On a preference-based instrumental variable approach in reducing unmeasured confounding-by-indication

Treatment preferences of groups (e.g., clinical centers) have often been proposed as instruments to control for unmeasured confounding-by-indication in instrumental variable (IV) analyses. However, formal evaluations of these group-preference-based instruments are lacking. Unique challenges include the following: (i) correlations between outcomes within groups; (ii) the multi-value nature of the instruments; (iii) unmeasured confounding occurring between and within groups. We introduce the framework of between-group and within-group confounding to assess assumptions required for the group-preference-based IV analyses. Our work illustrates that, when unmeasured confounding effects exist only within groups but not between groups, preference-based IVs can satisfy assumptions required for valid instruments. We then derive a closed-form expression of asymptotic bias of the two-stage generalized ordinary least squares estimator when the IVs are valid. Simulations demonstrate that the asymptotic bias formula approximates bias in finite samples quite well, particularly when the number of groups is moderate to large. The bias formula shows that when the cluster size is finite, the IV estimator is asymptotically biased; only when both the number of groups and cluster size go to infinity, the bias disappears. However, the IV estimator remains advantageous in reducing bias from confounding-by-indication. The bias assessment provides practical guidance for preference-based IV analyses. To increase their performance, one should adjust for as many measured confounders as possible, consider groups that have the most random variation in treatment assignment and increase cluster size. To minimize the likelihood for these IVs to be invalid, one should minimize unmeasured between-group confounding.