A noniterative sample size procedure for tests based on t distributions. (6th June 2018)

• Record Type: Journal Article
• Authors: Tang, Yongqiang
• Is Part Of: Statistics in medicine. Volume 37:Number 22(2018)
• Page Start: 3197
• Page End: 3213
• Publication Date: 2018-06-06
• Subjects: analysis of covariance -- crossover trial -- equivalence and bioequivalence trials -- exact power -- Kenword‐Roger variance -- mixed effects models for repeated measures -- noninferiority trial; Medical statistics -- Periodicals; Statistique médicale -- Périodiques; Statistiques médicales -- Périodiques; 610.727
• DOI: 10.1002/sim.7807
• Languages: English
• ISSNs: 0277-6715

Abstract

Abstract : A noniterative sample size procedure is proposed for a general hypothesis test based on the t distribution by modifying and extending Guenther's6 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 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 mixed effects model for repeated measures, and the formula for ANCOVA is exact for normally distributed covariates. Numerical examples demonstrate the accuracy of the proposed methods particularly in small samples.