Analysis of Covariance in General Factorial Designs Through Multiple Contrast Tests Under Variance Heteroscedasticity

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>F</mml:mi></mml:mrow> <mml:annotation>$$ F $$</mml:annotation></mml:semantics> </mml:math> -test. However, in several samples, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>F</mml:mi></mml:mrow> <mml:annotation>$$ F $$</mml:annotation></mml:semantics> </mml:math> -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. ["Analysis of Covariance Under Variance Heteroscedasticity in General Factorial Designs," Statistics in Medicine 40 (2021): 4732-4749] 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.