Multivariate Statistical Methods for Complex Data Structures: A Comprehensive Case Study in High-dimensional Genomic Analysis

Abstract

This article reviews recent developments and applications of advanced multivariate statistical methods for the analysis of complex data structures. By incorporating a genuine case study using real-world genomic data, the core aim of this work is to clarify the effectiveness, limitations, and future prospects of integrating conventional and contemporary techniques for high-dimensional, multicollinear, and heterogeneous datasets.

Design/methodology/approach – This study presents a critical synthesis of progress in multivariate analysis, focusing on the adaptation of Principal Component Analysis, Canonical Correlation Analysis, and Factor Analysis, and compares these with modern machine learning algorithms. A specific case study applies these methods to a breast cancer genomics dataset comprising over 300 genetic features and associated clinical patient data. The analytical workflow includes feature selection, dimensionality reduction, cross-source data integration, and model predictive evaluation.

Findings – The findings demonstrate that integrating classical multivariate strategies with machine learning expands the analytical scope and improves accuracy in disease status prediction. Combining these approaches enables the identification of intricate patterns and relationships between genetic variables and clinical data that may be missed by single-method analyses. The case study highlights the importance of hybrid approaches for key variable selection and robust interpretation in large-scale, complex datasets.

Research limitations/implications – This research is so far limited to the breast cancer genomics domain and uses secondary data, indicating a need for validation across a broader range of datasets and disciplines. Furthermore, the development of more user-friendly software solutions is essential to facilitate wider adoption of hybrid techniques.

Originality/value – The article offers the latest practical synthesis and perspective on multivariate analysis for complex data, supported by a genuine case study. The stepwise exposition of the analytical process on genomic data provides valuable contributions to statisticians, data scientists, and research professionals seeking to strengthen analytic methods for big and heterogeneous data structures.