A validated model for predicting live birth after embryo transfer

Accurately predicting the probability of live birth and multiple gestations is important for determining a safe number of embryos to transfer after in vitro fertilization. We developed a model that can be fit to individual clinic data for predicting singleton, twin, and total live birth rates after human embryo transfer. The predicted and observed rates of singleton and twin deliveries were compared in a tenfold cross-validation study using data from a single clinic. The model presented accounts for patient age, embryo stage (cleavage or blastocyst), type of transfer cycle (fresh or frozen) and uterine/universal factors. The standardized errors for rates of singleton and twin deliveries were normally distributed and the mean errors were not significantly different from zero (all p > 0.05). The live birth rates per embryo varied from as high as 43% for fresh blastocysts in the 35-year-old age group to as low as 1% for frozen cleavage stage embryos in the 43-year-old age group. This quantitative model or a simplified version can be used for clinics to generate and analyze their own data to guide the number of embryos to transfer to limit the risk of multiple gestations.


MATLAB Code
For reproducibility, the MATLAB code used to generate all of the data for figures and tables in this manuscript is being made available through Mendeley Data 1 . All of the data analysis and pertinent figure generation can be performed by running the file "generate_data_and_figures.m" with MATLAB. Descriptions for each of the 12 included MATLAB programs are included in the comments section at the beginning of each program.

Calculation of 95% Confidence Intervals
Bootstrapping was used to simulate embryo transfers based on the logic in Figure 2B to determine 95% confidence intervals (CIs) for the live birth rates. A custom computer program in MATLAB was used to perform the bootstrapping. A random number generator was used to simulate universal factors that affect all embryos such that if universal factors were not favorable no embryos implanted. If factors were favorable, embryos were assumed to implant independently with a live birth rate of

LBR UNI
where UNI denotes a universal factors fraction and LBR denotes the overall live birth rate of an embryo. A universal factors fraction of 0.70 was used to model favorable universal factors 70% of the time for combined analysis of fresh and frozen embryo transfers. For analysis of fresh embryo transfers a value of 0.68 was used and for frozen embryo transfers a value of 0.75 was used. These are the approximate values from our embryo transfer data (Table S3) and that of others 2 . If the uterine factors were favorable, random number generation was again used to determine if each embryo would implant or not based on the logic in Figure 2B which is an example of logic for a double embryo transfer. For each group of embryo transfers the outcomes were simulated 100,000 times and for each simulation best fit live birth rates were calculated to create a probability distribution of predicted live birth rates. 95% CIs for the live birth rates were taken from the probability distribution determined by the simulation. The MATLAB code for the computer simulation is being provided through Mendeley Data and the analysis can be performed by running the "generate_data_and_figures.m" file 1 . The 95% CIs for live birth rates are given in supplemental table 2 for each age group.

In Vitro Fertilization Protocols Ovarian Stimulation
Ovarian stimulation was performed with recombinant human follicle stimulating hormone (FSH) 75-300IU SC daily (Follistim: Merck, Kenilworth, NJ; or Gonal-f: EMD Serono, Rockland, MD) and/or human menopausal gonadotropins (hMG) 75-150IU SC daily (Menopur: Ferring Pharmaceuticals, Parsippany, NJ). Pituitary suppression was achieved through the use of gonadotropin releasing hormone (GnRH) antagonist, GnRH agonist suppression, or GnRH flare suppression protocols. In antagonist cycles the GnRH antagonist (0.25mg SC ganirelix acetate daily or 0.25mg SC cetrorelix acetate daily) was started when the lead follicle reached 14mm in diameter at which time LH receptor stimulation was begun with SC hMG and/or 100IU SC human chorionic gonadotropin (hCG) daily. When two lead follicles reached 18mm in diameter or three follicles reached 17mm in diameter patients received a trigger medication for oocyte maturation and the GnRH antagonist was discontinued. 5,000IU hCG (or 10,000IU HCG for patients with a weight of 200lbs or greater) was used for the trigger in GnRH agonist and GnRH flare protocols. With GnRH antagonist protocols hCG, leuprolide (4mg SC every 12 hours for 2 doses), or a hCG (2,500IU SC) and leuprolide co-trigger was used. Follicular aspiration was performed 34-36 hours after the trigger administration. Doxycycline 100mg PO twice a day was prescribed starting in the morning prior to the follicular aspiration and continued for 3 days for patients freezing embryos and until the morning of embryo transfer for patients receiving a fresh embryo transfer.

Oocyte Collection, IVF, and ICSI
Oocyte cumulus complexes were identified in the follicular fluid with an Olympus SZX10 microscope and transferred to oocyte collection dishes in Multipurpose Handling Medium with Gentamicin (MHM, Irvine Scientific, Santa Ana, CA). Oocytes were placed in MHM before insemination or ICSI. IVF insemination was carried out 4-6 hours after the retrieval with each droplet being inseminated with 50,000 motile sperm. ICSI was performed on mature MII oocytes after removal of cumulus coronal cells. Removal of cumulus coronal cells was performed by exposure to hyaluronidase for 60 seconds followed by transfer to MHM and pipetting with 300µm, 170µm, 140µm, and 130µm diameter pipettes. ICSI was performed with an Olympus IX73 microscope microinjector (Olympus Corporation, Shinjuku City, Japan) with a heated stage (Tokai Hit, Shizuoka, Japan) and Narishige micromanipulator (Narishige, Tokyo, Japan). At 16-18 hours post insemination or ICSI a fertilization check was performed.

Embryo Culture
Embryos were cultured in 15 µL drops of Continuous Single Culture Complete with Gentamicin and Human Serum Albumin (HSA) media (CSCM-C, Irvine Scientific, Santa Ana, CA) which was replaced with fresh media on day 4 of culture. Embryos were cultured in 38Special GPS Dishes (Life Global, Guilford, Connecticut, USA) overlaid with Liteoil (Life Global) for 3 days for cleavage stage embryos and 4-7 days for blastocysts. The incubator conditions were set to temperature 37.0 o C, 5% O2, 8% CO2, and 87% N2. The % CO2 was titrated to maintain a culture media pH of 7.2-7.5 with a preferred pH range of 7.25-7.35. The embryos were cultured in either a Miri tabletop incubator (ESCO Medical, Changi, Singapore) or HERAcell 150i incubator (Thermo Scientific, Waltham, MA).

Fresh Embryo Transfer
After follicular aspiration patients were prescribed 2mg estradiol PO twice daily until a positive serum HCG and 200mg micronized vaginal progesterone twice daily until 10 weeks gestation.

Vitrification Technique
Blastocysts of grade 1CC or higher and cleavage stage embryos with 6-10 cells on day 3 were considered for vitrification. Blastocyst vitrification was performed according to the I.C.E. Blastocyst Vitrification Protocol (Innovative Cryo Enterprises LLC, Linden, New Jersey). Cryotop vitrification device (KitaZato, Tokyo, Japan) was used for blastocyst vitrification. Cryotip device (Irvine Scientific, Santa Ana, CA) was used for cleavage stage embryo vitrification. Prior to vitrification, blastocysts were collapsed with laser pulses directed at a thin portion of the trophectoderm away from the inner cell mass to prevent ice crystal formation. Vitrification was performed 10-30 minutes after the embryo was collapsed.

Frozen Embryo Transfer
The majority of frozen embryo transfers occurred in programmed cycles. Starting on day 2 of the menses a baseline transvaginal ultrasound was performed and 2mg oral estradiol was administered twice a day for 6 days then three times a day until embryo transfer. On approximately day 11 of estradiol a serum progesterone and endometrial thickness by transvaginal ultrasound were measured. Cycles were cancelled if the progesterone was greater than or equal to 1.5 ng/mL. Additional days of estradiol were prescribed if the endometrial thickness was less than 7.0mm. If the serum progesterone was less than 1.5 ng/mL and the endometrial thickness was equal to or greater than 7.0mm, then IM and vaginal progesterone was started. IM progesterone was started with 50mg progesterone in ethyl oleate starting at 9PM (day 1 of progesterone). Subsequent days of progesterone consisted of IM progesterone at 9AM and 200mg micronized progesterone vaginally at 1PM and 9PM. Cleavage stage transfers were scheduled on day 4 of progesterone (approximately 60 hours after the first IM progesterone dose) and blastocyst transfers were scheduled on day 6 of progesterone (approximately 108 hours after the first IM progesterone dose). This timing was adjusted to the implantation window if a patient had previously had an endometrial biopsy for receptivity testing. Doxycycline 100mg orally was prescribed twice a day starting in the morning the day prior to the embryo transfer for a total of three doses. After embryo transfer, patients were prescribed oral estradiol 2mg twice a day, 50mg IM progesterone in ethyl oleate once daily, and 200mg micronized progesterone vaginally twice a day for 13 weeks. The first serum HCG was measured 11 days after cleavage stage transfers and 9 days after blastocyst transfers.

B. Sample
5-year moving groups are used for ages 35 to 43. The universal factors fraction is calculated as a best fit value based on number of singleton live births that resulted from multiple embryo transfers. * This value could not be determined as results were not consistent with a best fit value of 1 or less. ** The best fit UNI values for live birth after fresh and frozen embryo transfers (for cleavage and blastocyst stage combined) are used in the main analysis and validation study.