Power and sample size evaluation for the Cochran–Mantel–Haenszel mean score (Wilcoxon rank sum) test and the Cochran–Armitage test for trend

Abstract

The power of a chi-square test, and thus the required sample size, are a function of the noncentrality parameter that can be obtained as the limiting expectation of the test statistic under an alternative hypothesis specification. Herein, we apply this principle to derive simple expressions for two tests that are commonly applied to discrete ordinal data. The Wilcoxon rank sum test for the equality of distributions in two groups is algebraically equivalent to the Mann-Whitney test. The Kruskal-Wallis test applies to multiple groups. These tests are equivalent to a Cochran-Mantel-Haenszel mean score test using rank scores for a set of C-discrete categories. Although various authors have assessed the power function of the Wilcoxon and Mann-Whitney tests, herein it is shown that the power of these tests with discrete observations, that is, with tied ranks, is readily provided by the power function of the corresponding Cochran-Mantel-Haenszel mean scores test for two and R > 2 groups. These expressions yield results virtually identical to those derived previously for rank scores and also apply to other score functions. The Cochran-Armitage test for trend assesses whether there is an monotonically increasing or decreasing trend in the proportions with a positive outcome or response over the C-ordered categories of an ordinal independent variable, for example, dose. Herein, it is shown that the power of the test is a function of the slope of the response probabilities over the ordinal scores assigned to the groups that yields simple expressions for the power of the test.

The Use of Radiation Therapy in Localized High-Grade Soft Tissue Sarcoma and Potential Impact on Survival

“…The trends were examined with the Cochran-Armitage test for trend. 20 Baseline characteristics and outcomes between groups were compared using Pearson's Chi square test for categorical variables and analysis of variance (ANOVA) for continuous variables. Multivariable logistic regression was used to predict factors that were associated with the administration of RT.…”

Predictive factors for longer length of stay in an emergency department: a prospective multicentre study evaluating the impact of age, patient's clinical acuity and complexity, and care pathways

“…For interval data, the non-parametric Kruskal–Wallis test or the Mann–Whitney U test was used. We used the Cochran–Armitage test for trend21 to order the effects of age on utilisation of ED resources and to asses if it varied linearly as a function of age group.…”

Clinical Significance of miR-210 and its Prospective Signaling Pathways in Non-Small Cell Lung Cancer: Evidence from Gene Expression Omnibus and the Cancer Genome Atlas Data Mining with 2763 Samples and Validation via Real-Time Quantitative PCR

“…Significant heterogeneity was defined when P < 0.1 or I 2 > 50% [21, 22]. Consequently, a random effects model was selected; otherwise, a fixed effects model was applied [23, 24]. In addition, if significant heterogeneity was observed, subgroup analysis was performed to explore the possible sources of heterogeneity.…”