Bayesian Shrinkage Versus Frequentist Variable Selection in Small-Sample Translational Research: A Monte Carlo Simulation Study Grounded in Regenerative Medicine Biomarker Discovery

Abstract

Introduction. Observational studies in regenerative medicine represent a promising frontier for the discovery of predictive biomarkers of therapeutic response, yet are structurally constrained by small sample sizes. This low-sample-size regime exposes variable selection methods to a high risk of overfitting and false discovery, with direct consequences for the reproducibility of findings. Although frequentist penalised approaches such as LASSO are widely adopted in this setting, their properties under small-sample conditions have not been systematically characterized relative to Bayesian shrinkage alternatives.

Objectives. To evaluate and compare the performance of frequentist and Bayesian variable selection methods across a range of sample sizes, with the aim of identifying which approach achieves the most robust trade-off between statistical power (TPR) and false discovery control (FDR) in small-sample translational research settings.

Methods. A Monte Carlo simulation study was conducted (2,000 replicates per sample size level) grounded in empirical parameters derived from a published clinical case study involving patients with Grade I Knee Osteoarthritis treated with Autologous Protein Concentrate (APC), classified as responders or non-responders based on NPRS variation. Five true signal variables (NPRS, IL-9, MIP-1β, RANTES, VEGF) and four noise variables were simulated across nine sample size levels (n = 20–100 per group). Seven methods were compared: standard logistic regression (GLM), LASSO with lambda.1se criterion, and five Bayesian approaches (Bayesian Ridge, Bayesian Lasso, Horseshoe, Horseshoe+, Spike-and-Slab). Performance metrics included TPR, FDR, Matthews Correlation Coefficient (MCC), Jaccard Index, and Exact Recovery rate.

Results. Bayesian Ridge demonstrated the most favourable and stable TPR/FDR trade-off across the full sample size range, maintaining FDR < 0.025 at all levels, systematically lower than LASSO (FDR 0.04–0.07) and GLM (FDR 0.03–0.06), while achieving TPR comparable to frequentist methods at n ≥ 60. MCC converged between Bayesian Ridge and LASSO at n ≥ 70; however, LASSO exhibited an anomalous FDR peak at n = 50–60, indicative of unstable signal-noise discrimination at the critical power threshold. Per-variable analysis confirmed a detectability hierarchy: NPRS, RANTES, and VEGF reached selection frequencies > 0.90 at n = 60 under Bayesian Ridge, whereas IL-9 and MIP-1β required larger samples.

Conclusions. In small-sample translational research, Bayesian Ridge regression offers a methodologically superior alternative to frequentist penalised approaches, combining adequate statistical power with robust false discovery control. Findings indicate a minimum sample size of n = 40–50 per group for reliable variable selection regardless of the method adopted, and support the pre-specification of Bayesian shrinkage models in biomarker discovery studies in regenerative medicine.