Are your covariates under control? How normalization can re-introduce covariate effects.

Area of Science:

• Statistics
• Biostatistics
• Data Analysis

Background:

• Statistical tests often require normally distributed residuals.
• Rank-based inverse normal transformation (INT) is a common method to achieve normality.
• Adjusting for covariates before normalizing residuals is a frequent but potentially problematic approach.

Purpose of the Study:

• To investigate the impact of the order of covariate adjustment and rank-based INT on statistical assumptions.
• To compare two distinct methods for handling covariate effects and normality in statistical modeling.

Main Methods:

• Simulated and real data were analyzed.
• Two primary methods were compared: 1) adjusting for covariates then applying INT to residuals, and 2) applying INT to the dependent variable first, then adjusting for covariates.
• The linear correlation between the dependent variable and covariates was assessed at each stage.

Main Results:

• Applying INT after covariate adjustment re-introduced linear correlation between dependent variables and covariates, increasing Type I errors and reducing statistical power.
• Applying INT before covariate adjustment resulted in normally distributed residuals that were linearly uncorrelated with covariates.
• The latter approach maintained desirable statistical properties in both simulated and real data.

Conclusions:

• The order of operations in statistical analysis significantly impacts the validity of results.
• Applying rank-based inverse normal transformation (INT) to the dependent variable *before* controlling for covariate effects is recommended.
• This recommended approach ensures normally distributed residuals and preserves statistical power, leading to more reliable analyses.