  Subgroup analysis of randomized controlled trials (RCTs) constitutes an
important component of the drug development process in precision medicine. In
particular, subgroup analysis of early phase trials often influences the design
and eligibility criteria of subsequent confirmatory trials and ultimately
impacts which subpopulations will receive the treatment after regulatory
approval. However, subgroup analysis is typically complicated by small sample
sizes, which lead to substantial uncertainty about the subgroup-specific
treatment effects. In this work we explore the use of external control (EC)
data to augment an RCT's subgroup analysis. We define and discuss harmonized
estimators of subgroup-specific treatment effects to leverage EC data while
ensuring that the subgroup analysis is coherent with a primary analysis using
RCT data alone. Our approach modifies subgroup-specific treatment effect
estimators obtained through popular methods (e.g., linear regression) applied
jointly to the RCT and EC datasets. We shrink these estimates so that their
weighted average is close to a robust estimate of the average treatment effect
in the overall trial population based on the RCT data alone. We study the
proposed harmonized estimators with analytic results and simulations, and
investigate standard performance metrics. The method is illustrated with a case
study in glioblastoma.
