Fig. 41

Bias versus the nonadherence rate using DAG 3 for 500 samples. Here, violation indicates the violation of the exclusion restriction assumption. The both-stages adjusted 2SLS and 2SRI methods share approximately the same line. These methods have high biases when the exclusion restriction violation is severe and thus out of the bound. The biases for ITT methods are also out of the bound for the non-null effect. Abbreviations: ITT: intention-to-treat, PP: per-protocol, AT: as-treated, IP-weighted PP: inverse probability-weighted per-protocol, 2SLS: two-stage least square, 2SRI: two-stage residual inclusion