Parametric versus non-parametric statistics in the analysis of randomized trials with non-normally distributed data

Area of Science:

• Biostatistics
• Clinical Trial Analysis
• Statistical Modeling

Background:

• Parametric statistics are often deemed unsuitable for non-normal distributions.
• The Mann-Whitney test traditionally offers greater power than the t-test for non-normal data.
• Randomized trials commonly assess treatment effects on endpoints like blood pressure or pain, necessitating appropriate statistical analysis.

Purpose of the Study:

• To compare the statistical power of Mann-Whitney and ANCOVA for analyzing non-normal data.
• To evaluate the unbiasedness of ANCOVA in estimating treatment group differences.
• To examine the distribution of change scores in non-normally distributed variables.

Main Methods:

• Simulated five non-normal distributions using polynomials for baseline and post-treatment scores.
• Conducted simulation studies to compare Mann-Whitney and ANCOVA power across distributions.
• Varied sample size, correlation, and treatment effect type (ratio or shift) in simulations.

Main Results:

• Change scores between skewed baseline and post-treatment data exhibited a trend towards a normal distribution.
• ANCOVA demonstrated superior power compared to Mann-Whitney in most scenarios, particularly with log-transformed data.
• ANCOVA yielded an unbiased estimate of the treatment effect.

Conclusions:

• ANCOVA is recommended for analyzing randomized trials with pre- and post-treatment measurements.
• While generally superior, ANCOVA can be less powerful than Mann-Whitney in extreme cases.
• In such extreme scenarios, the interpretability of ANCOVA's treatment effect estimate may be compromised.