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

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.