A statistician is designing a phase III clinical trial comparing a continuous outcome in two groups receiving experimental versus standard therapy with a total sample size of 168 patients. The team requires the study have $80 %$ power at the $5 %$ significance level to detect a difference of 1 . Assume that the standard deviation of the outcome is 2 . The design team would like to investigate whether it's possible to have four times as many patients in the experimental group versus the control group without having to increase the total sample size.

What is the power if there are four times as many patients in the experimental group? What should the statistician recommend to the team in order for the study to have at least $80 %$ power?

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Power 1.0 Power as a function of allocation ratio with fixed total sample size n = 168 and significance level = 0.05 0.8 0.6- 0.4- 0.2- 0.0- 2 3 Allocation ratio 50