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Resampling-Based Inference for the Mann-Whitney Effect for Right-Censored and Tied Data
Dennis Dobler, Ulm University

In a two-sample survival setting with independent survival variables $T_1$ and $T_2$ and independent right-censoring, the Mann-Whitney effect $p = P(T_1 > T_2) + \frac12 P(T_1 = T_2)$ is an intuitive measure for discriminating two survival distributions. Comparing two treatments, the case $p> 1/2$ suggests the superiority of the first. Nonparametric maximum likelihood estimators based on normalized Kaplan-Meier estimators naturally handle tied data, which are omnipresent in practical applications. Studentizations allow for asymptotically accurate inference for $p$. For small samples, however, coverage probabilities of confidence intervals are considerably enhanced by means of bootstrap and permutation techniques. The latter even yields finitely exact procedures in the situation of exchangeable data.Simulation results support all theoretic properties under various censoring and distribution set-ups.

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Eurandom 2012