  In multisite trials, researchers are often interested in several inferential
goals: estimating treatment effects for each site, ranking these effects, and
studying their distribution. This study seeks to identify optimal methods for
estimating these targets. Through a comprehensive simulation study, we assess
two strategies and their combined effects: semiparametric modeling of the prior
distribution, and alternative posterior summary methods tailored to minimize
specific loss functions. Our findings highlight that the success of different
estimation strategies depends largely on the amount of within-site and
between-site information available from the data. We discuss how our results
can guide balancing the trade-offs associated with shrinkage in limited data
environments.
