The development of nomograms to predict multiple pregnancy and multiple birth in frozen- thawed embryo transfer cycles: a retrospective study

Multiple pregnancy remains a major complication of assisted reproductive technology (ART) worldwide ( 1 , 2 ). The global incidence of multiple pregnancy after ART ranges from 2% to 35%, and the rate in FET cycles is approximately 13%, markedly higher than the 1.0%–1.2% observed in natural conception ( 3 , 4 ). Multiple pregnancy is strongly associated with elevated risks of preterm birth, low birth weight, cerebral palsy, neurodevelopmental disorders, and perinatal mortality ( 5 , 6 ). Iatrogenic multiple pregnancies cause substantial physical and psychological distress for patients and impose a considerable economic burden on healthcare systems ( 7 , 8 ). To mitigate multiple birth rates (MBR), the American Society for Reproductive Medicine (ASRM) recommends elective single embryo transfer (eSET) in patients aged ≤37 years ( 9 ). In 2018, the Chinese Expert Consensus on the Number of Embryos Transferred advocated eSET in the first transfer cycle and a maximum of two embryos per transfer cycle regardless of age ( 10 ). However, the adoption of eSET remains limited in many clinical settings, and clinicians face the persistent challenge of lowering MBR without compromising live birth rates (LBR) ( 11 , 12 ). Accurate predictive tools are urgently needed to balance pregnancy success and multiple pregnancy risk ( 13 , 14 ). Although numerous prediction models for ART outcomes have been developed, most focus on fresh embryo transfer or pooled fresh and FET cycles, and few are specifically designed and validated for MP and MB in FET cycles ( 15 , 16 ). This study aimed to develop and internally validate prediction nomograms for MP, MB, CP, and LB following FET using a large single-center cohort, to support personalized clinical decision-making.

A total of 8,687 frozen-thawed embryo transfer (FET) cycles were enrolled in this retrospective study, including 6,081 cycles in the training set and 2,606 cycles in the validation set. The overall clinical pregnancy rate was 56.1% (4,876/8,687), multiple pregnancy rate was 17.3% (1,502/8,687), live birth rate was 46.1% (4,007/8,687), and multiple birth rate was 12.7% (1,102/8,687). Baseline demographic, infertility, embryological, and endometrial preparation variables were well balanced between the training and validation cohorts, with no statistically significant differences (all P>0.05; Table 1 ). Baseline characteristics and clinical outcomes of the total cohort, training set, and validation set. Continuous variables are presented as mean ± standard deviation or median (interquartile range, IQR). Categorical variables are presented as number (percentage). Differences between the training and validation sets were analyzed using independent t-tests, Kruskal–Wallis tests, or chi-square tests, as appropriate. A P-value < 0.05 was considered statistically significant. The mean female age was 32.4 ± 4.6 years, mean male age was 34.5 ± 5.5 years, and mean body mass index (BMI) was 22.0 ± 3.2 kg/m². The median AMH level was 3.8 (2.2, 6.4) ng/ml, and median endometrial thickness on the transformation day was 9.7 ± 1.9 mm. Primary infertility accounted for 48.4% of cases, and secondary infertility for 51.6%. Tubal factor was the most common cause of infertility (50.6%), followed by double factors (19.8%) and male factors (17.8%). The majority of patients underwent 1 oocyte retrieval cycle (86.7%) and 1–2 FET cycles (92.6%). GnRHa-HRT was the most frequently used endometrial preparation protocol (58.5%), followed by conventional HRT (36.8%). Most cycles involved transfer of 2 embryos (69.3%), and 46.6% of cycles included transfer of 2 blastocysts. No significant intergroup differences were observed in sperm parameters, gonadotropin dosage and duration, insemination method, number of oocytes retrieved, number of frozen embryos, or number of remaining embryos after transfer (all P>0.05; Table 1 ). These data confirmed the homogeneity between the training and validation sets, providing a reliable foundation for subsequent model construction and validation. Lasso regression identified seven independent predictors for MP and MB: female age, male age, EMT on transformation day, number of transferred embryos, number of transferred high-quality embryos, number of transferred blastocysts, and total number of remaining embryos after transfer ( Figures 2A–D ). For CP, predictors were female age, AMH, EMT, number of transferred embryos, number of transferred high-quality embryos, number of transferred blastocysts, and total number of remaining embryos after transfer ( Figures 2E, F ). LB predictors further included male age ( Figures 2G, H ).Multicollinearity testing via GVIF^(1/(2*DF)) yielded all values < 2.5, showing no problematic collinearity among predictors. Based on the screened predictors, four visualized prediction nomograms were constructed for MP, MB, CP, and LB, respectively ( Figure 3 ). Each predictor was assigned a weighted score according to its regression coefficient, and the total score was mapped to the corresponding predicted probability on the bottom scale of the nomogram. Developed nomograms for predicting (A) multiple pregnancy, (B) multiple birth, (C) clinical pregnancy and (D) live birth in frozen-thawed embryo transfer (FET) cycles. To use the nomogram, locate the value of each variable on its corresponding axis, draw a vertical line to the points axis to determine the score for each variable, sum all scores to obtain the total points, and draw a vertical line from the total points axis to the bottom probability axis to obtain the individual predicted probability. To facilitate clinical application, web-based calculators embedded with complete regression formulas of the four nomograms were developed for rapid individualized risk assessment before embryo transfer ( Supplementary Figure S1 ). In a typical illustrative case: female age 33 years, male age 36 years, AMH 4.0 ng/ml, endometrial thickness 8 mm, 2 transferred blastocysts including 1 high-quality embryo, and 2 remaining embryos after transfer. The predicted probabilities were calculated as: clinical pregnancy ≈67.17%, multiple pregnancy ≈26.60%, live birth ≈55.23%, and multiple birth ≈18.65%. This example demonstrated that the nomograms could intuitively and quantitatively estimate individual probabilities before FET, supporting personalized clinical decision-making. Model performance is illustrated in Figure 4 . For the multiple pregnancy (MP) nomogram, the AUC was 0.798 (95%CI: 0.786–0.811) in the training set and 0.804 (95%CI: 0.785–0.824) in the validation set, with a sensitivity of 0.62 and specificity of 0.86. For the multiple birth (MB) nomogram, the AUC was 0.800 (95%CI: 0.786–0.814) in the training set and 0.809 (95%CI: 0.787–0.831) in the validation set, with a sensitivity of 0.85 and specificity of 0.63. Both models achieved good to excellent discriminative capacity, with AUC values greater than 0.80. Performance evaluation of the prediction nomograms. (A, D, G, J) Receiver operating characteristic (ROC) curves; (B, E, H, K) Calibration curves; (C, F, I, L) Decision curve analysis (DCA). (A–C) for multiple pregnancy (MP) models; (D–F) for multiple birth (MB) models; (G–I) for clinical pregnancy (CP) models; (J–L) for live birth (LB) models. Calibration curves showed excellent agreement between predicted probabilities and actual observed frequencies, closely approximating the ideal diagonal line, suggesting high consistency and reliability. Hosmer–Lemeshow goodness-of-fit tests confirmed no significant deviation from perfect calibration (MP: P = 0.28; MB: P = 0.178). Decision curve analysis (DCA) revealed that the MP nomogram provided positive net benefit within threshold probabilities ranging from 1% to 48%, and the MB nomogram within 1% to 60%, verifying favorable clinical applicability. For the clinical pregnancy (CP) and live birth (LB) nomograms, the discriminative performance was moderate. The AUC of the CP model was 0.690 in the training set and 0.689 in the validation set. The AUC of the LB model was 0.694 in the training set and 0.679 in the validation set. Both models achieved acceptable discriminative ability and goodness-of-fit, consistent with most published prediction models for live birth following ART. Internal validation via bootstrapping and random splitting further confirmed the stability and generalizability of all four models. Overall, the MP and MB models exhibited superior predictive performance, whereas the CP and LB models offered moderate-value references for individualized outcome estimation in clinical practice.

Determining the optimal number of embryos to transfer is one of the most complex decisions in IVF, requiring careful balancing between live birth and multiple pregnancy risks ( 13 , 20 ). Our study developed and validated four prediction nomograms for FET cycles, with the MP and MB models showing good discrimination, calibration, and clinical utility. To our knowledge, this is one of the few large-scale studies focusing specifically on MP and MB prediction in pure FET cycles ( 15 , 21 ). Female age was consistently predictive of all outcomes, consistent with well-established evidence that ovarian reserve and embryo competence decline with age ( 22 , 23 ). Female age is an independent risk factor for pregnancy outcomes in assisted reproductive technology, which further supports its essential role in pretreatment evaluation and prognostic stratification. With advancing female age, the quantity and quality of oocytes decrease progressively, leading to lower implantation potential and higher rates of pregnancy loss, which explains its stable predictive value across all endpoints in our models. Male age also entered the final models, supporting emerging evidence that advanced paternal age adversely affects embryo development and pregnancy outcomes ( 24 , 25 ). The identification of male age as a predictive factor underscores the growing recognition of paternal contributions to reproductive success. Advanced paternal age is associated with declined sperm quality, impaired embryo developmental competence, and elevated risk of early miscarriage, reinforcing the necessity of comprehensive couple-based fertility evaluation ( 25 ). These findings highlight the importance of assessing both partners for a holistic fertility evaluation, which can facilitate more targeted therapeutic strategies and optimize clinical outcomes in ART. Endometrial thickness on the transformation day was an independent predictor, confirming that adequate endometrial development improves implantation ( 26 , 27 ). Identifying the optimal range of endometrial thickness is critical for enhancing pregnancy outcomes in fertility treatment. A sufficiently thick and receptive endometrium provides a favorable microenvironment for embryo adhesion and invasion, and individualized endometrial preparation protocols may further improve implantation efficiency in FET cycles. The number of transferred embryos, high-quality embryos, and blastocysts were strong predictors of multiple pregnancy, reflecting the high implantation potential of morphologically good blastocysts ( 17 , 28 ). The number of high-quality embryos transferred emphasizes the pivotal role of embryo quality in achieving favorable clinical outcomes, which is consistent with previous prediction models in frozen-thawed embryo transfer cycles ( 29 ). Compared with cleavage-stage embryos, blastocysts undergo more rigorous natural selection during in vitro culture, which eliminates embryos with limited developmental potential. This enhanced selection process promotes better embryo-endometrium synchronization, thereby increasing implantation rates and shortening time to pregnancy. The total number of remaining embryos may serve as a surrogate marker of overall embryo cohort quality and ovarian response. A higher number of remaining embryos reflects a more robust ovarian response and a larger pool of viable embryos with diverse developmental stages and quality grades, which is indirectly associated with improved implantation and pregnancy potential. Notably, we separately incorporated the number of transferred high-quality embryos and transferred blastocysts into the prediction models to adjust for embryo quality and developmental stage; the total remaining embryo count remains an independent complementary predictor that captures the cumulative embryo reserve of each patient. Intriguingly, the MP and MB models achieved AUCs >0.80, outperforming CP and LB models (AUC≈0.69). This is consistent with previous reports that LB prediction remains challenging, with most models yielding AUC <0.70 ( 30 , 31 ). This performance discrepancy is biologically plausible: multiple pregnancy risk is predominantly governed by clearly documented embryological indicators such as the number and quality of transferred embryos, which are fully captured in our database. In comparison, clinical pregnancy and live birth are affected by a wider range of uncollected variables including subtle endometrial immune status, individual lifestyle habits and psychological factors, leading to limited predictive accuracy of CP and LB nomograms. For clinical application, we propose a hierarchical usage strategy for these four nomograms. The MP and MB nomograms with AUC >0.80 are the primary tool for stratifying multiple gestation risk, which addresses the core objective of the present study. The CP and LB models with moderate discriminative ability can only serve as auxiliary references rather than independent decision-making instruments. When clinicians decide the number of embryos to transfer, they should prioritize risk probabilities generated by MP/MB models and take CP/LB predicted results as secondary background information. Our study has several notable strengths. It features a relatively large sample size and rigorous internal validation, with comprehensive evaluation covering discrimination, calibration, and clinical utility. Furthermore, the exclusive focus on FET cycles helps minimize confounding factors caused by heterogeneous fresh-cycle conditions, strengthening the homogeneity of the study population. These nomograms offer a quantitative, patient-specific tool to inform embryo-transfer decision-making, moving beyond purely empirical strategies. By identifying high-risk patients, clinicians may consider recommending eSET to reduce multiple-pregnancy risk while preserving acceptable live-birth rates, which aligns with global efforts to improve ART safety ( 9 , 10 , 12 ). Limitations include its retrospective single-center design and the lack of external validation in independent cohorts, which may restrict its generalizability to populations with different patient characteristics, endometrial preparation regimens, and embryo laboratory protocols. Additionally, objective standardized scoring for embryo transfer difficulty was not routinely documented in electronic medical records and could not be incorporated into the present analysis, which might introduce residual prediction bias. In addition, live and multiple birth were defined using a gestational cutoff of 28 weeks according to local clinical practice, which may reduce direct comparability with ART studies adopting different gestational thresholds for live birth endpoints. Multi-level regression approaches for future multi-center prospective studies with external validation are warranted before widespread clinical adoption of these nomograms.

We developed and internally validated four nomograms incorporating routine clinical and embryological indicators to estimate individual risks of MP, MB, CP and LB before FET. These tools enable personalized pre-transfer risk assessment and can serve as auxiliary references for clinicians’ patient counselling. External multicenter validation and prospective trials are required to confirm their clinical value before broad routine application.

This retrospective study collected all frozen-thawed embryo transfer (FET) cycles performed at the Department of Assisted Reproductive Medicine, Sichuan Provincial People’s Hospital between January 2014 and January 2024 as the initial candidate pool. Cycles were sequentially excluded if they met any of the predefined exclusion criteria: donor sperm cycles, donor oocyte cycles, chromosomal abnormalities in either partner, preimplantation genetic testing (PGT) cycles, and cycles with missing key data. After stepwise screening and removal of ineligible records, a total of 8,687 valid FET cycles were ultimately retained for analysis. Among these cycles, 4,876 resulted in clinical pregnancies, within which 1,502 were multiple pregnancies; 4,007 cycles achieved live birth, and 1,102 of these live-birth cycles corresponded to multiple births. The complete participant screening workflow is visually summarized in Figure 1 . The study was approved by the Hospital Ethics Committee (No.: 2026-420), and informed consent was waived given its retrospective design. Study flow chart. Flow diagram of patient enrollment, exclusion criteria, grouping into training and validation sets, and outcomes included in the final analysis. Controlled ovarian hyperstimulation protocols and gonadotropin dosages were individualized. Human chorionic gonadotropin (hCG) was administered when at least one follicle reached ≥18 mm. Oocyte retrieval was performed 36 hours later under transvaginal ultrasound guidance. Conventional IVF or ICSI was used according to semen parameters. Embryos were cultured in a single medium at 37 °C under 5% O 2 , 6% CO 2 , and balanced nitrogen. All supernumerary embryos, regardless of whether fresh-embryo transfer was performed, were cryopreserved by vitrification. Endometrial preparation included GnRH-agonist hormone replacement therapy (GnRHa-HRT), HRT, natural cycles, and ovulation induction cycles. Embryo transfer was performed under abdominal ultrasound guidance. Cleavage-stage embryos of Grade I or II with uniform blastomeres and minimal fragmentation were defined as high-quality. Blastocysts graded ≥4BB by the Gardner system were considered high-quality ( 17 ). Endometrial thickness (EMT) was measured on the transformation day by transvaginal ultrasound, as the maximum anteroposterior diameter in the sagittal plane. All embryo-related predictors used in the models were uniformly operationalized according to routine clinical recording standards at our center. The number of transferred embryos referred to the total embryos placed into the uterine cavity per FET cycle; transferred high-quality embryos were counted based on standardized morphological grading as defined above; the number of transferred blastocysts referred to the count of blastocyst-stage embryos that were actually transferred after thawing; the total number of remaining embryos denoted all supernumerary cryopreserved cleavage-stage and blastocyst-stage embryos. All embryological data were prospectively documented in electronic medical records by laboratory embryologists, enabling consistent variable collection and reproducible model application in routine ART practice. Clinical pregnancy (CP): Presence of a gestational sac with fetal heartbeat on ultrasound 4–5 weeks after transfer. Multiple pregnancy (MP): Two or more fetal heartbeats detected. Live birth (LB): At least one live neonate delivered at ≥28 weeks of gestation.This gestational cutoff follows the standard classification of viable preterm infants in Chinese clinical perinatal practice; infants born before 28 weeks are categorized as extremely preterm infants with markedly different survival and clinical management characteristics. Multiple birth (MB): At least two live neonates delivered at ≥28 weeks of gestation, with the same ≥28-week gestational cutoff rationale as live birth definition. Data were analyzed using R software (v2.1.1). Continuous variables were expressed as mean ± SD or median (IQR); categorical variables as counts (percentages). Groups were compared using t-tests, Kruskal-Wallis tests, or chi-square tests. A two-sided P<0.05 was considered statistically significant. Cycles were randomly split into training (70%) and validation (30%) sets. Lasso regression was used for variable selection ( Figure 2 ). Prior to model building, multicollinearity was assessed using GVIF^(1/(2*DF)). All values were below 2.5, and no predictors were excluded due to collinearity concerns. Nomograms were developed and evaluated for discrimination (AUC), calibration (calibration curves with bootstrapping), and clinical utility via decision curve analysis (DCA) ( 18 , 19 ). To counteract the optimistic bias inherent to single random-split validation, internal bootstrapping with 500 resamples was performed to generate optimism-corrected AUC and calibration estimates. Variable selection for prediction models using Lasso regression. (A, C, E, G) Lasso coefficient profiles of the candidate features; (B, D, F, H) the selection of optimal parameters (lambda) by tenfold cross-validation, in which dotted vertical lines were drawn at the optimal values by using the minimum criteria and limits defined by 1 standard deviation. (A, B) for multiple pregnancy (MP) models; (C, D) for multiple birth (MB) models; (E, F) for clinical pregnancy (CP) models; (G, H) for live birth (LB) models.