Validating Medical Treatment Effects by Projected F-tests under High Dimension with a Small Sample Size
DOI:
https://doi.org/10.6000/1929-6029.2025.14.73Keywords:
Dimension reduction, F-test, Monte Carlo study, Multiple mean comparison, Principal component analysisAbstract
This paper introduces a statistical method for validating treatment effects in high-dimensional medical data with small sample sizes. The method compares multiple multivariate population means under multivariate normality, using spherical matrix distribution theory and principal component analysis (PCA) for dimension reduction. The resulting test statistic follows an exact F-distribution under the null hypothesis of equal means, even when the sample size is smaller than the data dimension. Unlike classical MANOVA, the approach does not require equal covariance matrices across groups, making it more robust for real-world biomedical data where variance-covariance homogeneity rarely holds. Monte Carlo simulations show the test achieves accurate type I error control and favorable power. Application to real medical datasets with high-dimensional biomarkers further demonstrates its practicality and interpretability. This work provides a rigorous and versatile advancement for high-dimensional inference in biomedical research and related fields.
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