A noniterative sample size procedure for tests based on t distributions

TL;DR

This paper introduces a noniterative method for calculating sample sizes in t-distribution based tests, applicable to various clinical trial models, improving accuracy especially in small samples without needing covariate distribution assumptions.

Contribution

It extends Guenther's approach to a broader class of tests, providing a simple correction-based sample size procedure that is exact or nearly exact and does not require covariate distribution specification.

Findings

Accurate sample size estimates in small samples.

Method applicable to superiority, noninferiority, and equivalence tests.

Exact power calculations for ANCOVA and MMRM models.

Abstract

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.