A practical approach for comparing means of two groups without equal variance assumption

Abstract

In this paper we consider two-groups of i.i.d. normally distributed random variables (N(mu(x),sigma(x) (2)) and N(mu(y),sigma(y) (2))) without assuming equal variance (sigma(x) (2) = sigma(y) (2)). We propose a simple method for constructing confidence bounds based on Howe's approximation I. Its applications in parallel clinical trial (testing H(0) : mu(x)-mu(y)=0 versus H(1) : mu(x)-mu(y)<0) and parallel bioequivalence (BE) trial (testing H(0):mid R:mu(x)-mu(y)mid R:delta versus H(1):mid R:mu(x)-mu(y)mid R:<delta) are studied. Sample size calculation formulae for both cases are derived. Their performances are evaluated by simulation. Our study shows that the proposed procedure can control type I error satisfactorily compared with Cochran-Cox's and Satterthwaite's approximations while maintaining a relatively high power. The proposed approach is not only simple for constructing the confidence limit, but also provides a simple and accurate formula for sample size calculation.

Reference Datasets for Bioequivalence Trials in a Two-Group Parallel Design

“…Furthermore, preliminary testing for equality of variances is flawed and should be avoided (12). If assumptions are violated, the t test becomes liberal, i.e., the patient's risk might exceed the nominal level and an alternative (e.g., based on the Welch correction) is suggested (11,13). FDA's guidance states: "For parallel designs […] equal variances should not be assumed" (14).…”

“…The conventional t test is fairly robust against violations of homoscedasticity but quite sensitive to unequal group sizes (11). Furthermore, preliminary testing for equality of variances is flawed and should be avoided (12).…”

On group sequential procedures under variance heterogeneity

“…It is also easy to show that, if the design is balanced, a ratio such as the one shown in Equation (2) has an approximate standard normal distribution even when the sample size is only moderately large. 8 However, we will demonstrate that our modified procedure is more accurate than the method based on LS in small samples, regardless of how well balanced the design is and how large the degree of variance heterogeneity is.…”

A Bayesian Approach on Sample Size Calculation for Comparing Means

“…Note that * is purely determined by the sample size used in the pilot study, which decreases to 1 as the sample size goes to infinity. Also, note that the most commonly used sample size calculation formulas are linear functions in terms ofˆ 2 (see, for example, Chow and Wang, 2001;Chow et al, 2002aChow et al, ,b, 2003aWang and Chow, 2002). Therefore, the Bayesian sample size can be obtained by simply multiplying the traditional sample size by a factor of * .…”