Fig. 20

Bias versus the nonadherence rate for the null and non-null effect using DAG 3. Here, violation indicates the violation of the exclusion restriction assumption. The naive and both-stages adjusted 2SLS and 2SRI, and the first-stage adjusted 2SLS and 2SRI methods share the same line as they produce the same amount of bias. The ITT, 2SLS, and 2SRI methods have high bias in some scenarios and thus out of the bound [-0.6,0.6]. 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