Multiple comparisons of treatment against control under unequal variances using parametric bootstrap

Area of Science:

• Biostatistics
• Statistical Modeling
• Data Analysis

Background:

• Simultaneous comparisons of multiple treatment groups against a control are common in one-way analysis of variance (ANOVA).
• Dunnett's test is a standard method but assumes equal variances, an assumption often violated in real-world data.
• Data transformations may not always resolve heteroscedasticity or balance group sizes.

Purpose of the Study:

• To develop and evaluate a parametric bootstrap (PB) method for comparing multiple treatment group means against a control group.
• To address limitations of Dunnett's test, specifically when dealing with unequal variances and unbalanced data.
• To provide a robust statistical tool for complex experimental designs.

Main Methods:

• A parametric bootstrap (PB) method was developed for multiple comparisons against a control.
• Simulation studies were conducted to compare the PB method with Dunnett's test under various conditions (equal/unequal variances, balanced/unbalanced data).
• The method was applied to a real-world dataset on isotope levels in elephant tusks.

Main Results:

• The PB method demonstrated superior control of Type I error rates compared to Dunnett's test, especially with heteroscedastic variance and unbalanced designs.
• Statistical power of the PB method was comparable or higher than Dunnett's test in settings with unequal variances, unbalanced data, and larger sample sizes.
• The PB method successfully analyzed elephant tusk isotope data, which exhibited significant heterogeneity and imbalance, without data transformation.

Conclusions:

• The proposed parametric bootstrap (PB) method is a viable and robust alternative to Dunnett's test for comparing treatment groups with a control, particularly under unequal variances and unbalanced data.
• This method simplifies analysis by removing the need for data transformations to meet homogeneity of variance assumptions.
• The PB method offers improved statistical accuracy and easier interpretation in complex data scenarios.