Asymptotic tests for tree ordered alternatives in one-way heteroscedastic ANOVA with application to clinical data

In clinical studies, treatment effects often follow a tree ordered structure, such as when multiple drug doses are compared with a placebo or therapies with a standard treatment. Motivated by such cases, we have developed two asymptotic tests based on multiple comparisons to test the hypothesis of equal treatment mean effects against the tree ordered alternatives in a one-way analysis of variance under heteroscedasticity. The asymptotic distribution of the test statistics has been obtained. A comprehensive simulation is performed utilizing the parametric bootstrap method to determine the critical points, sizes, and power of these tests. The accuracy of the bootstrap procedure was established for these tests. A comparative analysis of these tests with two other tests was conducted concerning their size and power values. The robustness of these tests was also investigated when data deviated from normality by considering five non-normal distributions: skew-normal, t, Laplace, mixture-normal, and exponential distributions. For practical use, the proposed tests were implemented as “R” packages and shared on GitHub for easy access. The proposed tests were implemented to two real-world medical datasets: one assessing memory performance across various antianxiety treatments, and another analyzing MiniPONS scores of individuals with bipolar disorder.