Reducing Multiples A Mathematical Formula that Accurately Predicts Rates of Singletons Twins and Higher Order Multiples in Women Undergoing in vitro fertilization

A mathematical formula is developed that predicts the likelihood of singleton, twins, or higher-order multiples according to the number of embryos transferred and implantation rate.

Zev Williams, M.D., Ph.D., Eric Banks, Ph.D., Mario Bkassiny, M.S., Sudharman K. Jayaweera, Ph.D., Rony Elias, M.D., Lucinda Veeck, Ph.D., Zev Rosenwaks, M.D.

Volume 98, Issue 6, Pages 1474-1480.e2, December 2012


To develop a mathematical formula that accurately predicts the probability of a singleton, twin, and higher-order multiple pregnancy based on implantation rate and number of embryos transferred.

A total of 12,003 IVF cycles from a single center resulting in embryo transfer were analyzed. Using mathematical modeling we developed a formula, the Combined Formula, and tested for the ability of this formula to accurately predict outcomes.

Academic Hospital.

Patients undergoing IVF.


Main Outcome Measure:
Goodness of fit of data from our center and previously published data to the Combined Formula and 3 previous mathematical models.

The Combined Formula predicted the probability of singleton, twin, and higher-order pregnancies more accurately than 3 previous formulas (1.4% vs. 2.88%, 4.02%, and 5% respectively) and accurately predicted outcomes from five previously published studies from other centers. An on-line applet is provided (

The probability of pregnancy with singletons, twins and higher order multiples based on number of embryos transferred is predictable and not random and can be accurately modeled using the Combined Formula. The embryo itself is the major predictor of pregnancy outcomes but there is an influence from “barriers” such as the endometrium and collaboration between embryos (embryo-embryo interaction). This model can be used to guide the decision regarding number of embryos to transfer following in vitro fertilization.

  • The idea by Williams et al to use a mathematical formula to predict the probability of singleton and multiple pregnancy is brilliant. It is very interesting to try the provided on-line applet, using different numbers of embryos transferred and implantation rates. The only challenge in the application of the formula may be to accurately predict the implantation rate, but nevertheless this may assist in the care and counseling of ART patients.

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