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Asymptotic properties of resampling‐based processes for the average treatment effect in observational studies with competing risks

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  • Jasmin Rühl
  • Sarah Friedrich

Abstract

In observational studies with time‐to‐event outcomes, the g‐formula can be used to estimate a treatment effect in the presence of confounding factors. However, the asymptotic distribution of the corresponding stochastic process is complicated and thus not suitable for deriving confidence intervals or time‐simultaneous confidence bands for the average treatment effect. A common remedy are resampling‐based approximations, with Efron's nonparametric bootstrap being the standard tool in practice. We investigate the large sample properties of three different resampling approaches and prove their asymptotic validity in a setting with time‐to‐event data subject to competing risks. The usage of these approaches is demonstrated by an analysis of the effect of physical activity on the risk of knee replacement among patients with advanced knee osteoarthritis.

Suggested Citation

  • Jasmin Rühl & Sarah Friedrich, 2024. "Asymptotic properties of resampling‐based processes for the average treatment effect in observational studies with competing risks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(4), pages 1506-1532, December.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:4:p:1506-1532
    DOI: 10.1111/sjos.12714
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    References listed on IDEAS

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    1. Torben Martinussen & Mats Julius Stensrud, 2023. "Estimation of separable direct and indirect effects in continuous time," Biometrics, The International Biometric Society, vol. 79(1), pages 127-139, March.
    2. Friedrich, Sarah & Brunner, Edgar & Pauly, Markus, 2017. "Permuting longitudinal data in spite of the dependencies," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 255-265.
    3. Mats J. Stensrud & Jessica G. Young & Vanessa Didelez & James M. Robins & Miguel A. Hernán, 2022. "Separable Effects for Causal Inference in the Presence of Competing Events," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 175-183, January.
    4. 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.
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