Addressing Complete Separation in Male Infertility Risk Factor Modeling: A Firth Logistic Regression of BMI and Vitamin E

Abstract

Background: About 7% of men are affected by male infertility, up to 50% of cases remaining idiopathic. Proposed risk factors such as elevated BMI and reduced vitamin E show inconsistent evidence. Standard logistic regression often fails against Quasi-complete separation, a common statistical issue in case-control studies, and no data exist from Iraqi populations. Objective: To assess the independent associations of BMI and serum vitamin E with idiopathic male infertility using Firth's penalised logistic regression to overcome separation. Materials and Methods: This case control study included 160 men (80 infertile men, 80 controls) from Najaf, Iraq. BMI was recorded, and serum vitamin E was measured by a validated colorimetric assay. Firth's logistic regression was applied. Results: Infertile men have significantly increased BMI compared to control (median 28.6 vs. 25.9 kg/m²; p<0.001), and decreased levels of vitamin E (median 11.4 vs. 12.5 μg/mL; p<0.001). Each 1-kg/m² increase in BMI increased odds for infertility OR=2.53; 95% CI, 1.89–3.61; p<0.001, and each 1-μg/mL increase of vitamin E decreased odds by 61% (OR=0.39; 95% CI, 0.24–0.60; p<0.001). The model demonstrated to have an excellent discrimination (AUC=0.912; 95% CI, 0.869-0.955) and good calibration (Hosmer-Lemeshow p=0.586). Conclusions: Higher BMI and low vitamin E are independently associated with male infertility. Firth's regression effectively resolved quasi complete separation. BMI may be considered a useful screening tool in routine andrological assessment, while vitamin E's therapeutic role requires further study.