Sample Size Calculation for the van Elteren Test Adjusting for Ties

Abstract

In this article we study sample size calculation methods for the asymptotic van Elteren test. Because the existing methods are only applicable to continuous data without ties, in this article we develop a new method that can be used on ordinal data. The new method has a closed form formula and is very easy to calculate. The new sample size formula performs very well because our simulations show that the corresponding actual powers are close to the nominal powers.

Key Words:

• Adjusting for ties
• Ordinal data
• Power calculation
• Sample size calculation
• Van Elteren test

ACKNOWLEDGMENTS

The authors thank the two anonymous referees for their suggestions which have led to a much improved presentation of the article.

Notes

Note: k = 1 for BIEF < 28; k = 2 for BIEF ≥ 28.

The stratum fractions are s ₁ = 78% and s ₂ = 22%.

The response proportions in placebo are fixed at (0.51, 0.39, 0.10) for patients with BIEF < 28 and (0.27, 0.55, 0.18) for patients with BIEF ≥ 28.

 = Pr (placebo > duloxetine) + 0.5 × Pr (placebo = duloxetine), at stratum k, see Equation (15).

 = Pr (placebo > duloxetine) + 0.5 × Pr (placebo = duloxetine), across strata, see Equation (16).