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Dynamic inference in general nested case‐control designs

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  • J. Feifel
  • D. Dobler

Abstract

Nested case‐control designs are attractive in studies with a time‐to‐event endpoint if the outcome is rare or if interest lies in evaluating expensive covariates. The appeal is that these designs restrict to small subsets of all patients at risk just prior to the observed event times. Only these small subsets need to be evaluated. Typically, the controls are selected at random and methods for time‐simultaneous inference have been proposed in the literature. However, the martingale structure behind nested case‐control designs allows for more powerful and flexible non‐standard sampling designs. We exploit that structure to find simultaneous confidence bands based on wild bootstrap resampling procedures within this general class of designs. We show in a simulation study that the intended coverage probability is obtained for confidence bands for cumulative baseline hazard functions. We apply our methods to observational data about hospital‐acquired infections.

Suggested Citation

  • J. Feifel & D. Dobler, 2021. "Dynamic inference in general nested case‐control designs," Biometrics, The International Biometric Society, vol. 77(1), pages 175-185, March.
  • Handle: RePEc:bla:biomet:v:77:y:2021:i:1:p:175-185
    DOI: 10.1111/biom.13259
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    References listed on IDEAS

    as
    1. Ørnulf Borgan & Ying Zhang, 2015. "Using cumulative sums of martingale residuals for model checking in nested case‐control studies," Biometrics, The International Biometric Society, vol. 71(3), pages 696-703, September.
    2. 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.
    3. C. Rivera & T. Lumley, 2016. "Using the whole cohort in the analysis of countermatched samples," Biometrics, The International Biometric Society, vol. 72(2), pages 382-391, June.
    4. Jan Feifel & Madlen Gebauer & Martin Schumacher & Jan Beyersmann, 2020. "Nested exposure case-control sampling: a sampling scheme to analyze rare time-dependent exposures," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 21-44, January.
    5. 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.
    6. Jan Beyersmann & Susanna Di Termini & Markus Pauly, 2013. "Weak Convergence of the Wild Bootstrap for the Aalen–Johansen Estimator of the Cumulative Incidence Function of a Competing Risk," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 387-402, September.
    7. Tobias Bluhmki & Dennis Dobler & Jan Beyersmann & Markus Pauly, 2019. "The wild bootstrap for multivariate Nelson–Aalen estimators," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 97-127, January.
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