Analysis approaches to address treatment nonadherence in pragmatic trials with point-treatment settings: a simulation...

Two-stage least square [2SLS] and two-stage residual inclusion [2SRI] are popularly used instrumental variable (IV) methods to address medication nonadherence in pragmatic trials with point treatment settings. These methods require assumptions, e.g., exclusion restriction, although they are known to handle unmeasured confounding. The newer IV-method, nonparametric causal bound [NPCB], showed promise in reducing uncertainty compared to usual IV-methods. The inverse probability-weighted per-protocol [IP-weighted PP] method is useful in the same setting but requires different assumptions, e.g., no unmeasured confounding. Although all of these methods are aimed to address the same nonadherence problem, comprehensive simulations to compare performances of them are absent in the literature.

We performed extensive simulations to compare the performances of the above methods in addressing nonadherence when: (1) exclusion restriction satisfied and no unmeasured confounding, (2) exclusion restriction is met but unmeasured confounding present, and (3) exclusion restriction is violated. Our simulations varied parameters such as, levels of adherence rates, unmeasured confounding, and exclusion restriction violations. Risk differences were estimated, and we compared performances in terms of bias, standard error (SE), mean squared error (MSE), and 95% confidence interval coverage probability.

For setting (1), 2SLS and 2SRI have small bias and nominal coverage. IP-weighted PP outperforms these IV-methods in terms of smaller MSE but produces high MSE when nonadherence is very high. For setting (2), IP-weighted-PP generally performs poorly compared to 2SLS and 2SRI in term of bias, and both-stages adjusted IV-methods improve precision than naive IV-methods. For setting (3), IV-methods perform worst in all scenarios, and IP-weighted-PP produces unbiased estimates and small MSE when confounders are adjusted. NPCB produces larger uncertainty bound width in almost all scenarios. We also analyze a two-arm trial to estimate vitamin-A supplementation effect on childhood mortality after addressing nonadherence.

Understanding finite sample characteristics of these methods will guide future researchers in determining suitable analysis strategies. Since assumptions are different and often untestable for IP-weighted PP and IV methods, we suggest analyzing data using both IP-weighted PP and IV approaches in search of a robust conclusion.