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Instrumental Variables with Time-Varying Exposure: Dynamic Effects of Revascularization on Quality of Life

Author

Listed:
  • Joshua D. Angrist
  • Bruno Ferman
  • Carol Gao
  • Peter Hull
  • Otavio L. Tecchio
  • Robert W. Yeh

Abstract

This paper develops instrumental variables (IV) estimators for dynamic causal effects in randomized trials with imperfect compliance. These methods are applied to a randomized trial that assigned patients with ischemic heart disease to either an invasive treatment arm centered on revascularization or a control group meant to receive non-invasive medical therapy. As is common in such ``strategy trials,'' many participants assigned to treatment remained untreated while many assigned to control crossed over into treatment. Protocol non-compliance causes ITT estimates to diverge from the effect of treatment received, while conventional per-protocol analyses that condition on treatment received are compromised by selection bias. Extending the static potential-outcomes IV framework, the methods here identify average causal effects of treatment for dynamic compliers, the set of trial participants who comply with trial protocol at different follow-up horizons. IV estimates of revascularization effects on compliers' quality of life are markedly larger and more sustained than previously reported ITT and per-protocol estimates. We also show how to estimate average characteristics and marginal potential outcome means for dynamic compliers. These results are used to explain confounding in as-treated per-protocol estimates.

Suggested Citation

  • Joshua D. Angrist & Bruno Ferman & Carol Gao & Peter Hull & Otavio L. Tecchio & Robert W. Yeh, 2025. "Instrumental Variables with Time-Varying Exposure: Dynamic Effects of Revascularization on Quality of Life," Papers 2501.01623, arXiv.org, revised Jul 2026.
    • Handle: RePEc:arx:papers:2501.01623
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    References listed on IDEAS

    as
    1. Bruno Ferman & Ot'avio Tecchio, 2023. "Dynamic LATEs with a Static Instrument," Papers 2305.18114, arXiv.org, revised Jan 2025.
    2. Joshua D. Angrist, 2004. "Treatment effect heterogeneity in theory and practice," Economic Journal, Royal Economic Society, vol. 114(494), pages 52-83, March.
    3. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    4. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
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    6. Amanda E Kowalski, 2023. "Behaviour within a Clinical Trial and Implications for Mammography Guidelines," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(1), pages 432-462.
    7. Athey, Susan & Imbens, Guido W., 2022. "Design-based analysis in Difference-In-Differences settings with staggered adoption," Journal of Econometrics, Elsevier, vol. 226(1), pages 62-79.
    8. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
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