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On Mann–Whitney tests for comparing sojourn time distributions when the transition times are right censored

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  • Jie Fan
  • Somnath Datta

Abstract

We consider the problem of comparing sojourn time distributions of a transient state in a general multistate system in two samples (groups) when the transition times are right censored. Using the reweighting principle, a two-sample Mann–Whitney type of $$U$$ -statistic is constructed that compares only the uncensored sojourn times from the two distributions. A second Mann–Whitney type of statistic is also constructed using a different reweighting that allows for comparisons when one of the two sojourn times is either uncensored or singly censored. Both these statistics are asymptotically unbiased, asymptotically normally distributed and reduce to the standard Mann–Whitney statistic when there is no censoring. A test of equality of sojourn time distributions in two independent samples is constructed by symmetrizing the second statistic. The testing methodology is illustrated using a data set on kidney disease patients. Copyright The Institute of Statistical Mathematics, Tokyo 2013

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  • Jie Fan & Somnath Datta, 2013. "On Mann–Whitney tests for comparing sojourn time distributions when the transition times are right censored," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 149-166, February.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:1:p:149-166
    DOI: 10.1007/s10463-012-0378-5
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    References listed on IDEAS

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    1. Fan, Jie & Datta, Somnath, 2011. "Fitting marginal accelerated failure time models to clustered survival data with potentially informative cluster size," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3295-3303, December.
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    4. Somnath Datta & Dipankar Bandyopadhyay & Glen A. Satten, 2010. "Inverse Probability of Censoring Weighted U‐statistics for Right‐Censored Data with an Application to Testing Hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 680-700, December.
    5. D. Y. Lin & Zhiliang Ying, 2001. "Nonparametric Tests for the Gap Time Distributions of Serial Events Based on Censored Data," Biometrics, The International Biometric Society, vol. 57(2), pages 369-375, June.
    6. Yijian Huang, 2002. "Censored regression with the multistate accelerated sojourn times model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 17-29, January.
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