical trial settings, the sequentially computed logrank statistic (Mantel, 1966) is shown (under the null hypothesis of identically distributed lifetimes) to have exactly uncorrelated increments, and is shown via Rebolledo's (1980) martingale invariance principle to satisfy a functional central limit theorem, justifying sequential logrank tests of Jones and Whitehead (1979). Generalizations are made to other two-sample rank tests for censored survival data, and practical applicability to real randomized clinical trials is discussed.
"Sequential Linear Rank Tests for Two-Sample Censored Survival Data." Ann. Statist. 12 (2) 551 - 571, June, 1984. https://doi.org/10.1214/aos/1176346505