  The randomized controlled trial (RCT) is the gold standard for estimating the
average treatment effect (ATE) of a medical intervention but requires
100s-1000s of subjects, making it expensive and difficult to implement. While a
cross-over trial can reduce sample size requirements by measuring the treatment
effect per individual, it is only applicable to chronic conditions and
interventions whose effects dissipate rapidly. Another approach is to replace
or augment data collected from an RCT with external data from prospective
studies or prior RCTs, but it is vulnerable to confounders in the external or
augmented data. We propose to simulate the cross-over trial to overcome its
practical limitations while exploiting its strengths. We propose a novel
framework, SECRETS, which, for the first time, estimates the individual
treatment effect (ITE) per patient in the RCT study without using any external
data by leveraging a state-of-the-art counterfactual estimation algorithm,
called synthetic intervention. It also uses a new hypothesis testing strategy
to determine whether the treatment has a clinically significant ATE based on
the estimated ITEs. We show that SECRETS can improve the power of an RCT while
maintaining comparable significance levels; in particular, on three real-world
clinical RCTs (Phase-3 trials), SECRETS increases power over the baseline
method by $\boldsymbol{6}$-$\boldsymbol{54\%}$ (average: 21.5%, standard
deviation: 15.8%).
