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Regression models for censored time-to-event data using infinitesimal jack-knife pseudo-observations, with applications to left-truncation

Author

Listed:
  • Erik T. Parner

    (Aarhus University)

  • Per K. Andersen

    (University of Copenhagen)

  • Morten Overgaard

    (Aarhus University)

Abstract

Jack-knife pseudo-observations have in recent decades gained popularity in regression analysis for various aspects of time-to-event data. A limitation of the jack-knife pseudo-observations is that their computation is time consuming, as the base estimate needs to be recalculated when leaving out each observation. We show that jack-knife pseudo-observations can be closely approximated using the idea of the infinitesimal jack-knife residuals. The infinitesimal jack-knife pseudo-observations are much faster to compute than jack-knife pseudo-observations. A key assumption of the unbiasedness of the jack-knife pseudo-observation approach is on the influence function of the base estimate. We reiterate why the condition on the influence function is needed for unbiased inference and show that the condition is not satisfied for the Kaplan–Meier base estimate in a left-truncated cohort. We present a modification of the infinitesimal jack-knife pseudo-observations that provide unbiased estimates in a left-truncated cohort. The computational speed and medium and large sample properties of the jack-knife pseudo-observations and infinitesimal jack-knife pseudo-observation are compared and we present an application of the modified infinitesimal jack-knife pseudo-observations in a left-truncated cohort of Danish patients with diabetes.

Suggested Citation

  • Erik T. Parner & Per K. Andersen & Morten Overgaard, 2023. "Regression models for censored time-to-event data using infinitesimal jack-knife pseudo-observations, with applications to left-truncation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 654-671, July.
    • Handle: RePEc:spr:lifeda:v:29:y:2023:i:3:d:10.1007_s10985-023-09597-5
    DOI: 10.1007/s10985-023-09597-5
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    References listed on IDEAS

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    1. Morten Overgaard & Erik Thorlund Parner & Jan Pedersen, 2018. "Estimating the variance in a pseudo‐observation scheme with competing risks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(4), pages 923-940, December.
    2. Thomas H. Scheike & Mei-Jie Zhang & Thomas A. Gerds, 2008. "Predicting cumulative incidence probability by direct binomial regression," Biometrika, Biometrika Trust, vol. 95(1), pages 205-220.
    3. Per Kragh Andersen, 2003. "Generalised linear models for correlated pseudo-observations, with applications to multi-state models," Biometrika, Biometrika Trust, vol. 90(1), pages 15-27, March.
    4. Morten Overgaard & Per K. Andersen & Erik T. Parner, 2015. "Regression analysis of censored data using pseudo-observations: An update," Stata Journal, StataCorp LP, vol. 15(3), pages 809-821, September.
    5. Ronald B. Geskus, 2011. "Cause-Specific Cumulative Incidence Estimation and the Fine and Gray Model Under Both Left Truncation and Right Censoring," Biometrics, The International Biometric Society, vol. 67(1), pages 39-49, March.
    6. Li, Ruosha & Peng, Limin, 2014. "Varying coefficient subdistribution regression for left-truncated semi-competing risks data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 65-78.
    7. Erik T. Parner & Per K. Andersen, 2010. "Regression analysis of censored data using pseudo-observations," Stata Journal, StataCorp LP, vol. 10(3), pages 408-422, September.
    8. Martin Jacobsen & Torben Martinussen, 2016. "A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo-observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 845-862, September.
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