  Leveraging external controls -- relevant individual patient data under
control from external trials or real-world data -- has the potential to reduce
the cost of randomized controlled trials (RCTs) while increasing the proportion
of trial patients given access to novel treatments. However, due to lack of
randomization, RCT patients and external controls may differ with respect to
covariates that may or may not have been measured. Hence, after controlling for
measured covariates, for instance by matching, testing for treatment effect
using external controls may still be subject to unmeasured biases. In this
paper, we propose a sensitivity analysis approach to quantify the magnitude of
unmeasured bias that would be needed to alter the study conclusion that
presumed no unmeasured biases are introduced by employing external controls.
Whether leveraging external controls increases power or not depends on the
interplay between sample sizes and the magnitude of treatment effect and
unmeasured biases, which may be difficult to anticipate. This motivates a
combined testing procedure that performs two highly correlated analyses, one
with and one without external controls, with a small correction for multiple
testing using the joint distribution of the two test statistics. The combined
test provides a new method of sensitivity analysis designed for data fusion
problems, which anchors at the unbiased analysis based on RCT only and spends a
small proportion of the type I error to also test using the external controls.
In this way, if leveraging external controls increases power, the power gain
compared to the analysis based on RCT only can be substantial; if not, the
power loss is small. The proposed method is evaluated in theory and power
calculations, and applied to a real trial.
