is possible that the implantation potential of a viable embryo will be compromised by the additional laboratory manipulation or that a false-positive genetic test will result in not transferring the one embryo that would have resulted in a viable pregnancy. There is also a statistical way of looking at the problem of how many embryos to transfer, by examining EI rates and then calculating the probabilities of pregnancy and multiple gestations. For these calculations, we must use the approximation that each embryo has an independent chance of implanting (‘‘EI is an independent event’’). The probability of pregnancy P after the transfer of n embryos can be expressed as: P ¼ 1 ð1 EIÞn For example, using an approximation of the IVF pregnancy rates from the Society for Assisted Reproductive Technologies registry and the ASRM guidelines for the number of cleavagestage embryos to transfer, it is possible to generate a table of P and EI rates for each age group (Table 1). Such a table may be generated by individual IVF programs to assist with patient counseling regarding the probability of pregnancy given a certain number of embryos available for transfer. This table also shows that the observed decrease in IVF pregnancy rates with increasing age actually understates the more rapid decline in EI rates. The binomial equation can then be used to calculate the probability of multiple implantations. The probability of m implantations after the transfer of n embryos can be expressed as: P m ¼ EIm ð1 EIÞnm $ n! ½m!ðn mÞ! For two implantations (twins), this reduces to: P 2 ¼ EI2 ð1 EIÞn2 $ n! ½2ðn 2Þ! and for triplets: P 3 ¼ EI3 ð1 EIÞn3 $ n! ½6ðn 3Þ!

TABLE 1 Relationship among the pregnancy rate (P), number of embryos transferred (n), and EI rate, as calculated by the equation P [ 1 L (1 L EI)n. Age (y) 34 35 36 37 38 39 40 41 42 43 44 45

P (%)

No. of embryos transferred (n)

EI rate (%)

50 48 46 44 41 38 35 30 25 20 15 10

2 2 2 2.5 3 3.5 4 4.5 5 5 5 5

29 28 26 21 16 13 10 8 6 4 3 2

Paulson. Reﬂections. Fertil Steril 2014.

1565

TABLE 2 Relationship among the EI rate, number of embryos transferred (n), calculated pregnancy rate P, calculated probability of twins and triplets, and proportion of the pregnancies that are twins (%twins) or triplets (%triplets). Age (y) 38 41

43

EI rate (%)

n

P (%)

Singletons (%)

16 16 16 8 8 8 8 8 4 4 4 4 4 4 4 4

1 2 3 1 2 3 4 5 1 2 3 4 5 6 7 8

16 29 41 8 15 22 28 34 4 8 12 15 18 22 25 28

16 27 34 8 15 20 25 29 4 8 11 14 17 20 22 24

Twins (%)

Triplets (%)

%Twins (twins/P)

%Triplets (triplets/P)

2.6 6.5

0.4

8.7 16

1.1

0.6 1.8 3.2 4.9

0.05 0.1 0.4

4.1 8.0 11 15

0.2 0.7 1.3

0.2 0.5 0.9 1.4 2.0 2.7 3.5

0.006 0.02 0.06 0.11 0.19 0.29

2.0 4.0 5.8 7.7 9.4 11 12

0.06 0.2 0.3 0.5 0.7 1.0

Note: Examples are provided for oocytes provided by women aged 38, 41, or 43; and EI rate estimates are those presented in Table 1. Paulson. Reﬂections. Fertil Steril 2014.

Using the approximate P and EI rates from Table 1, we can now look at the theoretical chances of twins and triplets at selected ages and generate some examples in Table 2. For good-prognosis women aged 38, the ASRM guidelines allow up to three embryos to be transferred. On the basis of the implantation rates in Table 1, EI ¼ 16% at the age of 38. In Table 2, the pregnancy rate as well as the multiple gestation rates increase with increasing n. With n ¼ 3, the calculated pregnancy rate is 41%, with 1.1% of those pregnancies being triplets. Analogously, a 41-year-old with ﬁve embryos transferred would expect a 34% pregnancy rate, with 1.3% of those pregnancies being triplets. A 43-year-old with an EI of 4% and eight embryos transferred would be expected to have a 28% pregnancy rate, with a 1% risk of triplets. (Note that Gunnala et al. report a 7% implantation rate for the 43year-old group. However, not all implantations resulted in live births, and the live-birth implantation rate was approximately 3%. Therefore, on the basis of the authors' database, the calculated rates for P and multiple gestations would be somewhat lower than those shown in Table 2). The only problem with these calculations is that the numbers are theoretical, not empiric, and based on the approximation that EI is an independent event—which it likely is not; HOM occur with probabilities that are higher than those predicted by the binomial equation; successful implantations are associated with other implantations. But the example of Table 2 does provide an estimate of the expected values for twins and triplets for a given number of embryos transferred. And it also underscores the concept that the ‘‘maximum number of embryos to be transferred’’ is necessarily arbitrary. There is always a possibility of multiple implantations, and the only question is, what level of risk is acceptable? The maximum number of embryos to be transferred is a number based on a reasonable expectation of a reasonably low probability of HOM. In the case of women over 43, a larger number of embryos can be transferred than in younger women. The calculations presented here 1566

support the conclusion of Gunnala et al: if it is reasonable to transfer three embryos in a 38-year-old, and ﬁve embryos in a 41-year-old, then it is also reasonable to transfer eight embryos in a 43-year-old. Richard J. Paulson, M.D. Division of Reproductive Endocrinology and Infertility, LAC+USC Medical Center, University of Southern California, Los Angeles, California http://dx.doi.org/10.1016/j.fertnstert.2014.10.030 You can discuss this article with its authors and with other ASRM members at http://fertstertforum.com/paulsonr-number-embryossafe-transfer/ Use your smartphone to scan this QR code and connect to the discussion forum for this article now.* * Download a free QR code scanner by searching for “QR scanner” in your smartphone’s app store or app marketplace.

REFERENCES 1. 2.

3.

4.

Paulson RJ, Sauer MV, Lobo RA. Factors affecting embryo implantation after human in vitro fertilization: a hypothesis. Am J Obstet Gynecol 1990;163:2020–3. Practice Committee of American Society for Reproductive MedicinePractice Committee of Society for Assisted Reproductive Technology. Criteria for number of embryos to transfer: a committee opinion. Fertil Steril 2013;99:44–6. Gunnala V, Reichman DE, Meyer L, Davis OK, Rosenwaks Z. Beyond the ASRM transfer guidelines: how many cleavage stage embryos are safe to transfer in women > 43 years old? Fertil Steril 2014;102:1626–32. Scott RT, Upham KM, Forman EJ, Hong KH, Scott KL, Taylor D, et al. Blastocyst biopsy with comprehensive chromosome screening and fresh embryo transfer signiﬁcantly increases in vitro fertilization implantation and delivery rates: a randomized controlled trial. Fertil Steril 2013;100:697–703. VOL. 102 NO. 6 / DECEMBER 2014