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Conditional Studentized Survival Tests for Randomly Censored Models

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  • Arnold Janssen
  • Claus‐Dieter Mayer

Abstract

It is shown that in the case of heterogenous censoring distributions Studentized survival tests can be carried out as conditional permutation tests given the order statistics and their censoring status. The result is based on a conditional central limit theorem for permutation statistics. It holds for linear test statistics as well as for sup‐statistics. The procedure works under one of the following general circumstances for the two‐sample problem: the unbalanced sample size case, highly censored data, certain non‐convergent weight functions or under alternatives. For instance, the two‐sample log rank test can be carried out asymptotically as a conditional test if the relative amount of uncensored observations vanishes asymptotically as long as the number of uncensored observations becomes infinite. Similar results hold whenever the sample sizes and are unbalanced in the sense that and hold.

Suggested Citation

  • Arnold Janssen & Claus‐Dieter Mayer, 2001. "Conditional Studentized Survival Tests for Randomly Censored Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 283-293, June.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:2:p:283-293
    DOI: 10.1111/1467-9469.00237
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    Cited by:

    1. Michael Brendel & Arnold Janssen & Claus-Dieter Mayer & Markus Pauly, 2014. "Weighted Logrank Permutation Tests for Randomly Right Censored Life Science Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 742-761, September.
    2. Arnold Janssen, 2005. "Resampling student'st-type statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 507-529, September.
    3. Ditzhaus, Marc & Pauly, Markus, 2019. "Wild bootstrap logrank tests with broader power functions for testing superiority," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 1-11.
    4. Marc Ditzhaus & Arnold Janssen, 2020. "Bootstrap and permutation rank tests for proportional hazards under right censoring," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 493-517, July.
    5. Janssen Arnold & Völker Dominik, 2007. "Most powerful conditional tests," Statistics & Risk Modeling, De Gruyter, vol. 25(1), pages 41-62, January.
    6. Marc Ditzhaus & Jon Genuneit & Arnold Janssen & Markus Pauly, 2023. "CASANOVA: Permutation inference in factorial survival designs," Biometrics, The International Biometric Society, vol. 79(1), pages 203-215, March.

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