Apples and oranges? Interpretations of risk adjustment and instrumental variable estimates of intended treatment effects using observational data.

Instrumental variable (IV) and risk adjustment (RA) estimators, including propensity score adjustments, are both used to alleviate confounding problems in nonexperimental studies on treatment effects, but it is not clear how estimates based on these 2 approaches compare. Methodological considerations have shown that IV and RA estimators yield estimates of distinct types of causal treatment effects regardless of confounding problems. Many investigators have neglected these distinctions. In this paper, the authors use 3 schematic models to explain visually the relations between IV and RA estimates of intended treatment effects as demonstrated in the methodological studies. When treatment effects are homogeneous across a study population or when treatment effects are heterogeneous across the study population but treatment decisions are unrelated to the treatment effects, RA and IV estimates should be equivalent when the respective assumptions are met. In contrast, when treatment effects are heterogeneous and treatment decisions are related to the treatment effects, RA estimates of treatment effect can asymptotically differ from IV estimates, but both are correct even when the respective assumptions are met. Appropriate interpretations of IV or RA estimates can be facilitated by developing conceptual models related to treatment choice and treatment effect heterogeneity prior to analyses.