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Makuch and Simon [Sample size considerations for non-randomised comparative studies. J Chronic Dis 1980; 33: 175-81.] developed a sample size formula for historical control trials. When assessing power, they assumed the true control treatment effect to be equal to the observed effect from the historical control group. Many researchers have pointed out that the Makuch-Simon approach does not preserve the nominal power and type I error when considering the uncertainty in the true historical control treatment effect.

Calculating sample size in trials using historical controls