Complier Average Causal Effect Estimation Using an Instrumental Variables Approach

Our primary strategy for estimation of the CACE was an instrumental variables (IV) approach.31 A rigorous discussion of IV is beyond the scope of this paper, for which we guide the reader to Hernán and Robins (see Section 16.1 and Technical Point 16.1 therein for more rigorous exposition on this topic). Although fundamental to the approach, identifying a valid IV can be challenging. Briefly: (1) the instrument must be associated with treatment receipt; (2) the instrument must not have a causal effect on the outcome of interest except through treatment receipt; and (3) the instrument and outcome must not have a common cause (that is not accounted for in the analysis). Figure ​Figure33 graphically depicts the causal relationships assumed for the preplanned IV analysis for the COMPASS study.

Directed acyclic graph representing the COMprehensive Post-Acute Stroke Services cluster-randomized trial where randomization assignment is the instrumental variable (IV) and Y represents the outcome of interest. U1 and U2 represent unmeasured confounders of the randomization-outcome and treatment-outcome relationships, respectively. C represents measured confounders that were adjusted for in the analysis. Direct causal effects are represented by solid arrows. Instrumental conditions require that (1) the IV is associated with treatment; (2) there is no effect of IV on Y except through treatment; and (3) there is no common cause of IV and Y. The dotted arrows are included to illustrate the effects assumed to be absent under conditions 2 and 3. Of note, the solid arrow between C and IV is included to represent observed associations present after randomization, although these are not causal effects.

One of the key benefits of IV analysis is that, if the analyst adequately adjusts for the effects of the measured confounders (C) of the relationship between study arm and outcome, and there are no unmeasured confounders (U1), inference on the effect of treatment receipt on the outcome is valid, even if there are unmeasured confounders of that relationship (U2). The statistical analysis plan for the COMPASS study provides a thorough description of the rationale for using randomized study arm (a cluster-level variable) as an instrument. Briefly, the fact that criterion 1 is met is obvious. For criterion 2, the research team felt that the majority of the intervention’s effectiveness came through attending a specialized clinic visit and receiving an individualized eCare plan. Thus, simply being enrolled at a hospital that was randomized to provide the COMPASS-TC was not viewed as having the potential to provide a meaningful degree of efficacy and thus criterion 2 holds, if only approximately. Criterion 3 requires appropriate adjustment for prognostic characteristics that were imbalanced across study arms, which we attempted to achieve using strategies described above.

It is important to note that, in the context of the COMPASS study, having an instrument that meets criteria 1−3 above is not sufficient for the IV estimator to adequately target the CACE. Further assumptions are necessary. Specifically, one must assume that patients enrolled in UC hospitals who were compliers (an unobservable characteristic) did not have the option to receive specialized post-acute care akin to COMPASS-TC (ie, compliance is defined with respect to specialized post-acute care, which was assumed to be unavailable in the UC setting). In addition, one must further assume that intervention arm patients who do not receive the eCare plan (ie, noncompliers) received minimal specialized post-acute care, consistent with the level of intervention provided in UC settings to all patients. These assumptions are admittedly strong, but not unreasonable in our opinion, for several reasons. First, before randomization, hospitals did not provide comprehensive post-acute care fully consistent with COMPASS-TC.32 Second, a key reason for noncompliance to COMPASS-TC was preference for alternative follow-up, for example, primary care, consistent with that offered in UC.29

Two-stage least squares estimation was performed for IV analysis and robust standard errors were computed to account for the cluster-level heterogeneity of patient outcomes.31,33 Briefly, the first stage regression model regresses treatment receipt on hospital-level and patient-level characteristics using intervention arm data. In the second stage regression, the outcome is regressed on the same set of characteristics except that treatment receipt is replaced by the estimated probability of receipt from the first stage regression (and set to zero for UC patients). Use of IVs offers no protection from selection bias related to outcome ascertainment.34 Thus, the same methods for employing IPW coupled with MI described above were also incorporated into the IV analysis. This has been shown to improve the quality of IV estimation in the presence of selection bias.35