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A generalized theory of separable effects in competing event settings

Author

Listed:
  • Mats J. Stensrud

    (Ecole Polytechnique Fédérale de Lausanne)

  • Miguel A. Hernán

    (Harvard T. H. Chan School of Public Health
    Harvard T. H. Chan School of Public Health
    Harvard T.H. Chan School of Public Health)

  • Eric J Tchetgen Tchetgen

    (University of Pennsylvania)

  • James M. Robins

    (Harvard T. H. Chan School of Public Health
    Harvard T. H. Chan School of Public Health
    Harvard T.H. Chan School of Public Health)

  • Vanessa Didelez

    (Leibniz Institute for Prevention Research and Epidemiology - BIPS
    University of Bremen)

  • Jessica G. Young

    (Harvard T. H. Chan School of Public Health
    Harvard T.H. Chan School of Public Health
    Harvard Medical School and Harvard Pilgrim Health Care Institute)

Abstract

In competing event settings, a counterfactual contrast of cause-specific cumulative incidences quantifies the total causal effect of a treatment on the event of interest. However, effects of treatment on the competing event may indirectly contribute to this total effect, complicating its interpretation. We previously proposed the separable effects to define direct and indirect effects of the treatment on the event of interest. This definition was given in a simple setting, where the treatment was decomposed into two components acting along two separate causal pathways. Here we generalize the notion of separable effects, allowing for interpretation, identification and estimation in a wide variety of settings. We propose and discuss a definition of separable effects that is applicable to general time-varying structures, where the separable effects can still be meaningfully interpreted as effects of modified treatments, even when they cannot be regarded as direct and indirect effects. For these settings we derive weaker conditions for identification of separable effects in studies where decomposed, or otherwise modified, treatments are not yet available; in particular, these conditions allow for time-varying common causes of the event of interest, the competing events and loss to follow-up. We also propose semi-parametric weighted estimators that are straightforward to implement. We stress that unlike previous definitions of direct and indirect effects, the separable effects can be subject to empirical scrutiny in future studies.

Suggested Citation

  • Mats J. Stensrud & Miguel A. Hernán & Eric J Tchetgen Tchetgen & James M. Robins & Vanessa Didelez & Jessica G. Young, 2021. "A generalized theory of separable effects in competing event settings," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 588-631, October.
    • Handle: RePEc:spr:lifeda:v:27:y:2021:i:4:d:10.1007_s10985-021-09530-8
    DOI: 10.1007/s10985-021-09530-8
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. Torben Martinussen & Stijn Vansteelandt & Per Kragh Andersen, 2020. "Subtleties in the interpretation of hazard contrasts," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 833-855, October.
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    Cited by:

    1. Yuhao Deng & Haoyu Wei & Xia Xiao & Yuan Zhang & Yuanmin Huang, 2024. "Sequential Ignorability and Dismissible Treatment Components to Identify Mediation Effects," Mathematics, MDPI, vol. 12(15), pages 1-20, July.
    2. 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.

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