Mathematical modeling and statistical analysis for predicting success in intrauterine insemination, intracytoplasmic sperm injection, and frozen embryo transfer

Infertility affects millions of couples worldwide, and assisted reproductive technologies (ART) such as intrauterine insemination (IUI), intracytoplasmic sperm injection (ICSI), and frozen embryo transfer (ET Freeze) are commonly used to treat it. However, the success rates of these methods vary considerably, and the factors that predict successful outcomes are not fully understood. Identifying these predictors is crucial for personalized treatment planning and improving clinical decision-making. This study aims to identify and compare the significant predictors of treatment success across three ART methods: IUI, ICSI, and ET Freeze. We also seek to develop statistical and mathematical models to evaluate the relationship between patient-related factors and pregnancy outcomes, and to assess which model provides the best fit for predicting treatment success. This retrospective cohort study was conducted at Royan Institute, Tehran, Iran, using data from 2011–2014. The unit of analysis was the ART treatment cycle. After data cleaning, 6240 cycles remained. The final ordinal logistic regression analyses included 4592 cycles with a known ordinal outcome (blighted ovum, abortion, or live birth). Repeated cycles from the same couple were accounted for using generalized estimating equations (GEE) with couple ID as the clustering variable. Ordinal logistic regression was used to model the association between predictors and treatment outcome. Of the 6240 participants, 209 underwent IUI, 2598 underwent ICSI, and 1783 underwent ET Freeze. For IUI, significant predictors of reduced success were increasing age (OR 0.94, 95% CI 0.87–1.00, p < 0.058), BMI \(≥ \) 30 kg/m \(^2\) (OR 0.46, 95% CI 0.19–1.10, p \(=\) 0.076), and longer duration of infertility (OR 0.93, 95% CI 0.86–1.02, p = 0.116). For ICSI, significant predictors included age (OR 0.93, 95% CI 0.92–0.95, p < 0.001), BMI \(≥ \) 30 kg/m \(^2\) (OR 0.74, 95% CI 0.58–0.95, p \(=\) 0.018), fertilization rate (OR 1.73, 95% CI 1.21–2.50, p \(=\) 0.003), number of mature oocytes (OR 2.31, 95% CI 1.41–3.83, p \(=\) 0.001), and number of grade A embryos (OR 1.37, 95% CI 1.04–1.82, p \(=\) 0.025). For ET Freeze, age (OR 0.97, 95% CI 0.95–0.99, p \(=\) 0.002) and number of previous abortions (OR 0.77, 95% CI 0.60–0.99, p \(=\) 0.037) were significant negative predictors of success. The predictors of treatment success differ significantly across the three ART methods. For IUI, BMI, duration of infertility, and age were the main predictors. For ICSI, a broader set of factors including BMI, age, number of embryos, fertilization rate, and PCOS were influential. For ET Freeze, only age and number of previous abortions were significant. These findings highlight the importance of patient-specific factors in ART outcomes and suggest that tailored treatment strategies based on individual predictors may improve success rates. The proposed statistical and mathematical models provide valuable tools for clinicians to better counsel patients and optimize treatment selection.