  In multicenter randomized trials, when effect modifiers have a different
distribution across centers, comparisons between treatment groups that average
over centers may not apply to any of the populations underlying the individual
centers. Here, we describe methods for reinterpreting the evidence produced by
a multicenter trial in the context of the population underlying each center. We
describe how to identify center-specific effects under identifiability
conditions that are largely supported by the study design and when associations
between center membership and the outcome may be present, given baseline
covariates and treatment ("center-outcome associations"). We then consider an
additional condition of no center-outcome associations given baseline
covariates and treatment. We show that this condition can be assessed using the
trial data; when it holds, center-specific treatment effects can be estimated
using analyses that completely pool information across centers. We propose
methods for estimating center-specific average treatment effects, when
center-outcome associations may be present and when they are absent, and
describe approaches for assessing whether center-specific treatment effects are
homogeneous. We evaluate the performance of the methods in a simulation study
and illustrate their implementation using data from the Hepatitis C Antiviral
Long-Term Treatment Against Cirrhosis trial.
