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Testing quasi-independence for truncation data. (English) Zbl 1352.62148
Summary: Quasi-independence is a common assumption for analyzing truncated data. To verify this condition, we propose a class of weighted log-rank type statistics that include existing tests proposed by W.-Y. Tsai [Biometrika 77, No. 1, 169–177 (1990; Zbl 0692.62045)] and E. C. Martin and R. A. Betensky [J. Am. Stat. Assoc. 100, No. 470, 484–492 (2005; Zbl 1117.62397)] as special cases. To choose an appropriate weight function that may lead to a more power test, we derive a score test when the dependence structure under the alternative hypothesis is modeled via the odds ratio function proposed by L. Chaieb et al. [Biometrika 93, No. 3, 655–669 (2006; Zbl 1109.62084)]. Asymptotic properties of the proposed tests are established based on the functional delta method which can handle more general situations than results based on rank-statistics or U-statistics. Extension of the proposed methodology under two different censoring settings is also discussed. Simulations are performed to examine finite-sample performances of the proposed method and its competitors. Two datasets are analyzed for illustrative purposes.

MSC:
62N01 Censored data models
62N03 Testing in survival analysis and censored data
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