A data-driven and interpretable hybrid quantum-classical model for male infertility risk assessment

Nearly 15% of couples worldwide experience infertility, with Male Infertility (MI) accounting for 30-50% of these cases. Despite this burden, research on MI lags behind female infertility, particularly in understanding how demographic, clinical, lifestyle, and environmental factors interact to shape reproductive outcomes. Traditional approaches typically examine isolated indicators and struggle to capture the high-dimensional, nonlinear patterns present in Electronic Health Record (EHR) data. This study proposes a data-driven, interpretable framework integrating global fertility rate trends with EHR-derived male fertility data to (i) identify key determinants of MI, (ii) compare multiple classical Long Short-Term Memory (LSTM) architectures against a novel Quantum LSTM model embedding a Variational Quantum Circuit (VQC) directly within the LSTM gating mechanism, and (iii) evaluate the feasibility of quantum-enhanced sequential learning on small, heterogeneous healthcare datasets.

Two public datasets were used: a global fertility rate time series (1960-2020) and an EHR-derived male fertility dataset (n = 100, 10 features). After preprocessing (scaling, encoding, multicollinearity checks, and class-imbalance correction), several classical LSTM variants and the proposed Quantum LSTM were trained and validated using 5-fold cross-validation, repeated random train-test splits, and bootstrap resampling. Performance was assessed via accuracy, precision, recall, F1-score, and computational time, with statistical significance evaluated using Friedman and Wilcoxon signed-rank tests. SHAP (SHapley Additive exPlanations) was applied for feature-level and model-level interpretability.

Among classical models, unilateral LSTM performed most consistently (91.2% accuracy on fertility-rate data; 92.1% on male-fertility data). The Quantum LSTM achieved the highest accuracy on both datasets (92.6% and 93.8% respectively), a modest but statistically significant improvement (Wilcoxon p = 0.031 and p = 0.024; Cohen's d = 0.42-0.48) with narrower bootstrap confidence intervals, indicating greater stability. SHAP analysis identified daily sitting duration and age as the most influential predictors of male fertility outcomes, followed by season and alcohol consumption frequency, with clinical history variables contributing comparatively less.

These findings demonstrate the feasibility of embedding quantum circuits within LSTM gating for small-scale healthcare prediction tasks, yielding incremental rather than transformative gains over classical architectures. Observed associations are exploratory and non-causal, and given the limited sample size (n = 100), single-center source, and simulator-based quantum execution, results should be interpreted as hypothesis-generating rather than clinically conclusive. This work establishes a reproducible benchmarking framework combining classical and quantum-enhanced LSTM models with SHAP-based explainability for early MI risk stratification; future work should validate findings on larger, multi-center cohorts and real quantum hardware.