How to estimate the probability of a live birth after one or more complete IVF cycles? the development of a novel model in a single-center.

A retrospective study was conducted in the IVF clinical center of Shenzhen Zhongshan Obstetrics & Gynecology Hospital (formerly Shenzhen Zhongshan Urology Hospital). From January 2012 to April 2015, a total of 4413 patients who completed ovarian stimulation treatment and a fresh cycle with subsequent FET were involved in this study. This project was approved by the Institutional Review Board of the Shenzhen Zhongshan Obstetrics & Gynecology Hospital (formerly Shenzhen Zhongshan Urology Hospital) on 15 February 2021 (FM-YXLL-026). The inclusion criteria were: (1) women who were diagnosed with infertility; (2) women aged 18–45 years; (3) women who had undergone their first cycle of IVF or ICSI; and (4) women with a retrieved number of oocytes > 0. The exclusion criteria were: (1) women who undergone preimplantation genetic testing (PGT); (2) reproductive malformation or intrauterine adhesions; (3) untreated unilateral or bilateral hydrosalpinx; (4) recurrent pregnancy loss or repeated implantation failure. All patients underwent a short luteal gonadotropin releasing hormone (GnRH) protocol. Controlled ovarian stimulation was achieved using a daily dose of gonadotropin (150–300 UI/d) after confirmation of pituitary down-regulation. The dosage of rFSH was adjusted according to female age, ovarian response: antral follicle count (AFC), which was assessed by ultrasound、serum hormone、anti-mullerian hormone (AMH, ng/ml, measured by using the chemical luminescence method (Yahuilong Company, Shenzhen, China)) and body mass index (BMI, kg/m2) [ 14 – 17 ]. When a mean diameter of two follicles reached > 18 mm, human chorionic gonadotropin (hCG; LiZhu, Zhuhai, China) was given, and oocyte retrieval was performed 36 h later. Fresh embryo transfer was performed on Day 3 (cleavage embryos) or Day 5 (blastocysts) after the oocyte retrieval. Subsequent FET was performed on Day 3 (cleavage embryos) or Day 5 (blastocysts) after ovulation in a natural cycle, or Day 4 (cleavage embryos) or Day 6 (blastocysts) after progesterone administration in a hormone replacement cycle. The number of embryos transferred varied from one to two based on the recommendation of the Health Ministry of China and the requests of patients. Luteal support was performed using dydrogesterone tablets 20 mg twice a day (Abbott, America) plus vaginal or anal progesterone (90 mg/d, Merck-Serono, Germany, or 200 mg, three times a day; Cyndea Pharma, S.L). All the data were obtained from the electrical medical record system of IVF in the fertility center of Shenzhen Zhongshan Obstetrics & Gynecology Hospital (formerly Shenzhen Zhongshan Urology Hospital). The following baseline characteristics were recorded and analyzed: female age (years), duration of infertility (years), infertility factors (ovulation disorder, endometriosis, tubal factor, male factor, couple factors(the cause of infertility is mainly by both female and male factors), unexplained factor), body mass index (BMI, kg/m2), antral follicle count (AFC), basal follicle-stimulating hormone (b-FSH) levels (pg/mL), initiated gonadotropin (Gn) dosage, Gn days, serum progesterone (P) level (pg/mL)、E2 level (pg/mL)、follicle-stimulating hormone (FSH) level (pg/mL) and luteinizing hormone (LH) level (pg/mL) on the day initiated with Gn (GnP、GnE2、GnFSH、GnLH), serum P level (pg/mL)、E2 level (pg/mL) and LH level (pg/mL) on the day of trigger (tP、tE2、tLH), number of follicles on the day of HCG trigger, insemination method (IVF/ICSI), number of retrieved oocytes, metaphase II (MII), fertilized oocytes, two pronucleus zygotes (2PN zygotes), good quality embryos and viable embryos for transfer. The primary outcome was cumulative live birth rate. Live birth was defined as a neonate showing any sign of life, irrespective of gestational age, as defined by the World Health Organization (WHO). CLBR within one complete IVF/ICSI treatment cycle was defined as the probability of a live birth from an ovarian stimulation, including all embryo transfers (fresh and frozen) from that stimulation [ 7 , 18 , 19 ]. The second outcome was fresh live birth. The optimal estimate is based on the observed data and assumes that the CLBR in women who discontinue ART treatment without a live birth would be equal to the rate in those who continue. The conservative estimate assumes that those who did not continue the ART treatment would not have a live birth [ 20 ]. Statistical analysis was performed using SPSS v. 26.0 and R v. 4.0.3. The basal characteristics of patients and stimulation cycles are listed in Table  1 according to live birth or not. Normally distributed data were expressed as mean \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\pm\:$$\end{document} SD, whereas skewed distributed data were expressed as median (interquartile range). Categorical variables were shown as n and were compared using the chi-square test or fisher exact test. Comparison of continuous variables was performed using the Mann–Whitney U-test or Student’s t-test depending on data distribution. Categorical variables were plotted using the graphical method of Kaplan-Meier survival curves grouped by that variable, or by plotting ln[-ln(S ^(t)) against survival time t grouped by that variable, and observing whether the curves crossed to determine whether the PH assumption was satisfied. Continuous variables were tested for the PH assumption of the Cox regression model using the Schoenfeld residual method, and if the PH assumption held, the biased residuals were plotted (Schoenfeld residuals) and estimated for the Cox model, which should fluctuate above or below zero level with time. Table 1 Characteristics of patients and stimulation cycles were described according to live birth or not Variable no live birth( N  = 1691) live birth( N  = 2722) P value Female age (years) 32.00 (29.00,36.00) 31.00 (28.00,33.00) < 0.001 Duration of infertility (years) 3.00 (2.00,5.00) 3.00 (2.00,5.00) < 0.001 BMI (kg/m 2 ) 20.96 (19.35,23.05) 20.70 (19.20,22.71) 0.006 AFC 8.00 (6.00,10.00) 10.00 (8.00,12.00) < 0.001 Infertility factors 0.017 Female 1038(37.5%) 1729(62.5%) Tubal factor 815 (37.4%) 1366 (62.6%) Endometriosis 145 (44.3%) 182 (55.7%) Ovulation disorder 78 (30.1%) 181 (69.9%) Male 249(35.9%) 445(64.1%) Couple factors 2(50.0%) 2(50.0%) Unexplained 402(42.4%) 546(57.6%) b-FSH 5.38 (4.55,6.50) 5.34 (4.54,6.36) 0.126 Gn P(pg/mL) 0.10 (0.10,0.20) 0.10 (0.10,0.20) 0.071 GnLH (pg/mL) 0.60 (0.45,0.79) 0.61 (0.46,0.81) 0.489 GnE 2 (pg/mL) 12.00 (10.00,15.00) 12.00 (10.00,14.00) 0.014 Gn FSH(pg/mL) 2.53 (2.05,3.11) 2.36 (1.93,2.88) < 0.001 tP (pg/mL) 0.60 (0.40,0.80) 0.60 (0.40,0.80) 0.043 tLH (pg/mL) 0.71 (0.50,0.98) 0.66 (0.48,0.91) < 0.001 tE 2 (pg/mL) 2105.00 (1418.00,2908.00) 2700.00 (1910.75,3596.50) < 0.001 No. of follicles on the day of HCG trigger 8.00 (6.00,10.00) 10.00 (8.00,11.00) < 0.001 Initiated Gn dosage (75/IU) 4.00 (3.00,4.00) 3.00 (2.00,4.00) < 0.001 Gn days 9.00 (8.00,10.00) 9.00 (8.00,10.00) 0.609 Insemination method 0.917 IVF 1562(38.3%) 2512(61.7%) ICSI 129(38.1%) 210(61.9%) No. of retrieved oocytes 11.00 (7.00,15.00) 15.00 (11.00,19.00) < 0.001 No. of MII 9.00 (6.00,13.00) 13.00 (10.00,17.00) < 0.001 No. of fertilized oocytes 8.00 (5.00,12.00) 12.00 (8.00,16.00) < 0.001 No. of 2PN zygotes 5.00 (3.00,8.00) 8.00 (5.00,12.00) < 0.001 No. of viable embryos for transfer 4.00 (2.00,6.00) 7.00 (5.00,9.00) < 0.001 No. of good quality embryos 3.00 (1.00,5.00) 6.00 (4.00,9.00) < 0.001 Characteristics of patients and stimulation cycles were described according to live birth or not According to the pre-experimental data, the incidence of successful pregnancy was 61.68%, the standard deviation of the variable was 1.204, the expected log-hazard ratio was 0.185 (lnHR = 0.185), and the coefficient of determination was 0.047. Under the condition of a significance level of 0.05 and test power of 0.90, the sample size was calculated using PASS, and the estimated sample size was 361 [ 21 , 22 ]. In order to verify the rationality of sampling among variables of the training set and the validation set, we conducted stratified sampling for the whole sample ( n  = 4413) according to live birth, no birth and loss of follow-up. 70% of the subjects were randomly placed into a training set ( n  = 3089) and 30% of the subjects were placed into a validation set ( n  = 1324). A Cox regression model was built on the basis of the training set, and ROC curves were used to test the specificity and sensitivity of the prediction model. Finally, the validation set was used to verify the validity of the model. To assess the possibility of CLBR more intuitively for clinicians, we established a Nomogram model on the basis of various clinical factors that might affect CLB. Calculating the goals of the model, the clinicians might predict the probability for patients to obtain at least one live birth within 1 to 3 years. We plotted calibration curves to assess the calibration of the model. Based on the model’s prediction of the probability of live birth for patients, arranged from lowest to highest, we divided the cohort into 5 groups according to quantiles. We then calculated the predicted probability of live birth and the corresponding actual probability of live birth for each group. In the calibration plot, the horizontal axis represents the model-predicted probability of live birth, and the vertical axis represents the actual probability of live birth. From the grouping, we obtained 5 calibration points, and finally connected these 5 points to form the predicted calibration curve. Theoretically, the standard curve is a straight line passing through the origin of the coordinate axes with a slope of 1. The closer the predicted calibration curve is to the standard curve, the better the performance of the model.

A total of 4413 patients who had undergone their first cycle of IVF/ICSI in the fertility center of Shenzhen Zhongshan Obstetrics & Gynecology Hospital (formerly Shenzhen Zhongshan Urology Hospital) were involved in this study. The data analysis flowchart is shown in Fig.  1 . After tracing the data to its source, we have filled all abnormal data with the actual variable values, so our sample contains complete covariate data. However, there are cases of censored data due to loss to follow-up for some patients, and Table  2 presents the corresponding censored data for each cycle. Table  2 ; Fig.  2 and Figure S1 show the cumulative live birth rate among different embryo transfer cycles and the relationship among them. In the fresh embryo transfer cycles, the live birth rate was 38.7%. In the first to fifth FET cycles, the optimal estimate and conservative estimate CLBR were 59.95%, 65.41%, 66.35%, 66.58%, 66.61% and 56.81%, 60.84%, 61.50%, 61.66%, 61.68%, respectively. Fig. 1 The data analysis flowchart The data analysis flowchart Table 2 Cumulative live birth rates of different cycles Cycles No. of cycles Cycles of live birth Cycles of no birth Cycles of loss of follow-up Live birth rate of the cycle Optimistic estimate Conservative estimate Cycles of Correction Live birth rate of the cycle Cumulative live birth rate Cycles of Correction Live birth rate of the cycle Cumulative live birth rate Fresh 4413 1708 553 400 38.70% 4413 38.70% 38.70% 4413 38.70% 38.70% FET1 1752 799 302 200 45.61% 2305 34.66% 59.95% 2705 29.54% 56.81% FET2 451 178 124 56 39.47% 1306 13.63% 65.41% 1906 9.34% 60.84% FET3 93 29 26 24 31.18% 1072 2.71% 66.35% 1728 1.68% 61.50% FET4 14 7 2 3 50.00% 1019 0.69% 66.58% 1699 0.41% 61.66% FET5 2 1 1 50.00% 1009 0.10% 66.61% 1692 0.06% 61.68% Cumulative live birth rates of different cycles Fig. 2 Kaplan-Meier curve for the treatment period of the patient. ( A ) Cumulative live birth rate of patient embryo transfer cycles; ( B ) Cumulative live birth rate per month for the patient Kaplan-Meier curve for the treatment period of the patient. ( A ) Cumulative live birth rate of patient embryo transfer cycles; ( B ) Cumulative live birth rate per month for the patient The basal characteristics of patients and cycles between the training set and the validation set are listed in Tables  3 and 4 . There was no difference among the data of two cohorts, which indicated that stratified sampling based on live birth, no birth, and lost follow-up was reasonable. Table 3 Characteristics of patients between training set and validation set(median and interquartile ranges) Variable Training set ( N  = 3089) Validation set ( N  = 1324) P value Female age (years) 31.00 (28.00,34.00) 31.00 (29.00,34.00) 0.273 Duration of infertility (years) 3.00 (2.00,5.00) 3.00 (2.00,5.00) 0.680 BMI (kg/m 2 ) 20.81 (19.23,22.86) 20.83 (19.35,22.76) 0.844 AFC 9.00 (8.00,10.00) 9.00 (8.00,10.00) 0.769 Infertility factors 0.145 Female 1907 (68.9%) 860 (31.1%) Tubal factor 1512 (69.3%) 669 (30.7%) Endometriosis 211 (64.5%) 116 (35.5%) Ovulation disorder 184 (71.0%) 75 (29.0%) Male 507 (73.1%) 187 (26.9%) Couple factors 3 (75%) 1 (25%) Unexplained 672 (70.9%) 276 (29.1%) b-FSH 5.36 (4.55,6.39) 5.34 (4.54,6.47) 0.976 70% of the samples were divided into training set ( N =3089) and 30% of the samples were divided into validation set ( N =1324) Characteristics of patients between training set and validation set(median and interquartile ranges) 70% of the samples were divided into training set ( N =3089) and 30% of the samples were divided into validation set ( N =1324) Table 4 Characteristics of cycles between training set and validation set Variable Training set ( N  = 3089) Validation set ( N  = 1324) P value GnP (pg/mL) 0.10 (0.10,0.20) 0.10 (0.10,0.20) 0.465 GnLH(pg/mL) 0.60 (0.46,0.81) 0.61 (0.46,0.79) 0.461 GnE 2 (pg/mL) 12.00 (10.00,14.00) 12.00 (10.00,14.00) 0.711 GnFSH (pg/mL) 2.42 (1.97,2.94) 2.43 (1.97,3.01) 0.485 tP (pg/mL) 0.60 (0.40,0.80) 0.60 (0.40,0.80) 0.744 tLH(pg/mL) 0.67 (0.48,0.93) 0.68 (0.49,0.96) 0.119 tE 2 (pg/mL) 2472.00 (1704.00,3381.00) 2439.00 (1686.25,3344.25) 0.584 No. of follicles on the day of HCG trigger 9.00 (7.00,11.00) 9.00 (7.00,11.00) 0.537 Initiated Gn dosage (75/IU) 3.00 (2.00,4.00) 3.00 (2.00,4.00) 0.482 Gn days 9.00 (8.00,10.00) 9.00 (8.00,10.00) 0.677 Insemination method 0.368 IVF 2859 (70.2%) 1215 (29.8%) ICSI 230 (67.8%) 109 (32.2%) No. of retrieved oocytes 13.00 (9.00,18.00) 13.00 (9.00,18.00) 0.646 No. of MII 12.00 (8.00,16.00) 12.00 (8.00,16.00) 0.677 No. of fertilized oocytes 11.00 (7.00,15.00) 11.00 (7.00,15.00) 0.780 No. of 2PN zygotes 7.00 (4.00,10.00) 7.00 (4.00,10.00) 0.268 No. of viable embryos for transfer 6.00 (3.00,8.00) 6.00 (3.00,8.00) 0.504 No. of good quality embryos 5.00 (2.00,8.00) 5.00 (2.00,7.00) 0.495 Characteristics of cycles between training set and validation set The PH test is a test of whether the effect of the covariates on the live birth rate changes over time; in other words, it is a test of whether the risk ratio h(t)/h0(t) is fixed. Based on the results of the PH test, the potential predictive factors of live birth were insemination method, infertility factor, GnP level (pg/mL, R  = 0.043, p  = 0.059) and GnLH level (pg/mL, R  = 0.015, p  = 0.499), basal FSH ( R = -0.042, p  = 0.069) and BMI ( R = -0.035, p  = 0.123), which are shown in Table  5 ; Fig.  3 . Table 5 Predictive factors for continuous variables of live birth in PH test Variables R * P -value Female age (years) -0.144 < 0.001 Duration of infertility (years) -0.051 0.026 BMI (kg/m 2 ) -0.035 0.123** AFC 0.102 < 0.001 b-FSH -0.042 0.069** GnP (pg/mL) 0.043 0.059** GnLH(pg/mL) 0.015 0.499** GnE 2 (pg/mL) -0.045 0.048 GnFSH(pg/mL) -0.112 < 0.001 tP (pg/mL) 0.217 < 0.001 tLH (pg/mL) -0.102 < 0.001 No. of follicleson the day of HCG trigger 0.263 < 0.001 Initiated Gn dosage (75/IU) -0.144 < 0.001 Gn days 0.068 0.003 No. of retrieved oocytes 0.317 < 0.001 No. of 2PN zygotes 0.296 < 0.001 No. of viable embryos for transfer 0.317 < 0.001 No. of good quality embryos 0.293  0.05, means Schoenfeld residual is considered to have a wireless relationship with time rank, which satisfies the pH assumption. The variables that finally meet the pH assumption including GnP(pg/mL)、GnLH(pg/mL), basal FSH and BMI Predictive factors for continuous variables of live birth in PH test * R means the correlation coefficient between Schoenfeld residuals estimated by Cox model and time rank ** P-value > 0.05, means Schoenfeld residual is considered to have a wireless relationship with time rank, which satisfies the pH assumption. The variables that finally meet the pH assumption including GnP(pg/mL)、GnLH(pg/mL), basal FSH and BMI Fig. 3 Predictive factors for categorical variables of live birth in PH test. The Kaplan Meier curve and the relation graph of ln [-ln(S ^(t)) ] for ( A ) infertility factor and ( B ) insemination method. There was no cross among the curves which meant these two factors satisfied the PH test Predictive factors for categorical variables of live birth in PH test. The Kaplan Meier curve and the relation graph of ln [-ln(S ^(t)) ] for ( A ) infertility factor and ( B ) insemination method. There was no cross among the curves which meant these two factors satisfied the PH test Based on the results of the PH test, the Cox regression model was built. The relationship of predictive factors and live births is shown in Table  6 . With the increasing levels of b-FSH and BMI, the live birth rate decreased (HR = 0.970, 95% CI: 0.945–0.996, p  = 0.025; and HR = 0.982, 95% CI: 0.966–0.998, p  = 0.025, respectively for b-FSH and BMI). While for infertility factors, the live birth rate was 1.204-fold higher for couples with male factor than for those with unexplained infertility factor (HR = 1.204, 95% CI: 1.036–1.398; p  = 0.015). Table 6 The relationship between predictive factors and live birth HR 95% CI P Lower Upper GnP(pg/ml) 0.965 0.548 1.698 0.901 GnLH(pg/ml) 1.029 0.916 1.157 0.631 b-FSH 0.970 0.945 0.996 0.025* BMI 0.982 0.966 0.998 0.025* Infertility factor Unexplained 1.000 - - - Female factor 1.113 0.991 1.250 0.070 Male factor 1.204 1.036 1.398 0.015* Couple factors 0.479 0.067 3.407 0.462 Insemination method ICSI 1.000 - - - IVF 0.953 0.799 1.136 0.589 * p  < 0.05, ** p  < 0.01,*** p  < 0.001 The relationship between predictive factors and live birth * p  < 0.05, ** p  < 0.01,*** p  < 0.001 We used the ROC curve to test the specificity and sensitivity of the CLBR prediction model. When the maximum value of sensitivity plus specificity was 1.531, the cut-off value was 0.410 and AUC was 0.782 ( p  < 0.01, 95%CI: 0.764–0.801). That is to say, the sensitivity was 0.877, specificity was 0.654, and accuracy was 0.792. Subsequently, the model was verified in the validation data. When the maximum value of sensitivity plus specificity was 1.541, the cut-off value was 0.392 and AUC was 0.801 ( p  < 0.01, 95%CI: 0.774–0.828). As the sensitivity was 0.902, specificity was 0.639, and accuracy was 0.801. The ROC curve is shown in Fig.  4 . Fig. 4 ROC curve of the CLBR predictive model in the training and validation data ROC curve of the CLBR predictive model in the training and validation data In addition, when we categorized infertility factors as tubal factor, endometriosis, and ovulation disorder, the Cox regression analysis was as shown in Table S1 . Considering the statistically significance ( p  < 0.05), with the increasing of b- FSH, the live birth rate decreased. Furthermore, with the increasing of BMI, the live birth rate decreased; meanwhile for infertility factors, the live birth rate with ovulation disorder and male factor was higher than that in couples with unexplained infertility. We first constructed a multivariable Cox regression model. Based on the regression coefficients of each variable in the model, we assigned corresponding scores to different levels of each influencing factor. Using the regplot package in R, we visualized the Cox regression model built from the training set by plotting a Nomogram (Fig.  5 ) and calculated the respective scores for each variable. The detailed scoring information for the main values of each variable can be found in Table S3 . By summing the scores of all influencing factors, we obtain a total score. The higher the total score, the higher the probability of a live birth for the patient. Through the functional transformation relationship between the total score and the probability of live birth, we can convert the total score into the specific predicted probability of live birth for that patient. The calibration curve of 1 to 3 years to evaluate the accuracy of the model is shown in Fig.  6 A. The closer the predictive calibration curve was to the standard curve, the better the prediction ability of the histogram. For the validation data, the calibration curve of 1 to 3 years to evaluate the accuracy of the model is shown in Fig.  6 B. Fig. 5 The nomogram model of predictive factors and live birth The nomogram model of predictive factors and live birth Fig. 6 Plotting calibration curves. ( A ) showed the calibration curve of 1 year、2 years and 3 years to evaluate the accuracy of the model in the training data, ( B ) Showed the calibration curve of 1 year、2 years and 3 years to evaluate the accuracy of the model in the validation data Plotting calibration curves. ( A ) showed the calibration curve of 1 year、2 years and 3 years to evaluate the accuracy of the model in the training data, ( B ) Showed the calibration curve of 1 year、2 years and 3 years to evaluate the accuracy of the model in the validation data

Infertility has become a global public health tissue, and the prevalence of infertility has increased gradually, from 9 to 26%, and even to 31.1% in low-to-middle-income countries [ 1 – 3 ]. In vitro fertilization (IVF) has become an effective method for infertile patients to fulfill their fertility wishes. Globally, an estimated 7 million children have been born as a result of IVF since 1978 [ 4 ],and in the year 2013, almost 1,160,474 embryo transfers (ETs) were performed resulting in > 344,317 babies [ 5 ]. As for patients who came to an infertility center for the first time, their most important question was:“what is the probability of taking a baby home?” There are many indicators to evaluate the outcome of IVF, and the most efficient indicator is cumulative live birth rate (CLBR) after complete cycles, which is defined as all fresh and frozen-thawed embryos transfer (FET) attempts resulting from one episode of ovarian stimulation [ 6 , 7 ]. Many scholars have studied different factors that might have an effect on live birth outcomes. In 1995, Collins firstly studied the influence of pregnancy history, duration of infertility and female partner’s age on live birth, and proposed a negative correlation between age and live birth. The prediction score based on these factors would be accurate in approximately 62% of cases. While the subjects of the study were untreated infertile couples, the estimation of live birth among them was sufficiently accurate to be useful in the clinical management of infertility and their future planning [ 8 ]. In 1996, Templeton et al. studied a large-scale retrospective analysis by using logistic regression to explore the influence of age on cumulative live birth; they pointed out that the highest live birth rate was in patients aged 25–30 years Moreover, there was a significant decrease in age-adjusted live birth rates with increasing duration of infertility between 1 and 12 years [ 9 ]. This research was a major leap forward, because few pervious studies had taken account of these factors before. In 2016, McLernon model has been established, which could provide an individualized estimate of a couple’s cumulative chances of having a baby over a complete package of IVF both before treatment and after the first fresh embryo transfer [ 10 ]. This discrete time logistic regression model would help to shape couples’ expectations allowing them to plan their treatment more efficiently and to prepare emotionally and financially. A subsequent study in a different geographical context has been conducted to verify and confirm its effectiveness [ 11 ]. Recently, a Nomogram predictive model by using multivariable linear regression based on a retrospective database was built to estimate the likelihood of a live birth after surgery followed by assisted reproductive technology (ART) for endometriosis-related infertility. Though the AUC of the Nomogram model was 0.77, the sample was small and limited [ 12 ]. Laura van Loendersloot provided a significant contribution in building prediction models in IVF. She proposed three phases of prediction model development and provided key principles to assess the effectiveness of different prediction models [ 13 ]. Many previous studies have used different predictors to explore the effect of each factor on live birth and to build predictive models. Considering that some models already developed may show inconsistent predictive results across different study populations and validation processes, this may be related to sample size, study design, patient characteristics, and the diversity of data collection methods. However, rebuilding the model can achieve better control over data quality, with more unified and standardized data collection and management, while also making the model easier to implement, flexible, and allowing for continuous monitoring and evaluation for ongoing improvement. The establishment and application of the model are closely centered around a specific single-center patient population, which also makes it easier to provide personalized treatment recommendations to patients. At the same time, we employed a more rigorous variable selection method, including only variables that passed the proportional hazards (PH) assumption test in the model. The PH assumption is a core hypothesis in Cox regression analysis, which specifically refers to the constant influence of each covariate over time. If the PH assumption is violated, the results of the Cox regression model may be inaccurate because the model may not correctly estimate the impact of covariates on the timing of live birth. For Cox regression models established with multicenter data or national data, it is also necessary to meet the PH assumption test to make the model’s estimates more accurate and reliable. Our main research objective is to develop a predictive tool based on the Cox regression model Nomogram, incorporating the influence of treatment cycle length on live birth outcomes, to assess the reproductive potential of patients after the transfer of all fresh embryos and subsequent frozen-thawed embryos throughout the entire treatment cycle, providing patients with a risk assessment that is easy to understand and visualize. The model constructed based on a single center serves as a foundation for collaboration with other centers. In the future, multi-center validation can be conducted by sharing experiences and data, improving the model to ensure its effectiveness in multi-center applications, and promoting wider research and application of predictive models.

We have developed a Cox regression and Nomogram model to predict the probability of at least a live birth after a complete IVF cycle and its FET cycles for infertile couples. Furthermore, the model was verified effectively by inside validation. The model showed that the predictive factors of live birth were insemination method, infertility factor, GnP level, GnLH level, b- FSH and BMI. Our preliminary results, as described in the abstract published in ESHRE, has demonstrated the effectiveness of the model [ 23 ]. In the model, b-FSH had a negative relationship with live birth rate. It is well known that serum b-FSH is a marker for evaluating the ovarian reserve, and an elevated b-FSH reflects not only a quantitative but also qualitative decline in the ovarian reserve. The average number of oocytes collected and average number of available embryos for transfer were significantly reduced in patients with elevated FSH. Moreover, high levels of FSH predict a poor pregnancy outcome. With an increasing basal level of FSH, pregnancy rate and live birth rate were decreased [ 24 ]. A predictive model to estimate the relationship between factors and live birth rate was recently built. The model shows that women delivering a live birth had a significantly lower median age and FSH and a significantly higher AMH and AFC. The authors suggested that age, FSH and AMH were independent predictors [ 25 ]. High BMI was considered to negatively impact live birth following IVF [ 26 ]. Researchers in Spain noted that live birth rates were reduced progressively with each unit of BMI (kg/m 2 ) with a significant odds ratio of 0.981 (95% CI: 0.967–0.995); however, the embryo quality was not affected. This might be attributed to an alteration in the uterine environment when the BMI was increased [ 27 ]. Nevertheless, a recent study has suggested an “inverted U shape” association between BMI and CLBR, with the turning point of BMI being 18.5 and 30.4 kg/m 2 . The CLBR increases in underweight women, plateaus in normal weight and overweight women, and then decreases in obese women [ 28 ]. In our model, with the increase of BMI, the live birth rate decreased. The mechanism of how obesity affects the pregnancy outcome is still not clear. Some researchers suggest that obesity negatively impacts the developmental competence of oocytes and embryo quality [ 29 , 30 ]; while others consider that the altered endometrial gene expression in obese patients might contribute to lower implantation rates [ 31 ]. AMH is also an important predictor of ovarian reserve and response [ 32 ]. One study reported that AMH was the best predictor for identifying patients with poor and high ovarian response [ 33 ]. An AFA model for assessing the true ovarian reserve has also been established in China [ 34 ] which showed a positive association between AMH and CLBR after fresh and FET cycles [ 25 ]. Some researchers took AMH into consideration when exploring the relationship with live birth rate [ 35 – 37 ]. However, in our model, AMH was not an independent predictor for live birth. A meta-analysis considered that AMH had some association with predicting live birth rate, while the predictive accuracy was poor [ 38 ]. As we know, age is also a significant factor to the outcome of pregnancy; many studies and predictive models have described a negative influence on outcome [ 8 , 9 ]. We found that the risk ratio h(t)/h0(t) for the age variable was not a fixed value, the influence of age on the live birth rate decreased slightly with time ( R =-0. 144, p  < 0.001). As the time of live birth went on, more patients with short time of live birth were better basic conditions, but more patients with long time of live birth were recurrent implantation failure or recurrent miscarriage, which led to the influence of age on the live birth rate could not be consistent with time, which violated the PH hypothesis. However, violating the PH hypothesis may lead to biased effect estimates in Cox regression analysis [ 39 ]. We will not include the patient age into the model to obtain the unbiased effect estimator of the model. In our study, the age range of patients was wide, and some of the patients had advanced age. In order to analyze the influence of age in pregnancy, we analyzed those patients who were older than 35 years. Based on PH test results, the Cox regression model showed the same result that we described previously (Table S2 ). Though the chance of success of IVF in this cohort of patients was low, the model could effectively predict the pregnancy outcome. As we known, infertility is a couple’s concern, where the male factor must be taken into account. In our analysis, live birth rate was 1.204-fold higher for couples with male factor than those with unexplained infertility factor. Furthermore, a retrospective cohort study reported that more than half of couples under consultation for male infertility succeeded in having a child [ 40 ]. Though the subgroup Cox regression analysis showed that the live birth rate with ovulation disorder was higher than that in couples with unexplained infertility, it might not indicate that ovulation disorder was considered with live birth. The Nomogram method was used to make an earlier prediction of the probability of live birth [ 41 ] and it was more efficient and rapid at assessing the probability of having a baby. For example, a patient’s BMI was 22.58 kg/m 2 , b-FSH was 5.62 pg/mL, female infertility factor, traditional IVF insemination method, GnLH was 1.19pg/mL, GnP was 0.2 pg/mL; she wanted to know the probability of taking a baby home after a course of IVF treatment. According to the Nomogram model, the score of these factors was 74.5、78、89、73、79.5 and 77, and the total score was 471. So, the chance of having a live birth was 60.1% in the first year of the treatment, 62.8% in the second year, and 62.9% in the third year (Fig.  5 ). The use of this model can provide a more personalized analysis for pregnancy evaluation for patients. And compared to other Nomogram models( 41 – 42 ), our research has several advantages. First, we have a larger sample size, which enhances statistical power. Second, we take into account the impact of treatment cycle length on live birth outcomes, providing a more nuanced understanding of the findings. Furthermore, our model exhibits relatively high discrimination, indicating stronger predictive accuracy. Finally, we conducted a PH hypothesis test to ensure that the estimated results are more accurate and reliable. In our study, the approach used was to model the Cox regression for variables that met the PH assumptions. The confidence degree of the statistical analysis methods was higher when compared to univariate or multivariate regression analysis. At the same time, we will also attempt to collect more comprehensive data features, and plan to use the more effective estimation method of Inverse Probability Weighting in future studies, to provide a more accurate estimate of treatment success adjusting for drop-out participants [ 42 ]. This study is a single-center retrospective analysis. Although the Nomogram model has been well validated for its effectiveness and specificity internally, it lacks multi-center data validation to enhance its generalizability. And several challenges we need to face, including, but are not limited to, resource constraints, the wide geographical distribution, and the complexity of data sharing and coordination between different centers. Nonetheless, we remain committed to improving the external validity of the model and plan to address these limitations in future research. To overcome these challenges, we are actively exploring opportunities for collaboration with more centers, planning to enhance data sharing and analysis capabilities by establishing a standardized database platform. In addition, considering more potential characteristics that could affect the live birth rate outcome, such as participants’ blood pressure, drinking habits, smoking habits, etc. Try to collect more samples, and use big data mining technology such as machine learning to establish a prediction model to improve the accuracy and generalization of the model. In our study, we employed the AUC value, sensitivity, specificity, and accuracy to measure the discrimination and precision of our model, and used calibration curves to assess the calibration of the model. The AUC values in the training and validation sets were 0.782 and 0.801, respectively, demonstrating effective internal validation and good consistency in the calibration curves. However, there are several limitations to our study. Firstly, this is a single-center retrospective analysis. Due to resource constraints and the complexity of data sharing and coordination between different centers, we lack multi-center data validation to enhance the model’s generalizability. Secondly, the sample size for cases with infertility due to both male and female factors is relatively small, which may introduce a certain degree of sample selection bias. Lastly, patient characteristics were based on existing data in the electronic medical record system, and we were unable to consider potential influencing factors on the live birth outcome that were not collected. In future research, we will actively explore opportunities for collaboration with more centers, aiming to enhance data sharing and analytical capabilities through the establishment of a standardized database platform to achieve multi-center validation of the model. Additionally, we will consider collecting more potential influencing factors that may affect the live birth outcome, such as blood pressure, drinking habits, and smoking habits. We will attempt to use more effective inverse probability weighting estimation methods to provide more accurate adjusted estimates of treatment success for participants who drop out [ 43 ]. At the same time, we will also collect a larger sample size and explore predictive models using neural networks, machine learning algorithms, and other big data mining technologies to improve the overall performance of the model and promote widespread research and application of predictive models.

In conclusion, the potential predictive factors of live birth were insemination method, infertility factor, GnP level (pg/mL), GnLH level (pg/mL) and BMI. The new model could effectively predict the probability of infertile couples having a live birth. In addition, this model could also support clinicians making clinical decisions and providing guidance for patients.

Below is the link to the electronic supplementary material. Supplementary Material 1 Supplementary Material 1