## INTRODUCTION

This JAMA Guide to Statistics and Methods discusses instrumental variable analysis, a method designed to reduce or eliminate unobserved confounding in observational studies, with the goal of achieving unbiased estimation of treatment effects.

A randomized clinical trial (RCT) can be used to estimate the average treatment effect for a population. Some patients experience a treatment effect that is larger than the average, while others experience a smaller-than-average treatment effect. Subgroup analyses often are used to evaluate heterogeneity in the treatment effect.1 When it is infeasible or unethical to randomize patients to a treatment, the average treatment effect may be a combination of the true treatment effect and the effects of confounders—factors that influence both the treatment selected and patient outcomes.2 When confounding factors are unknown or unobserved, correcting for their effect in statistical analyses is challenging. Instrumental variable analysis is one approach to address unobserved confounding.

Instrumental variable analysis is designed to reduce or eliminate unobserved confounding in observational studies and thus allow unbiased estimation of treatment effects. Results from an instrumental variable analysis typically apply to a subgroup of patients in the study. In a publication in JAMA Internal Medicine, Werner and colleagues3 reported the results of an instrumental variable analysis that compared postacute care outcomes between Medicare beneficiaries discharged from the hospital to home with home health care or discharged to a skilled nursing facility. The authors also described how their results applied not to all patients but instead to a distinct subgroup of patients.

## USE OF THE INSTRUMENTAL VARIABLE METHOD

### Why Use an Instrumental Variable Analysis in the Setting of Heterogeneity of the Treatment Effect?

An instrumental variable analysis is conducted to reduce bias from unmeasured confounding in the estimation of the effect of a treatment or exposure from an observational study.2 Instrumental variable analysis begins by identifying an observed explanatory variable that, like randomization, influences assignment to the treatment, but has no direct effect on the outcome of interest, referred to as an “instrumental variable.” Unlike randomization, however, the instrumental variable may not act like randomization for all patients but only for a subset of patients who were effectively quasi-randomized to treatment or no treatment based on the value of the instrumental variable. In this analytic approach, those patients are referred to as the “marginal patients.” The overall goal of an instrumental variable analysis is to measure the treatment effect free of bias. A major trade-off for reducing bias (increased internal validity) is a loss of generalizability, because results apply only to marginal patients and it cannot be known with certainty what subset of the overall cohort are the marginal patients (although methods exist to be able to describe them).

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