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Confidence bands for survival curves from outcome‐dependent stratified samples

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  • Takumi Saegusa
  • Peter Nandori

Abstract

We consider the construction of confidence bands for survival curves under the outcome‐dependent stratified sampling. A main challenge of this design is that data are a biased dependent sample due to stratification and sampling without replacement. Most literature on regression approximates this design by Bernoulli sampling but variance is generally overestimated. Even with this approximation, the limiting distribution of the inverse probability weighted Kaplan–Meier estimator involves a general Gaussian process, and hence quantiles of its supremum is not analytically available. In this paper, we provide a rigorous asymptotic theory for the weighted Kaplan–Meier estimator accounting for dependence in the sample. We propose the novel hybrid method to both simulate and bootstrap parts of the limiting process to compute confidence bands with asymptotically correct coverage probability. Simulation study indicates that the proposed bands are appropriate for practical use. A Wilms tumor example is presented.

Suggested Citation

  • Takumi Saegusa & Peter Nandori, 2024. "Confidence bands for survival curves from outcome‐dependent stratified samples," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1086-1102, September.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:3:p:1086-1102
    DOI: 10.1111/sjos.12700
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    References listed on IDEAS

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    1. Qingning Zhou & Jianwen Cai & Haibo Zhou, 2018. "Outcome†dependent sampling with interval†censored failure time data," Biometrics, The International Biometric Society, vol. 74(1), pages 58-67, March.
    2. Tianxi Cai & Yingye Zheng, 2013. "Resampling Procedures for Making Inference Under Nested Case--Control Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1532-1544, December.
    3. Winnett A. & Sasieni P., 2002. "Adjusted Nelson-Aalen Estimates With Retrospective Matching," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 245-256, March.
    4. Dennis Dobler & Markus Pauly & ThomasH. Scheike, 2019. "Confidence bands for multiplicative hazards models: Flexible resampling approaches," Biometrics, The International Biometric Society, vol. 75(3), pages 906-916, September.
    5. Donglin Zeng & D. Y. Lin, 2014. "Efficient Estimation of Semiparametric Transformation Models for Two-Phase Cohort Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 371-383, March.
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