Unlocking Insights: Enhanced Analysis of Covariance in General Factorial Designs through Multiple Contrast Tests under Variance Heteroscedasticity

TL;DR

This paper enhances ANCOVA analysis in factorial designs by introducing a multiple contrast test procedure that tests individual hypotheses, handles variance heteroscedasticity, and is effective even with small samples, supported by simulations and real data.

Contribution

It extends existing ANCOVA methods to allow testing of multiple hypotheses with confidence intervals, accommodating heteroscedasticity and small sample sizes.

Findings

Method performs well in small samples.

Wild-bootstrap improves test accuracy.

Applicable to real clinical trial data.

Abstract

A common goal in clinical trials is to conduct tests on estimated treatment effects adjusted for covariates such as age or sex. Analysis of Covariance (ANCOVA) is often used in these scenarios to test the global null hypothesis of no treatment effect using an $F$-test. However, in several samples, the $F$-test does not provide any information about individual null hypotheses and has strict assumptions such as variance homoscedasticity. We extend the method proposed by Konietschke et al. (2021) to a multiple contrast test procedure (MCTP), which allows us to test arbitrary linear hypotheses and provides information about the global as well as the individual null hypotheses. Further, we can calculate compatible simultaneous confidence intervals for the individual effects. We derive a small sample size approximation of the distribution of the test statistic via a multivariate t-distribution. As an alternative, we introduce a Wild-bootstrap method. Extensive simulations show that our methods are applicable even when sample sizes are small. Their application is further illustrated within a real data example.