Empirically-derived synthetic populations to mitigate small sample sizes.

Area of Science:

• Biostatistics
• Computational Biology
• Data Science

Background:

• Limited sample sizes in biomedical research can yield unreliable modeling results.
• Generating synthetic populations (SPs) is crucial for augmenting small datasets.
• Existing methods may not adequately capture complex data distributions.

Purpose of the Study:

• To present a novel method for generating synthetic populations from limited matched case-control data.
• To validate the statistical similarity between generated synthetic samples and original observed samples.
• To assess the utility of the synthetic data in a modeling context.

Main Methods:

• Multivariate kernel density estimations (KDEs) with unconstrained bandwidth matrices were employed to generate SPs.
• Differential Evolution (DE) optimization was used to determine optimal bandwidth matrices.
• Similarity was assessed using maximum mean discrepancy (MMD) tests and Principal Component Analysis (PCA) derived metrics (DModX).

Main Results:

• Four SPs were successfully generated from the limited sample (180 pairs).
• MMD tests confirmed statistical similarity between observed and synthetic sample empirical probability density functions (EPDFs).
• PCA scores and residuals showed no significant deviation between observed and synthetic samples, indicating data integrity.

Conclusions:

• The proposed methodology, combining KDE with DE optimization and PCA-based similarity metrics, effectively generates statistically similar synthetic data at the individual level.
• This approach demonstrates feasibility for creating larger synthetic samples from limited datasets.
• Further research is needed to evaluate performance with higher dimensionality and compare with techniques like bootstrapping.