  Trials enroll a large number of subjects in order to attain power, making
them expensive and time-consuming. Sample size calculations are often performed
with the assumption of an unadjusted analysis, even if the trial analysis plan
specifies a more efficient estimator (e.g. ANCOVA). This leads to conservative
estimates of required sample sizes and an opportunity for savings. Here we show
that a relatively simple formula can be used to estimate the power of any
two-arm, single-timepoint trial analyzed with a semiparametric efficient
estimator, regardless of the domain of the outcome or kind of treatment effect
(e.g. odds ratio, mean difference). Since an efficient estimator attains the
minimum possible asymptotic variance, this allows for the design of trials that
are as small as possible while still attaining design power and control of type
I error. The required sample size calculation is parsimonious and requires the
analyst to provide only a small number of population parameters. We verify in
simulation that the large-sample properties of trials designed this way attain
their nominal values. Lastly, we demonstrate how to use this formula in the
"design" (and subsequent reanalysis) of a real clinical trial and show that
fewer subjects are required to attain the same design power when a
semiparametric efficient estimator is accounted for at the design stage.
