• Causal inference;
  • Deterministic compliance;
  • Local average treatment effect;
  • Potential outcomes;
  • Population average treatment effect

In randomized trials with imperfect compliance, it is sometimes recommended to supplement the intention-to-treat estimate with an instrumental variable (IV) estimate, which is consistent for the effect of treatment administration in those subjects who would get treated if randomized to treatment and would not get treated if randomized to control. The IV estimation however has been criticized for its reliance on simultaneous existence of complementary “fatalistic” compliance states. The objective of the present paper is to identify some sufficient conditions for consistent estimation of treatment effects in randomized trials with stochastic compliance. It is shown that in the stochastic framework, the classical IV estimator is generally inconsistent for the population-averaged treatment effect. However, even under stochastic compliance, with certain common experimental designs the IV estimator and a simple alternative estimator can be used for consistent estimation of the effect of treatment administration in well-defined and identifiable subsets of the study population.