  Instrumental variable methods are popular choices in combating unmeasured
confounding to obtain less biased effect estimates. However, we demonstrate
that alternative methods may give less biased estimates depending on the nature
of unmeasured confounding. Treatment preferences of clusters (e.g., physician
practices) are the most f6requently used instruments in instrumental variable
analyses (IVA). These preference-based IVAs are usually conducted on data
clustered by region, hospital/facility, or physician, where unmeasured
confounding often occurs within or between clusters. We aim to quantify the
impact of unmeasured confounding on the bias of effect estimators in IVA, as
well as alternative methods including ordinary least squares regression, linear
mixed models (LMM) and fixed effect models (FE) to study the effect of a
continuous exposure (e.g., treatment dose). We derive bias formulae of
estimators from these four methods in the presence of unmeasured within- and/or
between-cluster confounders. We show that IVAs can provide consistent estimates
when unmeasured within-cluster confounding exists, but not when between-cluster
confounding exists. On the other hand, FEs and LMMs can provide consistent
estimates when unmeasured between-cluster confounding exits, but not for
within-cluster confounding. Whether IVAs are advantageous in reducing bias over
FEs and LMMs depends on the extent of unmeasured within-cluster confounding
relative to between-cluster confounding. Furthermore, the impact of unmeasured
between-cluster confounding on IVA estimates is larger than the impact of
unmeasured within-cluster confounding on FE and LMM estimates. We illustrate
these methods through data applications. Our findings provide guidance for
choosing appropriate methods to combat the dominant types of unmeasured
confounders and help interpret statistical results in the context of unmeasured
confounding
