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

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.