Comprehensive mathematical modeling of age-dependent oocyte quality and quantity for predicting live birth rate

Age-related decline in fertility is widely recognized. However, a quantitative evaluation of changes in oocyte quality and quantity remains insufficient. Therefore, developing a mathematical model to quantitatively predict live birth rates affected by these changes is essential for supporting decision-making in assisted reproductive technology.

In this retrospective cohort study, we developed a mathematical model to predict live birth rates based on oocyte quality and quantity using IVF treatment data from our clinic over an 8-year period. In the first stage, medically meaningful model functions were selected, and curve fitting was performed using weighted nonlinear least-squares regression to quantify age-related changes in oocyte quality and quantity. For oocyte quality, a comparative analysis was conducted on our clinical data and other large-scale datasets, modeling the live birth rate per single vitrified-warmed blastocyst transfer (SVBT) in correlation with the euploidy rate. For oocyte quantity, the distributions of anti-Müllerian hormone levels, antral follicle count, mature oocyte count, and transferable embryo count were analyzed by two-dimensional weighted nonlinear least-squares regression. In the second stage, logistic regression was applied to analyze live birth rates per SVBT and oocyte pick-up, incorporating multiple explanatory variables.

The adjusted R-squared values for the curve fitting results were above 0.9, indicating high fitting accuracy. In oocyte quality evaluation, all datasets showed that the values declined to half their peak by the age of 40 years. With respect to oocyte quantity, complete distribution characteristics were successfully modeled, enabling calculations at any percentile value. Logistic regression analysis incorporating blastocyst grade and culture duration as explanatory variables allowed for embryo selection based on a single indicator (i.e., the live birth rate). In the predictive model for live birth rate per oocyte pick-up, which included age, AMH levels, and number of retrieval cycles as explanatory variables, logistic regression analysis showed an AUC of 0.84 and an accuracy of 76.4%, demonstrating high predictive performance.

Mathematical models of age-dependent oocyte quality and quantity were successfully developed. These models were integrated to construct a multi-variable predictive tool for estimating live birth rates, offering valuable insights for reproductive decision-making.