  Augmenting the control arm of a randomized controlled trial (RCT) with
external data may increase power at the risk of introducing bias. Existing data
fusion estimators generally rely on stringent assumptions or may have decreased
coverage or power in the presence of bias. Framing the problem as one of
data-adaptive experiment selection, potential experiments include the RCT only
or the RCT combined with different candidate real-world datasets. To select and
analyze the experiment with the optimal bias-variance tradeoff, we develop a
novel experiment-selector cross-validated targeted maximum likelihood estimator
(ES-CVTMLE). The ES-CVTMLE uses two bias estimates: 1) a function of the
difference in conditional mean outcome under control between the RCT and
combined experiments and 2) an estimate of the average treatment effect on a
negative control outcome (NCO). We define the asymptotic distribution of the
ES-CVTMLE under varying magnitudes of bias and construct confidence intervals
by Monte Carlo simulation. In simulations involving violations of
identification assumptions, the ES-CVTMLE had better coverage than
test-then-pool approaches and an NCO-based bias adjustment approach and higher
power than one implementation of a Bayesian dynamic borrowing approach. We
further demonstrate the ability of the ES-CVTMLE to distinguish biased from
unbiased external controls through a re-analysis of the effect of liraglutide
on glycemic control from the LEADER trial. The ES-CVTMLE has the potential to
improve power while providing relatively robust inference for future hybrid
RCT-RWD studies.
