If you go from 10 expected births to 1000, the expected gain only increases by 70%. That’s great, but we’re still limited to selecting the maximum value from a normal distribution. So the increase is smaller than many people believe.
This is because the expected gain of embryo selection using a predictor is roughtly directly proportional to the correlation between the predictor and the trait of interest but only the square-root of the log of the number of embryos! Having more embryos to choose from is great, but the best embryo of 1000 or even 10 isn’t likely to be chosen for implantation if your predictor isn’t very good.
Having more embryos to choose from is great, but the best embryo of 1000 or even 10 isn’t likely to be chosen for implantation if your predictor isn’t very good.
Choosing ‘the best’ is irrelevant and a distraction in most contexts. It is not the case that you will be ‘likely’ to choose ‘the best’ if you have a ‘good’ predictor—because for any ‘good’ predictor, no matter how good it is, the probability of ‘choosing the best’ still becomes arbitrarily close to zero as n increases (specifically, it goes to 1/n). Nor does it particularly matter if you do select the #1, by chance, because you still have high odds of not yielding a downstream success like a live birth.
(Of course, the expected gain—which is what matters—just keeps going up and up with n...)
This is because the expected gain of embryo selection using a predictor is roughtly directly proportional to the correlation between the predictor and the trait of interest but only the square-root of the log of the number of embryos! Having more embryos to choose from is great, but the best embryo of 1000 or even 10 isn’t likely to be chosen for implantation if your predictor isn’t very good.
https://doi.org/10.1016/j.cell.2019.10.033
Choosing ‘the best’ is irrelevant and a distraction in most contexts. It is not the case that you will be ‘likely’ to choose ‘the best’ if you have a ‘good’ predictor—because for any ‘good’ predictor, no matter how good it is, the probability of ‘choosing the best’ still becomes arbitrarily close to zero as n increases (specifically, it goes to 1/n). Nor does it particularly matter if you do select the #1, by chance, because you still have high odds of not yielding a downstream success like a live birth.
(Of course, the expected gain—which is what matters—just keeps going up and up with n...)