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Instrumental variable methods are popular choices in combating unmeasuredconfounding to obtain less biased effect estimates. However, we demonstratethat alternative methods may give less biased estimates depending on the natureof unmeasured confounding. Treatment preferences of clusters (e.g., physicianpractices) are the most f6requently used instruments in instrumental variableanalyses (IVA). These preference-based IVAs are usually conducted on dataclustered by region, hospital/facility, or physician, where unmeasuredconfounding often occurs within or between clusters. We aim to quantify theimpact of unmeasured confounding on the bias of effect estimators in IVA, aswell as alternative methods including ordinary least squares regression, linearmixed models (LMM) and fixed effect models (FE) to study the effect of acontinuous exposure (e.g., treatment dose). We derive bias formulae ofestimators from these four methods in the presence of unmeasured within- and/orbetween-cluster confounders. We show that IVAs can provide consistent estimateswhen unmeasured within-cluster confounding exists, but not when between-clusterconfounding exists. On the other hand, FEs and LMMs can provide consistentestimates when unmeasured between-cluster confounding exits, but not forwithin-cluster confounding. Whether IVAs are advantageous in reducing bias overFEs and LMMs depends on the extent of unmeasured within-cluster confoundingrelative to between-cluster confounding. Furthermore, the impact of unmeasuredbetween-cluster confounding on IVA estimates is larger than the impact ofunmeasured within-cluster confounding on FE and LMM estimates. We illustratethese methods through data applications. Our findings provide guidance forchoosing appropriate methods to combat the dominant types of unmeasuredconfounders and help interpret statistical results in the context of unmeasuredconfounding

The Impact of Unmeasured Within- and Between-Cluster Confounding on the  Bias of Effect Estimators from Fixed Effect, Mixed effect and Instrumental  Variable Models