ABSTRACT
Purpose
To develop a simulation model to guide single embryo transfer (SET) versus double embryo transfer (DET) decisions by minimizing twin risk per transfer while maintaining treatment efficiency.
Methods
This retrospective observational study included individuals undergoing SET or DET with frozen blastocysts in hormone replacement therapy. Three generalized estimating equation‐based models were developed: ongoing pregnancy after SET (Model 1) and DET (Model 2), and twin pregnancy after DET (Model 3). Model 1 was constructed using propensity score‐matched SETs comparable to DETs. The simulation aimed to identify the optimal transfer sequence for patients with multiple blastocysts using a stepwise optimization that selects SET or DET at each transfer while maximizing pregnancy probability and constraining twin risk below predefined thresholds.
Results
5721 DET and 5719 matched SET cycles were included in the analysis. The ongoing pregnancy rate was 20.1% in matched SET and 25.1% in DET, while the ongoing twin pregnancy rate following DET was 5.5%. Area under the curve was 0.77, 0.73, and 0.82 for Model 1–3, respectively. Simulation demonstrated an optimal sequence combining SET/DET under the individualized twin risk in a variety of scenarios (https://sites.google.com/view/det‐simulator/).
Conclusions
This model supports individualized embryo transfer planning by balancing treatment efficiency and twin risk.
Keywords: algorithm, decision curve analysis, model, prediction, simulation
1. Introduction
When multiple frozen blastocysts are available, single embryo transfers (SETs) should be prioritized to decrease twin risk [1], but patients may request double embryo transfers (DETs). In such a situation, clinicians have to provide information on the medical, psychological, financial, and ethical issues that might arise due to twin pregnancy, respecting patients' autonomy [2]. If patients request DETs after the well‐informed conversation, clinicians will select the optimal transfer strategy, maintaining the potential to achieve the best live birth rate at each transfer while minimizing the risk of twin pregnancy.
In clinical settings, clinicians should consider varied information such as medical risks, maternal age, infertility treatment history, causes of infertility, and blastocyst quality to balance between twin risk and achieving live birth [1, 2]. When DET is justified after careful consideration of each individual's own circumstances, in accordance with widely accepted guidelines such as those from the European Society of Human Reproduction and Embryology (ESHRE) and the American Society for Reproductive Medicine (ASRM) [1, 2], clinicians have to select a pair of blastocysts. However, it is challenging to calculate twin risk and live birth rate among all potential combinations of blastocysts in daily clinical practice.
Previous studies have proposed methods to estimate the probability of live birth after SET or DET, as well as the risk of twin pregnancy after DET [3, 4, 5, 6, 7]. However, few studies have addressed the selection between SET and DET while considering all possible combinations of blastocysts based on the estimated probabilities of live birth and twin risk. Furthermore, these models would not be used simultaneously in clinical practice due to differences in the settings in which they were developed.
Given the limited availability of tools or methods to assist in selecting optimal blastocyst combinations and advising against DET based on twin risk, we aimed to develop a simulation model integrating both SET and DET. The model was designed to support clinical decision making from two perspectives: (1) minimizing twin risk per transfer, while (2) maintaining treatment efficiency through the optimal combination of SET and DET under individualized twin risk thresholds.
2. Material and Methods
2.1. Study Design and Participants
This retrospective observational study was conducted at a private fertility clinic in Japan between January 2013 and October 2024. Data on patient characteristics and embryo parameters were extracted from electronic medical records and the institutional database. The study population included individuals who underwent SET or DET between January 2013 and August 2024. Oocytes retrieved from patients younger than 26 or older than 45 years were excluded due to a small number of cases. Transfer cycles involving nonblastocyst embryos or preimplantation genetic testing for aneuploidy or structural rearrangements were also excluded. Transfer cycles with missing information regarding maternal age at oocyte retrieval, blastocyst grade, number of transfers, or transfer outcomes were excluded. Transfer outcomes, ongoing pregnancy and ongoing twin pregnancy, were measured at 8–9 weeks of gestation, as pregnant patients are referred to hospitals for delivery at this gestational age in our institution. Although pregnancy outcomes were reported by both patients and hospitals after the pregnancy ended, we used outcomes at 8–9 weeks of gestation rather than live birth to minimize selection bias due to underreporting, because delivery outcomes were not consistently reported by all patients or hospitals. Patients with favorable outcomes may be more likely to report their delivery outcomes compared to those with unfavorable outcomes [8]. We obtained approval from our institutional review board for this analysis.
This study comprised four steps (Figure 1). First, we constructed a numeric grading score for embryo quality using data from all single embryo transfers (study population A). This approach was adopted because the original Gardner embryo grading scale is categorical and does not provide a single continuous measure of embryo quality or a clear ranking across embryos, which was necessary for the second and third steps [9]. Therefore, a numeric score was developed to assign an ordered scale reflecting the probability of ongoing pregnancy for each blastocyst. Second, using propensity score matching with the numeric embryo grading score and demographic data, we identified SET transfers with a comparable propensity for DET transfers (study population B). This matching was performed because we assumed that, in the simulation model, any transfer could be either SET or DET. Therefore, prediction models for SETs should be developed using a population with a similar likelihood of undergoing DET. Third, prediction models of ongoing pregnancy at 8–9 weeks of gestation were constructed among SETs (Model 1 based on study population B) and DETs (Model 2 based on study population C, defined as individuals who underwent DET). Additionally, a prediction model for ongoing twin pregnancy at 8–9 weeks of gestation among DETs was constructed (Model 3 based on study population C). A prediction model for twin pregnancy after SETs was not constructed due to the low prevalence of twin pregnancy among SETs. Fourth, we constructed a simulation model of transfers based on constructed prediction models.
FIGURE 1.
Overview of the analytic workflow. A numeric embryo grading score was first developed to quantify embryo quality. Propensity score matching was then performed to create comparable SET and DET groups. Prediction models were developed for ongoing pregnancy after SET (Model 1), ongoing pregnancy after DET (Model 2), and twin pregnancy after DET (Model 3). These models were subsequently applied in a simulation framework to identify optimal embryo transfer strategies under individualized twin risk thresholds. DET, double embryo transfer; SET, single embryo transfer.
The simulation was conducted under a clinical scenario in which an individual with a cohort of two to eight available frozen blastocysts considers DET while aiming to reduce the risk of twin pregnancy under the individualized thresholds. The maximum acceptable twin risk per transfer was predefined prior to simulation and ranged from 1% to 25%. For simulation, the following information was required: embryo characteristics (maternal age at oocyte retrieval, Gardner grade [9], and time to blastocysts) for all available frozen blastocysts and the current number of transfers. We simulated two transfer strategies: (1) all SET with stepwise optimization; (2) combination of SET and DET with stepwise optimization. The strategy logic of stepwise optimization was selecting the SET or DET with the highest likelihood of ongoing pregnancy at each transfer step, one transfer at a time under the threshold of twin risk selected a priori. The stepwise optimization algorithm used to identify the optimal sequence and combination of SET and DET is described in the statistical analysis section. For each simulated transfer, either a single embryo or a pair of embryos was selected, and the predicted pregnancy rate and twin risk per transfer were presented. In addition, cumulative pregnancy and twin risk were updated sequentially and summarized in both tables and graphical displays.
2.2. Ovarian Stimulation and Oocyte Retrieval
Ovarian stimulation protocols were individualized based on each individual's ovarian reserve, which was assessed using basal follicle‐stimulating hormone (FSH), anti‐Müllerian hormone (AMH), and antral follicle count. Details of protocols are presented in Appendix S1.
2.3. Embryo Culture
Fertilization of the retrieved oocytes was performed using conventional in vitro fertilization or intracytoplasmic sperm injection. Embryos were cultured under controlled conditions. Details of protocols are presented in Appendix S1.
2.4. Evaluation of Blastocysts
At least two embryologists graded each blastocyst according to the Gardner embryo grading scale [9]. To ensure consistency in assessment, all procedures adhered to an established protocol, and embryologists who had completed institutional training were permitted to perform embryo evaluations. The training involved evaluating whether trainees could consistently assign the same grades as experienced embryologists using identical embryo images.
2.5. Vitrification
Blastocysts graded higher than 3CC were vitrified using the vitrification kit VT101 (Kitazato Corporation, Tokyo, Japan) and Cryotop (Kitazato Corporation, Tokyo, Japan) and stored in liquid nitrogen storage tanks.
2.6. Embryo Transfer
All embryo transfers were performed in frozen–thawed embryo transfer under hormone replacement therapy cycles. Details of protocols are presented in Appendix S1.
2.7. Statistical Analysis
2.7.1. Numeric Embryo Grading Score
The numeric embryo grading score was calculated as a linear prediction of generalized estimating equation (GEE) with ongoing pregnancy at 8–9 weeks of gestation as a dependent variable [10, 11]. Independent variables included embryo morphological grading based on the Gardner scale (expansion stage, inner cell mass, and trophectoderm) [9] and time to blastocyst formation (days). Models were constructed under the assumption of exchangeable or independent correlations among embryos from the same individual. Model selection was guided by the quasi‐likelihood under the independence model criterion [12]. Model fit was assessed by the likelihood ratio chi‐square and calibration plot. The discriminative ability of a model was assessed by the receiver operating characteristic (ROC) curve. Internal validation was examined using 10‐fold cross‐validation. Details of model construction are presented in Appendix S2.
2.7.2. Propensity Matched SETs With DETs
A propensity score for undergoing DET was estimated at the transfer level using a logistic regression model with independent variables including maternal age at oocyte retrieval, AMH level, parity, number of prior transfers, and numeric embryo grading score. For DETs, the embryo with the higher score among the two transferred was used for the calculation of the propensity score. This approach allowed direct comparability with the single embryo in SET and was enabled by the use of a numeric embryo grading score. Propensity score matching was performed at the transfer level using one‐to‐one nearest‐neighbor matching under the common support without replacement. Because the matching was done at the transfer rather than the patient level, the same individual could contribute transfers to both the SET and DET groups. This approach was considered appropriate because the aim was not to compare SET and DET outcomes directly but to obtain a SET population with a similar likelihood of undergoing DET for subsequent model development [13]. Standardized mean differences (SMDs) for each variable were calculated before and after propensity score matching. Imbalances in the distribution of variables between SET and DET were assessed using standardized percent bias, with values less than −10% or greater than 10% considered indicative of potential imbalance [14]. Details of the matching procedure are provided in Appendix S3.
2.7.3. Model 1: Ongoing Pregnancy After SET
A prediction model of the probability of achieving an ongoing pregnancy at 8–9 weeks of gestation after SET was constructed based on study population B. Details of model construction are presented in Appendix S4 in the supplements. We initially constructed models under the assumption of exchangeable correlations among transfers from the same individual using generalized estimating equations. Predictors included maternal age at oocyte retrieval, number of transfers, and numeric embryo grading score. The relationships between continuous predictors and the outcomes were assessed for linearity. Nonlinear associations were modeled using spline terms, which were retained when they significantly improved model fit based on the Wald test. Interaction terms were also tested to evaluate potential effect modification and included if they contributed to model performance. We examined multicollinearity among the variables by calculating the variance inflation factor. When multicollinearity was noted due to a high variance inflation factor, exclusion of variables that were highly correlated with other variables would be considered. Model comparison was conducted using the Wald test and the quasi‐likelihood under the independence model criterion [12]. Model calibration was assessed via calibration plots and the Hosmer–Lemeshow goodness‐of‐fit test. Discrimination was evaluated using ROC curve analysis, and the AUC was reported. Internal validation was examined using 10‐fold cross‐validation. The optimal cutoff points for each model were determined using Yauden's index. The sensitivity, specificity, positive predictive value, negative predictive value, and accuracy were calculated based on the optimal cutoff point. The clinical utility of a model was assessed using decision curve analysis [15, 16]. The assumption of decision curve analysis for prediction models of ongoing pregnancy is presented in Appendix S4. The usefulness of a model was measured by the percentage increase in the number of ongoing pregnancies achieved without performing unnecessary transfers, compared to the treat‐all strategy, in which all embryos are transferred regardless of the likelihood of ongoing pregnancy. The usefulness was also evaluated by the percentage reduction in transfers, without missing any embryos that could have resulted in an ongoing pregnancy if transferred, compared to the treat‐all strategy.
2.7.4. Model 2: Ongoing Pregnancy After DET
A prediction model of the probability of achieving an ongoing pregnancy at 8–9 weeks of gestation after DET was constructed based on the study population C. Predictors included maternal age at oocyte retrieval, number of transfers, and numeric embryo grading score of two embryos. An embryo with a higher score was treated as the first embryo and one with a lower score as the second embryo in the prediction model. The modeling process and evaluation of clinical utility followed the same procedures described for Model 1. Details of model construction are presented in Appendix S5.
2.7.5. Model 3: Ongoing Twin Pregnancy After DET
A prediction model of the probability of ongoing twin pregnancy at 8–9 weeks of gestation after DET was constructed based on the study population C. Predictors included maternal age at oocyte retrieval, number of transfers, and numeric embryo grading score of two embryos. An embryo with a higher score was treated as the first embryo and one with a lower score as the second embryo in the prediction model. The modeling process followed the same procedures described for Model 1. Details of model construction and the assumption of decision curve analysis for a prediction model of twin risk are presented in Appendix S6. The clinical utility of a model was measured by the percentage decrease in the number of ongoing twin pregnancies compared to the treat‐all strategy, in which all embryos are transferred regardless of the likelihood of ongoing twin pregnancy.
2.7.6. Simulation Model
The stepwise optimization algorithm followed the four steps: (1) Evaluate all remaining embryos for SET and DET options. Ongoing pregnancy rate at 8–9 weeks of gestation and twin risk were calculated for all possible SET and DET options based on Model 1–3. (2) Filter out those exceeding the per‐transfer twin risk threshold selected a priori. (3) Select SET or DET with the highest predicted pregnancy rate. (4) Repeat until all embryos are used or no valid combinations remain. For explanatory purposes, cumulative ongoing pregnancy and cumulative twin risk were calculated. The formulas for the cumulative ongoing pregnancy rate and twin risk are presented in Appendix S7.
All statistical tests were 2‐sided, and the statistical significance level was α = 0.05. All statistical analyses were performed using Stata 19.5 (StataCorp, College Station, TX). The simulation model is available online (Appendix S8: https://sites.google.com/view/det‐simulator/).
3. Results
3.1. Numeric Embryo Grading Score
Of the 19 087 individuals who underwent SET or DET, 14 823 individuals with 39 396 transfers (SET: 33 675; DET: 5721) were included in the study population (Figure 2). For the construction of the numeric embryo grading score, data of 33 675 SET were used (Study population A). Among study population A, 27.5% (9270/33 675) of SET resulted in ongoing pregnancy at 8–9 weeks of gestation. The numeric scale of embryo grading was constructed based on Gardner grading and time to blastocyst. The AUC of numeric embryo grading for the ongoing pregnancy at 8–9 weeks of gestation was 0.70 (95% confidence interval (95% CI): 0.69–0.70). To support the visual interpretation of numeric grading, the line scale for embryo grading is presented in Appendix S2. This numeric grading was used for the propensity score matching of single embryo transfers to double embryo transfers and the following prediction models.
FIGURE 2.
Cohort diagram. AMH, anti‐Müllerian hormone; DET, double embryo transfer; PGT‐A/SR, preimplantation genetic testing for aneuploidy/structural rearrangements; SET, single embryo transfer.
3.2. Propensity Matched SETs With DETs
5719 SET that have a similar propensity to DET (Study population B) compared to 5721 DET (Study population C) were selected by propensity score matching. Two DET cases could not be matched to any SET because their propensity scores fell outside the common support range. Given the small number of unmatched cases, study population B was considered to have a comparable propensity to DET as study population C (Appendix S3). After matching, the distributions of most variables were well balanced, with SMDs approximately within ±0.10 (Table 1). Potential imbalances remained for maternal age at oocyte retrieval (SMD = 0.106) and infertility cause (other factor) (SMD = 0.149). However, maternal age at oocyte retrieval, an important predictor in the models, was similarly distributed between DET and SET, despite a small residual imbalance (SMD = 0.106), suggesting a limited impact on model development and simulation results. Among study populations B and C, embryo transfers resulting in ongoing pregnancy at 8–9 weeks of gestation were 20.1% (1150/5719) and 25.1% (1433/5721), respectively. Among study populations B and C, embryo transfers resulting in ongoing twin pregnancy at 8–9 weeks of gestation were 0.2% (11/5719) and 5.5% (315/5721), respectively.
TABLE 1.
Characteristics of transfers.
| Characteristics | DET (n = 5721) | SET (n = 5719) | SMD after matching |
|---|---|---|---|
| Maternal age at oocyte retrieval (years) | 38.0 (34.0–40.0) | 38.0 (35.0–40.0) | 0.106 |
| AMH (ng/mL) | 2.3 (1.2–4.0) | 2.0 (1.0–3.7) | −0.046 |
| BMI (kg/m2) | 20.7 (19.3–22.9) | 20.6 (19.2–22.5) | −0.062 |
| Parity | 0.0 (0.0–0.0) | 0.0 (0.0–0.0) | −0.060 |
| Pregnancy loss | 1.0 (0.0–1.0) | 1.0 (0.0–1.0) | −0.047 |
| Total number of oocyte retrieval | 1.0 (1.0–3.0) | 1.0 (1.0–3.0) | 0.042 |
| Current number of embryo transfer | 6.0 (4.0–8.0) | 5.0 (3.0–9.0) | −0.052 |
| Causes of infertility | |||
| Endometriosis | 458 (8.0) | 452 (7.9) | −0.004 |
| Male factor | 1744 (30.5) | 1723 (30.1) | −0.008 |
| Ovulatory factor | 532 (9.3) | 496 (8.7) | −0.095 |
| Tubal factor | 745 (13.0) | 572 (10.0) | −0.022 |
| Unknown | 800 (14.0) | 651 (11.4) | −0.078 |
| Others | 1442 (25.2) | 1825 (31.9) | 0.149 |
| Embryo quality (better one for DET) | −1.2 (−1.6 to −0.6) | −1.2 (−1.8 to −0.6) | −0.045 |
| Embryo quality (second one for DET) | −1.8 (−2.7 to −1.2) | — | — |
Note: Nonnormally distributed continuous variables were reported as median (IQR), and categorical variables as number (percentage).
Abbreviations: AMH, anti‐Müllerian hormone; BMI, body mass index; DET, double embryo transfer; SET, single embryo transfer; SMD, standardized mean difference.
3.3. Model 1: Ongoing Pregnancy After SET
The final model included maternal age at oocyte retrieval, number of transfers, and score of embryo, with spline terms incorporated for maternal age and number of transfers to improve model fit (Table 2). For maternal age, the decline in ongoing pregnancy probability was modest before 37 years but became substantially steeper thereafter. For the number of previous transfers, pregnancy probability decreased with each additional transfer, with the rate of decline becoming less steep after approximately the fifth transfer. For embryo quality, a one‐unit increase in this score was associated with nearly a twofold increase in the odds of achieving an ongoing pregnancy. The model demonstrated an AUC of 0.77 (95% CI: 0.75–0.78) and a cross‐validated AUC of 0.77 (95% CI: 0.75–0.78). At the optimal predicted probability threshold of 0.23, the model yielded a sensitivity of 0.70, specificity of 0.70, PPV of 0.37, NPV of 0.90, and an overall accuracy of 0.70. Decision curve analysis suggested that Model 1 may provide clinical utility across a range of threshold probabilities. Compared with the treat‐all strategy, the model demonstrated a higher net benefit within probability thresholds of approximately 10%–40%. This indicates that the model may help identify individuals more likely to achieve ongoing pregnancy at 8–9 weeks of gestation (Figure 3).
TABLE 2.
Final models and discriminative abilities.
| Outcome | Event rate | Predicted probability | AUC (95% CI) | Cross‐validated AUC (95% CI) | Optimal cutoff | Sensitivity | Specificity | PPV | NPV | Accuracy | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Model 1 | |||||||||||
| Final model | Ongoing pregnancy after SET | 20.1% (1150/5719) | (1 + e−logit1)−1 | 0.77 (0.75–0.78) | 0.77 (0.75–0.78) | 0.23 | 0.70 | 0.70 | 0.37 | 0.90 | 0.70 |
| Model 2 | |||||||||||
| Final model | Ongoing pregnancy after DET | 25.1% (1433/5721) | (1 + e−logit2)−1 | 0.73 (0.71–0.74) | 0.73 (0.71–0.74) | 0.26 | 0.70 | 0.65 | 0.40 | 0.87 | 0.66 |
| Model 3 | |||||||||||
| Final model | Twin pregnancy after DET | 5.5% (315/5721) | (1 + e−logit3)−1 | 0.82 (0.80–0.84) | 0.82 (0.80–0.84) | 0.06 | 0.07 | 0.99 | 0.25 | 0.95 | 0.94 |
Note: Model 1: A prediction model of the probability of achieving an ongoing pregnancy at 8–9 weeks of gestation after SET. Model 2: A prediction model of the probability of achieving an ongoing pregnancy at 8–9 weeks of gestation after DET. Model 3: A prediction model of the probability of ongoing twin pregnancy at 8–9 weeks of gestation after DET. Logit1 = −0.0217689*Age−0.2231575*(Age−37)−0.0537812*Transfer+0.0105698*(Transfer−5) + 0.9806063*Score + 0.9773164. Logit2 = −0.0127409*Age−0.2341916*(Age−37)−0.0231093*Transfer−0.0833019*(Transfer−7) + 0.6907298*Score1−0.5167250*(Score1−(−0.5)) + 0.2604407*Score2 + 0.0072662*(Age−37.1819600)*(Transfer−6.5667830) + 0.0237129*(Age−37.1819600)*(Score2−(−1.9093100)) + 1.1857060. Logit3 = −0.0952458*Age−0.2826623*(Age−37)−0.0566743*Transfer + 0.6808651*Score1 + 0.9139849*Score2−0.3674811*(Score1−(−1.2132400))*(Score2−(−1.9093100)) + 3.2763220.
Abbreviations: 95% CI, 95% confidence interval; Age, maternal age at oocyte retrieval; AUC, area under curve; DET, double embryo transfer; NPV, negative predictive value; PPV, positive predictive value; Score, numeric score of an embryo; Score1, numeric score of an embryo 1; Score2, numeric score of an embryo 2; SET, single embryo transfer; Transfer, number of transfers.
FIGURE 3.
Receiver operating characteristic curve analyses and Decision curve analyses. Model 1: A prediction model of the probability of achieving an ongoing pregnancy at 8–9 weeks of gestation after single embryo transfer. Model 2: A prediction model of the probability of achieving an ongoing pregnancy at 8–9 weeks of gestation after double embryo transfer. Model 3: A prediction model of the probability of ongoing twin pregnancy at 8–9 weeks of gestation after double embryo transfer. (A) Receiver operating characteristic curves of each model; (B) Decision curves for net benefit per 100 transfers; (C) Decision curves for intervention avoided per 100 transfers In the graphs for net benefit and intervention avoided per 100 transfers, green lines represent the prediction models, blue lines represent treat‐all strategy, and red lines represent treat‐none strategy.
3.4. Model 2: Ongoing Pregnancy After DET
The final model included maternal age at oocyte retrieval, number of transfers, and score of embryos, with spline terms incorporated for maternal age and an interaction term between the numeric grading of embryo 1 and 2 (Table 2). For maternal age, the decline in ongoing pregnancy probability was modest before 37 years but became significantly steeper thereafter. For the number of previous transfers, pregnancy probability declined with increasing transfer number, with a more pronounced decrease after approximately the seventh transfer. Embryo quality contributed independently and jointly to the probability of ongoing pregnancy. The embryo with the higher score was a strong predictor of ongoing pregnancy, while the quality of the second embryo provided an additional, albeit smaller, contribution. The contribution of the second embryo to pregnancy probability differed by maternal age, with a greater effect observed at older ages. The model demonstrated an AUC of 0.73 (95% CI: 0.71–0.74) and a cross‐validated AUC of 0.73 (95% CI: 0.71–0.74). At the optimal predicted probability threshold of 0.26, the model yielded a sensitivity of 0.70, specificity of 0.65, PPV of 0.40, NPV of 0.87, and an overall accuracy of 0.66. Decision curve analysis suggested that Model 2 may provide clinical utility across a range of threshold probabilities. Compared with the treat‐all strategy, the model demonstrated a higher net benefit within probability thresholds of approximately 10% to 40%. This indicates that the model may help identify individuals more likely to achieve ongoing pregnancy at 8–9 weeks of gestation (Figure 3).
3.5. Model 3: Ongoing Twin Pregnancy After DET
The final model included maternal age at oocyte retrieval, number of transfers, and score of embryos, with a spline term incorporated for maternal age and an interaction term between the numeric grading of embryo 1 and 2 (Table 2). For maternal age, the probability of twin pregnancy declined before 37 years and decreased more steeply thereafter. For the number of previous transfers, twin pregnancy probability declined with increasing transfer number. Embryo quality contributed independently and jointly to twin pregnancy risk. The probability of twin pregnancy depended on the quality of both embryos, and the effect of the second embryo was modified according to the quality of the first embryo. The model demonstrated an AUC of 0.82 (95% CI: 0.80–0.84) and a cross‐validated AUC of 0.82 (95% CI: 0.80–0.84). At the optimal predicted probability threshold of 0.07, the model yielded a sensitivity of 0.07, specificity of 0.99, PPV of 0.25, NPV of 0.95, and an overall accuracy of 0.94. Decision curve analysis suggested that Model 3 may provide clinical utility for predicting ongoing twin pregnancy at 8–9 weeks of gestation. Compared with the treat‐all strategy, the model demonstrated a potential value in identifying individuals at higher risk of twin pregnancy within probability thresholds of approximately 3%–20% (Figure 3).
3.6. Simulation Model
Under the restriction that per‐transfer twin risk remained below the predefined threshold, both the all SET strategy and the stepwise optimization strategy combining SET and DET achieved equivalent cumulative pregnancy rates. Although the simulation model could evaluate a variety of scenarios for individuals aged 26–45 years old with two to eight available embryos, we present an example case to illustrate the developed transfer strategies. In this example, an individual aged 35 years old considered DET for the third transfer with a maximum twin risk per transfer of ≤ 5% or ≤ 10%. The embryo cohort consists of six frozen blastocysts (format: expansion stage, inner cell mass, trophectoderm, days to blastocyst formation): 4AA(5), 3AA(5), 3AB(5), 3AB(5), 3BB(5), and 3BB(5). The summarized results are presented in Table 3. Under the all‐SET strategy, embryos were transferred in the order of 4AA(5), 3AA(5), 3AB(5), 3AB(5), 3BB(5), and 3BB(5), resulting in a cumulative pregnancy rate of 83.7% after all six transfers. Under a twin risk ≤ 5%, the optimized strategy selected the sequence 4AA(5), 3AA(5), 3BB(5)&3BB(5), 3AB(5), and 3AB(5), achieving a cumulative pregnancy rate of 83.8% with a maximum twin risk of 4.1% at the fifth transfer. Under the twin risk ≤ 10%, the optimized strategy selected 4AA(5), 3AB(5)&3BB(5), 3AB(5)&3BB(5), and 3AA(5), achieving a cumulative pregnancy rate of 83.8% with a maximum twin risk of 8.1% at the fifth transfer.
TABLE 3.
Summarized results of simulation: An example case.
| Strategy | Transfer order | Type | Grade | Pregnancy per transfer (%) | Cumulative pregnancy (%) | Twin risk per transfer (%) | Cumulative twin risk (%) |
|---|---|---|---|---|---|---|---|
| All SET | 1 | SET | 4AA(5) | 50.0 | 50.0 | 0.2 | 0.2 |
| 2 | SET | 3AA(5) | 32.5 | 66.3 | 0.2 | 0.3 | |
| 3 | SET | 3AB(5) | 20.5 | 73.2 | 0.2 | 0.3 | |
| 4 | SET | 3AB(5) | 19.8 | 78.5 | 0.2 | 0.4 | |
| 5 | SET | 3BB(5) | 13.1 | 81.3 | 0.2 | 0.4 | |
| 6 | SET | 3BB(5) | 12.6 | 83.7 | 0.2 | 0.4 | |
| SET&DET with twin risk ≤ 5% | 1 | SET | 4AA(5) | 50.0 | 50.0 | 0.2 | 0.2 |
| 2 | SET | 3AA(5) | 32.5 | 66.3 | 0.2 | 0.3 | |
| 3 | DET | 3BB(5) & 3BB(5) | 25.9 | 75.0 | 4.1 | 1.6 | |
| 4 | SET | 3AB(5) | 19.8 | 80.0 | 0.2 | 1.7 | |
| 5 | SET | 3AB(5) | 19.1 | 83.8 | 0.2 | 1.7 | |
| SET&DET with twin risk ≤ 10% | 1 | SET | 4AA(5) | 50.0 | 50.0 | 0.2 | 0.2 |
| 2 | DET | 3AA(5) & 3BB(5) | 42.7 | 71.4 | 8.0 | 4.2 | |
| 3 | DET | 3AB(5) & 3AB(5) | 34.5 | 81.2 | 8.1 | 6.5 | |
| 4 | SET | 3BB(5) | 13.6 | 83.8 | 0.2 | 6.5 |
Note: In this example, an individual aged 35 years old considered DET for the third transfer with a maximum twin risk per transfer of ≤ 5% or ≤ 10%. The embryo cohort consists of six frozen blastocysts (format: expansion stage, inner cell mass, trophectoderm, days to blastocyst formation): 4AA(5), 3AA(5), 3AB(5), 3AB(5), 3BB(5), and 3BB(5).
Abbreviations: DET, double embryo transfer; SET, single embryo transfer.
4. Discussion
We developed a simulation tool for transfer strategies based on prediction models for ongoing pregnancy at 8–9 weeks of gestation after SET, ongoing pregnancy at 8–9 weeks after DET, and twin pregnancy at 8–9 weeks after DET. Each prediction model demonstrated good to fair discriminative ability and clinical utility across a wide range of thresholds [17]. The simulation model was designed for clinical application and can suggest the optimal sequence of embryos to be transferred in a few steps, accounting for twin risk.
Our simulation model should be applied with caution. First, clinicians should consider whether DET could be justified based on each individual's own circumstances, in accordance with locally and widely accepted guidelines [1, 2, 18]. Second, this model should be used with full consideration of the clinical context in which the underlying prediction models were developed. The models were constructed using data from individuals who underwent DET. At our institution, the indication for DET followed the guidelines of the JSRM, ASRM, and ESHRE [1, 2, 18]. All individuals younger than 35 years old experienced at least two consecutive implantation failures before their initial DET. Those at 35 or older might undergo DET at the initial transfer, but most of them began with SET. Consequently, approximately 90% of DET in this study were conducted after the third transfer. Therefore, our simulation model should be used when clinicians and patients face difficulty in treatment after repeated unsuccessful embryo transfers and consider DET in accordance with the guidelines of JSRM, ASRM, and ESHRE [1, 2, 18]. If this model is used in settings with a higher baseline propensity for DET, for example, routine use of DET at the initial transfer in individuals aged 35 years or above, the model might underestimate the twin risk, as this model was developed using data predominantly from individuals with recurrent unsuccessful embryo transfers.
There have been some prediction models for twin risks [3, 4, 5, 6]. Most models were designed for the prediction of each transfer outcome, while Xi's model suggested transfer strategies combining SET and DET based on the embryos available, similar to the approach of our model [4]. However, their model was developed using data from fresh embryo transfer cycles and was not applicable to frozen embryo transfer cycles due to the variables included. In addition, their model did not account for the differences in propensity for DET between those who underwent SET and those who underwent DET, which might bias the predicted probability of SET outcomes. To address this limitation, we constructed our prediction model for SET using data from SET cycles that had similar propensity scores to DET cases.
Our simulation models could support clinical decision‐making or counseling with patients. This model was originally developed as a strategy‐sequencing tool across multiple transfers when clinicians consider DET or patients request DET. The optimal strategy under individualized twin risk does not necessarily include DET. In such cases, particularly when a patient prefers DET, clinicians may use the predicted twin risk as a rationale to recommend against DET during counseling. The quantitative risk may facilitate patient understanding. In addition, DET pair ranking by predicted ongoing pregnancy may be used to guide embryo selection for DET in the subsequent transfer cycle, regardless of the optimization. However, this approach may not be optimal when there is a single embryo that has a higher potential for ongoing pregnancy than the best DET embryo combination identified under the individualized twin risk.
The acceptable twin risk would be controversial, but we considered twin risk thresholds of lower than 5% would be acceptable, consistent with ESHRE recommendations targeting a twin rate of lower than 10% and more recent reports showing twin pregnancy rates of approximately 4%–5% in countries with high elective SET uptake [19, 20, 21]. This is also in line with ASRM guidance, noting that twin rates by assisted reproductive technology in the United States declined to below 10% of IVF births in 2018 [22]. Therefore, in our simulation model, we recommend setting the pulldown list for “Maximum Twin Risk per Transfer” at 4% or 5%.
We constructed our prediction models for clinical application and designed the simulation model as a stand‐alone tool independent of medical records. Although our models included fewer predictors than some previously published models [3, 4, 5], they demonstrated good to fair discriminative ability and clinical utility across a wide range of thresholds [17]. The models were internally validated; however, external validation was not performed given the single‐institutional nature of this study. Future research should evaluate external validity, and other institutions may also choose to construct or recalibrate their own institution‐specific models rather than applying the present model. If institutions have substantially different DET policies, or in countries or settings where transfer of more than two embryos is practiced, such a modification would be necessary. Our models were developed using traditional methods based on GEE, which might be easier to interpret and understand compared with more complex machine learning approaches [4]. We described the construction process step by step, allowing other researchers to reproduce the models using their own clinical data.
This study has several strengths. First, our simulation model would support clinical decision‐making visually. The simulation model provides graphs of all SET strategy and strategy combining SET and DET. It would help patients to understand that the cumulative ongoing pregnancy rate of both strategies after using all embryos would be equivalent, which patients might misunderstand and overestimate in favor of DET. Second, our simulation model had flexibility depending on the clinical situation. If patients are risk‐averse but still want to pursue treatment efficiency, lower thresholds for twin risk could be selected, such as below 3%. Additionally, the simplicity of the simulation model would improve its clinical applicability. The estimated twin risk and ongoing pregnancy rate could be calculated in a few steps. Third, transfers based on the prediction model of twin risk might have the potential to reduce the number of individuals with ongoing twin pregnancy at 8–9 weeks of gestation. This could be achieved at lower thresholds, such as below 5%.
This study has several limitations. First, external validation of the models was not feasible due to the single‐institution design. The validation in independent cohorts would be critical to account for potential heterogeneity in protocols, clinical practices, and embryo evaluation across institutions. Despite this limitation, the models demonstrated robust internal validity within the study cohort. Second, we could not use live birth as a primary outcome due to the unavailability of data. However, given the low probability of spontaneous abortion after 9 weeks of gestation [23], ongoing pregnancy at 8–9 weeks of gestation could be used as a surrogate outcome.
This study developed a simulation model of embryo transfer strategy combining SET and DET based on prediction models with good to fair discriminative ability and clinical utility. The model would help clinicians and patients lower twin risks when DET is considered. As the model was developed using data from a single institution, external validation is required before its application in other clinical settings.
Funding
The authors have nothing to report.
Disclosure
Related publication: Portions of the statistical methodology and the descriptions of laboratory procedures, oocyte retrieval, and embryo transfer protocols overlap with our previous publication [24], as they were conducted using the same institutional framework. The present study addresses a distinct research question and includes new analyses and outcomes.
Ethics Statement
All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1964 and its later amendments.
Consent
With approval from the institutional review board, informed consent was waived given the retrospective design, and patients were provided with an opt‐out opportunity.
Conflicts of Interest
The authors declare no conflicts of interest.
Supporting information
Appendix S1: In vitro fertilization protocols.
Appendix S2: Construction of numeric scores for embryo grades.
Appendix S3: Propensity score matching of single embryo transfers to double embryo transfers.
Appendix S4: Prediction for the probability of achieving ongoing pregnancy at 8–9 weeks of gestation after a double embryo transfer.
Appendix S5: Prediction for the probability of ongoing twin pregnancy at 8–9 weeks of gestation after a double embryo transfer.
Appendix S6: Prediction for the probability of achieving ongoing pregnancy at 8–9 weeks of gestation after a single embryo transfer.
Appendix S7: Calculation of cumulative ongoing pregnancy rate and cumulative twin risk.
Appendix S8: Online calculator.
Data Availability Statement
Individual participant data that underlie the results reported in this article will be shared after deidentification. Access to the data will be granted to qualified investigators for purposes such as verifying results, investigating concerns of scientific misconduct, or conducting peer review, in accordance with institutional and ethical guidelines. Proposals should be directed to xonishi3@gmail.com.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Appendix S1: In vitro fertilization protocols.
Appendix S2: Construction of numeric scores for embryo grades.
Appendix S3: Propensity score matching of single embryo transfers to double embryo transfers.
Appendix S4: Prediction for the probability of achieving ongoing pregnancy at 8–9 weeks of gestation after a double embryo transfer.
Appendix S5: Prediction for the probability of ongoing twin pregnancy at 8–9 weeks of gestation after a double embryo transfer.
Appendix S6: Prediction for the probability of achieving ongoing pregnancy at 8–9 weeks of gestation after a single embryo transfer.
Appendix S7: Calculation of cumulative ongoing pregnancy rate and cumulative twin risk.
Appendix S8: Online calculator.
Data Availability Statement
Individual participant data that underlie the results reported in this article will be shared after deidentification. Access to the data will be granted to qualified investigators for purposes such as verifying results, investigating concerns of scientific misconduct, or conducting peer review, in accordance with institutional and ethical guidelines. Proposals should be directed to xonishi3@gmail.com.