  We abstract the concept of a randomized controlled trial (RCT) as a triple
(beta,b,s), where beta is the primary efficacy parameter, b the estimate and s
the standard error (s>0). The parameter beta is either a difference of means, a
log odds ratio or a log hazard ratio. If we assume that b is unbiased and
normally distributed, then we can estimate the full joint distribution of
(beta,b,s) from a sample of pairs (b_i,s_i). We have collected 23,747 such
pairs from the Cochrane database to do so. Here, we report the estimated
distribution of the signal-to-noise ratio beta/s and the achieved power. We
estimate the median achieved power to be 0.13. We also consider the
exaggeration ratio which is the factor by which the magnitude of beta is
overestimated. We find that if the estimate is just significant at the 5%
level, we would expect it to overestimate the true effect by a factor of 1.7.
This exaggeration is sometimes referred to as the winner's curse and it is
undoubtedly to a considerable extent responsible for disappointing replication
results. For this reason, we believe it is important to shrink the unbiased
estimator, and we propose a method for doing so.
