A Continuous Sigmoidal Mathematical Model for Male Fertility Assessment from Semen and Hormonal Profiles, with Machine-Learning-Derived Weights
DOI:
https://doi.org/10.54361/LJMR.20.3.92Keywords:
Applied Mathematical Modeling, Sigmoidal Normalization, Male Infertility, ; Random Forest Feature Weighting, Endocrinology, Precision MedicineAbstract
Background: Male factor infertility accounts for 40–50% of reproductive failures worldwide. Conventional diagnostic strategies rely on rigid univariate reference cutoffs established by the World Health Organization (WHO), which frequently fail to capture complex, multi-factorial, and non-linear biological interactions.Objective: To formulate a continuous, equation-based scoring model in which semen and hormonal parameters are mapped through sigmoidal functions rather than fixed WHO cutoffs, using a Random Forest ensemble only as an auxiliary tool to estimate the relative weight of each parameter. Methods: Each raw semen and hormonal measurement was transformed into a continuous sub-score using sigmoidal functions anchored to WHO reference thresholds. A Random Forest ensemble was used solely to estimate the relative contribution of each parameter via Gini impurity reduction; these weights were then fixed and used inside the mathematical aggregation model rather than the ensemble itself performing the diagnosis. The resulting index was evaluated on a synthetic clinical cohort (N = 500) using 10-fold cross-validation, and two representative patient profiles were traced step by step through every equation to confirm that the reported outputs are reproducible by hand. Results: On this synthetic benchmark, the mathematical scoring model reached a diagnostic accuracy of 87.2%, sensitivity of 83.6%, specificity of 90.8%, F1-score of 0.865, and an Area Under the Receiver Operating Characteristic Curve (AUC-ROC) of 0.958, compared with 59.6% accuracy for static WHO threshold rules on the same cohort; a fully data-driven logistic regression and an SVM-RBF baseline reached 91.2% and 90.8% accuracy respectively, so the interpretable hybrid model traded a small amount of raw discrimination for full mathematical transparency rather than outperforming every black-box baseline. Conclusion: These results suggest that a continuous, equation-based scoring approach can represent combined semen and hormonal impairment more accurately than fixed WHO cutoffs on this synthetic cohort, and motivate validation on real patient data before any clinical use is considered.
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