An econometric framework extending instrumental variables methods to randomized strategy trials with dynamic non-random compliance, motivated by the ISCHEMIA revascularization trial where control-group crossovers occurred up to five years after assignment. Defines revascularization exposure as years since treatment, introduces wave ignorability and strong wave ignorability assumptions that restrict incremental complier effects to depend on exposure time rather than calendar wave, and proves that stacked 2SLS with assignment-by-wave instruments identifies incremental and cumulative dynamic causal effects. Also identifies baseline characteristics of dynamic compliers and always-takers under an Immediate Compliers Only restriction. Applied to ISCHEMIA, IV estimates of quality-of-life gains (SAQ summary and angina scores) are markedly larger and more sustained than intention-to-treat estimates, and increasingly divergent from as-treated OLS estimates because ever-sicker always-taker crossovers accumulate in the treated population.
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 pat…