  A noniterative sample size procedure is proposed for a general hypothesis
test based on the t distribution by modifying and extending Guenther's (1981)
approach for the one sample and two sample t tests. The generalized procedure
is employed to determine the sample size for treatment comparisons using the
analysis of covariance (ANCOVA) and the mixed effects model for repeated
measures (MMRM) in randomized clinical trials. The sample size is calculated by
adding a few simple correction terms to the sample size from the normal
approximation to account for the nonnormality of the t statistic and lower
order variance terms, which are functions of the covariates in the model. But
it does not require specifying the covariate distribution. The noniterative
procedure is suitable for superiority tests, noninferiority tests and a special
case of the tests for equivalence or bioequivalence, and generally yields the
exact or nearly exact sample size estimate after rounding to an integer. The
method for calculating the exact power of the two sample t test with unequal
variance in superiority trials is extended to equivalence trials. We also
derive accurate power formulae for ANCOVA and MMRM, and the formula for ANCOVA
is exact for normally distributed covariates. Numerical examples demonstrate
the accuracy of the proposed methods particularly in small samples.
