Internal pilot studies I: Type I error rate of the naive t-test

When sample size is recalculated using unblinded interim data, use of the u sual t-test at the end of a study may lead to an elevated type I error rate . This paper describes a numerical quadrature investigation to calculate th e true probability of rejection as a function of the time of the recalculat ion, the magnitude of the detectable treatment effect, and the ratio of the guessed to the true variance, We consider both 'restricted' designs, those that require final sample size at least as large as the originally calcula ted size, and 'unrestricted' designs, those that permit smaller final sampl e sizes than originally calculated, Our results indicate that the bias in t he type I error rate is often negligible, especially in restricted designs, Some sets of parameters, however, induce non-trivial bias in the unrestric ted design, Copyright (C) 1999 John Wiley & Sons, Ltd.