  It has long been noticed that the efficacy observed in small early phase
studies is generally better than that observed in later larger studies.
Historically, the inflation of the efficacy results from early proof-of-concept
studies is either ignored, or adjusted empirically using a frequentist or
Bayesian approach. In this article, we systematically explained the underlying
reason for the inflation of efficacy results in small early phase studies from
the perspectives of measurement error models and selection bias. A systematic
method was built to adjust the early phase study results from both frequentist
and Bayesian perspectives. A hierarchical model was proposed to estimate the
distribution of the efficacy for a portfolio of compounds, which can serve as
the prior distribution for the Bayesian approach. We showed through theory that
the systematic adjustment provides an unbiased estimator for the true mean
efficacy for a portfolio of compounds. The adjustment was applied to paired
data for the efficacy in early small and later larger studies for a set of
compounds in diabetes and immunology. After the adjustment, the bias in the
early phase small studies seems to be diminished.
