Identification of Causal Effects on Binary Outcomes Using Structural Mean Models

Structural mean models (SMMs) are used to estimate causal effects among those selecting treatment in randomised controlled trials affected by non-ignorable non-compliance. These causal effects can be identified by assuming that there is no effect modification, namely, that the causal effect is equal for the treated subgroups randomised to treatment and to control. By analysing simple structural models for binary outcomes, we argue that the no effect modification assumption does not hold in general, and so SMMs do not estimate causal effects for the treated. An exception is for designs in which those randomised to control can be completely excluded from receiving the treatment. However, when there is non-compliance in the control arm, local (or complier) causal effects can be identified provided that the further assumption of monotonic selection into treatment holds. We demonstrate these issues using numerical examples.