ABSTRACT
Chapter 9 presents instrumental variables methods to adjust for unmeasured confounding, specifically the principal stratification approach to estimate the complier average causal effect (CACE) and the structural nested mean model approach to estimate the average effect of treatment on the treated (ATT). It defines an instrumental variable and the exclusion and monotonicity assumptions, and then it proves validity of the principal stratification approach assuming exclusion and monotonicity. It explains the assumptions required for either a linear, loglinear, or logistic structural nested mean model to hold and then, assuming exclusion, it proves validity of the corresponding approach. For comparison, the intent-to-treat estimator, the as-treated analysis, and the per-protocol analysis are explained. An example is provided in which presence of a placebo effect is shown to violate the exclusion assumption and to lead to estimates of the CACE and ATT that are nonsensical. Thus, plausibility of the exclusion assumption is important to evaluate in any instrumental variables analysis. Examples and R code are also provided.
