Study design and participants

This retrospective cohort study was performed at two reproductive medicine centers: the First Affiliated Hospital of Guangxi Medical University and the Nanning Maternity and Child Health Hospital. It analyzed 1,168 single frozen-thawed blastocyst transfer cycles between June 2016 and December 2022. ART treatments were recorded in the ART database following the Technical Standard for Human-Assisted Reproduction by the Chinese Ministry of Health. The study included infertile women aged 35 years or older who underwent single frozen-thawed blastocyst transfers, with no preimplantation genetic testing.

Ethical approval and compliance

The study protocol obtained ethical approval from the Institutional Review Boards of the participating hospitals, specifically the First Affiliated Hospital of Guangxi Medical University Medical Ethics Committee (Approval Number: 2024-E445-01) and the Nanning Maternity and Child Health Hospital Medical Ethics Committee (Approval Number: YX20240627-1). Informed consent was secured from all participants.The authors confirm that the guidelines approved by the local institution were followed.

Ovarian stimulation and oocyte insemination

Ovarian stimulation protocols were not restricted, allowing for individualization based on the patient’s characteristics. The initial dose of recombinant follicle-stimulating hormone (rFSH, Gonal-F, Merck or Puregon, Organon) was determined by age, BMI, baseline FSH levels, and antral follicle counts [15]. Human chorionic gonadotropin (HCG, Ovitrelle, Merck) was administered when at least one follicle reached 18 mm or larger. Oocyte retrieval was performed 36 h post-HCG administration via transvaginal ultrasound-guided aspiration. Fertilization was carried out using either conventional IVF or intracytoplasmic sperm injection (ICSI) based on semen quality, following routine center protocols.

Embryo culture and blastocyst scoring

Embryos were cultured in G-TL media (Vitrolife) from fertilization to the blastocyst stage. The embryos were incubated at 37 °C in an atmosphere containing 5% O₂, 6% CO₂, and nitrogen as the balance gas, under oil. Blastocyst assessment was based on the Gardner grading system [16], evaluating expansion, inner cell mass, and trophectoderm quality.

Blastocyst vitrification and thawing procedures

Fully expanded blastocysts were artificially collapsed using a laser prior to cryopreservation. Vitrification was performed using Cryotop Safety Kits (KITAZATO), with embryos loaded onto cryotops on day 6 post-insemination and stored in liquid nitrogen. For warming, Blastocyst Warming Kits (KITAZATO) were used once the endometrium reached the required thickness for transfer. Blastocyst survival was assessed based on re-expansion two hours post-warming.

Endometrial Preparation and blastocyst transfer

Endometrial preparation for frozen embryo transfer (FET) was conducted using various protocols, including modified natural cycles, mild stimulation cycles, and hormone replacement therapy (HRT) cycles, with or without GnRH agonist pretreatment, as detailed below:

Modified natural cycle protocol

Follicular development was monitored via ultrasound starting on days 10–12 of the menstrual cycle. Once the dominant follicle reached a size of ≥ 18 mm, ovulation was triggered using recombinant human chorionic gonadotropin (Ovitrelle, Merck). Luteal support commenced after confirming ovulation, with a regimen of oral dydrogesterone (Duphaston, Abbott) 20 mg daily and vaginal progesterone gel (Crinone, Merck) 90 mg daily, facilitating the transition of the endometrium from the proliferative to the secretory phase. Blastocyst transfer was performed five days after ovulation.

Mild stimulation cycle protocal

In this protocol, if the dominant follicle measured < 12 mm by days 10–12, intramuscular human menopausal gonadotropin (LeBaode, Livzon) was administered to promote follicular growth. Ovulation was triggered with recombinant human chorionic gonadotropin (Ovitrelle, Merck) once the follicle reached ≥ 18 mm. Luteal support was initiated using the same regimen as in the modified natural cycle, with blastocyst transfer performed five days post-ovulation.

Hormone replacement therapy (HRT) protocol

HRT was initiated on days 3–5 of the menstrual cycle or after withdrawal bleeding, with estradiol valerate (Progynova, Bayer) administered at 2 mg three times daily. To reduce the risk of thrombosis, oral aspirin (50–100 mg daily) was prescribed, provided no contraindications were present. After 12–15 days, ultrasound was used to assess endometrial thickness, alongside serum estradiol (E2) and progesterone levels. Two options for progesterone support were available: (1) intramuscular progesterone (60 mg/day) combined with oral dydrogesterone (30 mg/day), or (2) vaginal progesterone gel (Crinone, Merck) (90 mg/day) combined with oral dydrogesterone (30 mg/day). The choice of regimen was based on patient preference. Blastocyst transfer was performed on the sixth day after initiating progesterone.

GnRH agonist combined with HRT protocol

This protocol involved downregulation with subcutaneous administration of triptorelin acetate (Diphereline, Ipsen) at 3.75 mg on days 2–5 of menstruation. Hormonal and endometrial parameters were monitored between days 28–35. Downregulation was confirmed when E2 levels were < 50 pg/mL, FSH < 5 IU/L, LH < 5 IU/L, and endometrial thickness < 5 mm. Once these criteria were met, estradiol valerate was administered, and the remaining steps followed the HRT protocol.

Clinical outcomes

The primary outcome measured was live birth, defined as the delivery of any viable infant at 28 weeks of gestation or later. Twins delivered by one mother were considered a single live birth.

Data Collection and candidate predictors

The original dataset included over 40 variables. Based on clinical expert recommendations, 19 variables relevant to live birth were selected: Maternal age at FET, Paternal age at FET, Maternal BMI, Basal FSH, Basal LH, Infertility duration, E2 on trigger day, Total gonadotropin dose, Number of oocytes retrieved, Endometrial thickness, Blastulation time, Blastocyst stage, Inner cell mass, Trophectoderm, Fragmentation on day 3, 8 blastomere on day 3, Infertility type, Fertilization method, and Endometrial preparation.

Data pre-processing and balancing

The study included 1,168 cycles, comprising 352 live birth cycles and 816 non-live birth cycles, with no missing values. Numerical data were standardized using z-score normalization for both training and validation sets to ensure comparability across features. Categorical variables were label-encoded for compatibility with machine learning models.Class imbalance was identified, with the live birth cycles representing approximately 30% of the total dataset. To address this, the Synthetic Minority Over-sampling Technique (SMOTE) was applied specifically to the live birth outcome variable in the training set to balance the data. The risk of potential oversampling and its implications, such as overfitting, were considered, and appropriate precautions were taken, as discussed in Alkhawaldeh et al. (2023). The balanced dataset was then split into training and validation sets at a ratio of 0.75 to 0.25.

The study included 1,168 cycles, comprising 352 live birth cycles and 816 non-live birth cycles, with no missing values. Numerical data were standardized for both training and validation sets. Categorical variables were label-encoded for compatibility with machine-learning models. Given the class imbalance, the Synthetic Minority Over-sampling Technique (SMOTE) was used to balance the data. The balanced data were divided into training and validation sets at a ratio of 0.75 to 0.25.

Feature selection

Feature selection aimed to enhance model predictability, interpretability, and performance by reducing dataset dimensionality and training time. Four classifiers—random forest, extreme gradient boosting (XGBoost), lasso regression, and extremely randomized trees (Extra Trees)—were applied to identify key predictors for live birth rate. The top four variables from each classifier were combined into a single feature subset, improving the model’s generalization on unknown data and ensuring coverage of all critical features.

Machine-learning Approach and evaluation

Various machine-learning models were employed to predict live birth rate, including XGBoost, logistic regression, support vector machine (SVM), random forest, multilayer perceptron (MLP), K-nearest neighbors (KNN), Extra Trees, light gradient boosting machine (LightGBM), gradient boosting, AdaBoost, Bagging, Gaussian Naive Bayes (Gaussian NB), Bernoulli Naive Bayes (Bernoulli NB), decision tree, quadratic discriminant analysis (QDA), ridge classifier, passive aggressive classifier, and CatBoost. The two best-performing models were combined into an ensemble model called Stacked Generalization (stacking) to enhance prediction performance and generalization.

A 10-fold cross-validation method, repeated three times, was used to create training and validation sets. The dataset was initially divided into 10 subsets. In each iteration, one subset served as the validation set while the remaining subsets were used for training. This process was repeated three times with different dataset partitions. Final results were obtained by averaging the outcomes from all rounds, ensuring stability and reliability.Predictive performance was evaluated using receiver operating characteristic (ROC) curves, area under the curve (AUC), accuracy, sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) with 95% confidence intervals (CI).

Statistical analysis

Statistical analysis was performed using Python software (version 3.12). Participant characteristics were summarized with means and standard deviations for continuous variables, and frequencies and percentages for categorical variables. T-tests were used to compare continuous variables, and chi-square tests or Fisher’s exact tests were used for categorical variables. A p-value of less than 0.05 was considered statistically significant.