A cutoff-based randomized clinical trial couples cutoff-based assignme
nt on an appropriate covariate with random assignment to help balance
ethical and scientific concerns in certain situations. A statistical p
ower algorithm based on the Fisher Z method is developed that is parti
cular to and inclusive of cutoff-based random clinical trials and the
single cutoff-point (regression-discontinuity) design, which has no ra
ndomization. This article quantifies power and sample size estimates f
or varying levels of randomization and cutoff-based assignment. Althou
gh more randomization engenders greater statistical power less randomi
zation requires a much larger increase in sample size for small treatm
ent effects.