Sample size calculations when outcomes will be compared with an historical control

The usual formulae for calculating sample size are not valid when a treated cohort will be compared with an historical control population. Methods appropriate for a single group study may greatly underestimate the required sample size because they, in effect, assume a control population of infinite size. Methods appropriate for a two-group study require specification of the proportions of patients in the two groups--a requirement that can not be met when the size of the historical control group is fixed. An easily programmed iterative solution is presented and simulations indicating the validity of the method are performed.