Probability & Parenthood: Making Sense of Fertility Odds

Ever wonder why trying the same fertility treatment more than once doesn’t just double your chances of success? Or how putting back two embryos could actually lower your overall chances of a live birth? In this episode of Taco Bout Fertility Tuesday, Dr. Mark Amols breaks down the math behind fertility treatments, exploring how probabilities, risks, and statistics truly impact your journey to parenthood. From understanding why more isn’t always better with embryo transfers to demystifying relative vs. absolute risk, this episode will change the way you think about fertility odds. Join us for eye-opening insights, relatable analogies, and practical advice that empower you to make informed decisions on your path to building a family.

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Transcript

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Today we talk about probability, making sense of, fertility odds. I'm Dr. Mark Amols, and this is Taco about Fertility Tuesday. I want you to imagine this scenario. You're in a room and there are three doors. Door one, door two and door three. I'm going to let you know that, there was a prize behind one of those doors. And for simplicity, you're going to pick door number two. And I'm going to let you know that the winning door is not door number three. This leaves you now with just the two doors, one and two. But heres the catch. I m going to give you an option. Now. You can either stay with door number two, or you can switch doors. And now go to door number one. Now, the question isnt really whats the right answer, but the question is, does your chances go up by changing or does it stay the same? You'going to be surprised what the answer is. But before I give you the answer, let's talk about some statistics. At the end, I'll reveal the answer to this puzzle. There are many reasons why we struggle with statistics. Sometimes it's the jargon of it. You hear a statistic that something is a higher chance and you assume it's higher. But what you may not realize is that it's a relative chance versus an absolute chance. Additionally, one of the things we struggle with is we really struggle with very large numbers and very small numbers, because that's not the world we live in. Let me give you an example. If you loot at time, let's say seconds, and so I had a million seconds, you would only get about, just short of 12 days of time. But then if I asked you if I give you a billion seconds, how much longer would that be? Now, take a second, think about that. A million seconds is just under 12 days. So how long would a billion seconds be? Have you thought of your answer? Well, it's just shy of 32 years. Now, for most of you, that's going to be pretty shocking. Now, if you're a nerd like me, you're like, yeah, I knew that already. But why is it that we are so far off on our guests? Well, the reason why is because we don't live in a world like that. None of us have ever had a billion dollars, let alone a million dollars. So to us, it just seems like it's not that far away differ when actually it's a tremendously bigger number. Well, the same thing happens when we talk about statistics. Some of these things we don't work with and so when we hear them, we try to compare them to things we see in our lives. Let's start with IUIs. If you are going to do artificial inseminations, also called IUIs, and let's just say you have a 20% chance of it working, then you would think if you did it three times, your chances would then be around 60% after doing three of them. Well, what's interesting is it's actually less than 50% after doing three of them. But how is that? Well, it's because you can't have more than 100%, meaning if you take 100 people and you did IUIs, you would expect 20 of the people to become pregnant. That only leaves 80 people left. You don't start again with another 100. So when those 80 people then go through IUI, again, another 20% will get pregnant. But now only 16 of, the people will get pregnant, which now gets you to 64% that are not pregnant. And then if you do it again with those 64 people and you figured out who got pregnant, you would find then another 13 people would get pregnant because you can't have half of a pregnancy, which leaves you around 49 people would be pregnant and 51 would not. Now for my math nerds, yes, it's actually 48.8%, but as I said, you can't really have a eighth of a pregnancy. So then it would be either 48 or 49. And I rounded it up to 49 because I'm pretty optimistic person. In probability and statistics, we call this integer constraints, meaning it can't have half of a person. So that means everything has to be rounded to either 0 or 1. I see this occur a lot when we talk about blastulation. When you start with, let's say nine embryos that fertilize, then that means about half will make it to blastocyst. Well, you can't have four and a half embryos, so you either are going to have four or five. And both of them would be correct if you got that many. So how patients come to me, they go, Well, I had nine embryos, but they only got four blastocyst. I didn't get 50% and I have to explain them. Well, you did, because you can't have half of an embryo, so you can only have four or five. And yet that still fits the equations statistically. Another way to think of the IUI example would be if you were going to have a sub sandwich for all of the people at your party, and you said everyone can have 25%. Well, if it's a 10 foot sandwich, then the first person is going to take 2.5 foot of the sandwich. And then if someone says well now there's 7.5, I only get 25% now they only get 25% of the 7.5 foot Samich has left over. May be easier to use 50% mean 10, 5, 2 and point half and so forth. But the point is you can't keep taking the same amount because you're losing some of the sandwich. And the same thing when you're talking about cumulative rates, you have to remember it, it doesn't start all over again such as if I said you can have 25% or 50% of the sub. Well then if I bring a new sub moount every time someone comes in, they will get the same amount each time. But that doesn't happen when we're talking about fertility probability. Here's another example of cumulative probability. When you hear IVF gives you a 60% chance of having a live birth, well then if you put two back, you should have now 120% chance. When we go back to that principle again in statistics, you can't have over 100% chance. So that's impossible. So then that means it must be 100%, right? Because 60 plus another 60 and you can't be over 100, must be than 100. But again, that's not true because once you have the 60%, if you put another empbryo back, it's only 60% of the 40% that is left of 100. The answer surprisingly is 84%. And this is actually one of the reasons why most clinics recommend putting back one embryo. Because there is another principle here, and that is the principle of risk. When you put one embryo back, your risk to that embryo is only the risk of that one embryo. Meaning, let's say we're talking about something like autism. Now, for simplicity sakes, I'm going to say 5%. It's not. But let's say it was a 5% chance if you put two embryos back. It's not the same thing as before about cumul probability. In this situation, it truly is 5% plus 5%. You actually now have a 10% chance of one of those babies now having autism. Now for my math nerds out there, you are right, it's not technically 10%. It would be more like 9.75%. And this is due to the overlap in independent probabilities. But that's probably a little too much for this Discussion. A simple example of this would be raincoats. If, let's say you had a raincoat that had a 5% chance of letting water through if it rains, then wearing both of them might feel like double protection. But it doesn't mean your chance of staying drives exactly 20%, because both raincoats would need to fail at the same time. So the chances of that happening is slightly less than just adding the two wrists together. So your real chance of getting wet is closer to 9.75%, not 10%. Now, as I digressed, the point of this was that even though you put back a second embryo, your chances only really increased by another 24% because you went from 60 now the 84% of having at least one live birth. But here's the interesting thing. Your chances of having twins the first time was purely identical twins, which occurs about, in 1 in 240, which is 0.42%. Yet if you put back two embryos now, your chances of twins is at least 36%. You risk of triplets, which was well below 1% before almost nonxistent naturally will now go up. Because now if you put back two embryos, each embryo has a possible risk of splitting at that one over 240, which then increases your risk of also triplets. This now gives you a 0.3 minimum chance of having triplets just by putting back the two embryos at a 60% chance of live birth. This means you went from a 1 in 8,000 and 100 chance of triplets occurring naturally with one embryo all the way to now 1 in 333. You also went from a 1 in 240 chance of having twins with one embryo now to a greater than 1 and 3 having twins. Now I can appreciate some people may say, hey, I want twins, I want triplets. I'm not worried about this. But the importance to understand here is that you're getting only a very small increase in the live birth with 1 versus 2, an absolute increase of only 24%. But you're astronomically increasing the risk of twins and triplets. So you get a very little benefit with a lot more risk, because we know twins and triplets have more risk. And this is where the statistics really matter. Because when you look at it from a standpoint of risk as, ah, you can think you can have things like subchran hemorrhages, you can have ectopic with maybe one pregnancy, which is called heterotopic, and one's in the uterus that can affect the other embryo. So by putting back two, you increase the risk by two as well. And so when you look at the math, what you find is, is that if you put back two single embryos cumulatively one at a time, you will actually come up with 84% chance of a live birth. But if you do one transfer with two embryos and you account for the increased risk of things like twins, preterm, labore, so the resulting adjusted live birth rate is 75.6%. Meaning by putting twobrs back at the same time, you actually only get a 75.6% live birth rate versus 84% by doing one at a time. One of the other areas of medicine is a relative risk versus absolute risk. And when you're given statistics, this is very important to understand the difference because a relative risk says this is what it is relative to another thing where it's absolutely saying how many absolute percentages is different. I'm going to give you an example. Let's say I say something is 500 times worse and you think oh my goodness, this is horrible, it's 500 times worse. But then I tell you it only occurs one in a billion. Well that is still then a very small number because it's 500 a billion, which is very tiny. So the absolute risk is very small. Let's use that autism analogy again, but this time lets talk about men. We know that when men get older you have a higher risk of having a child with an autism spectrum disorder. Matter of fact, fathers age 40 and older are about 20% more likely to have a child with autism compared to fathers under 30. And this risk increases approximately 2% for every additional year of paternal age over 40. Children born of father is over 50 years old may have up to a 66% higher risk of developing autism than those with fathers in their 20s. Now these are scary numbers. When you hear above 50% you think, wow, this gets very scary. But let's look at the absolute risk first. This is the baseline. So in the general population, the risk for autism spectrum disorders, again there's about 1 in 54 children in the U.S. that's 1.85%. Now again, these are all spectrums. This is not severity. We're talking about the whole spectrum. Now the relative risk of father's age between 4 and 49 is 20% higher relative risk 10 the baseline. Just like if they're age 50 and above, it's 66% higher to the baseline. But when we convert the relative risk to an absolute risk, that's 1.85 times 20%, you get 2.37%. That's less than a half percent increase. Even if you use men over 50, it just raises up to about 3.07%. So, as you see, it's not so scary anymore. You went from something that was just under 2% to something that went to 3%. Yet it sounded much scarier. You could even go a little further and say, well, what's the number needed to harm? Meaning how many individuals need to be exposed to this risk factor for one additional case occur? And what you would find is it takes 193 pregnancies from men 40 to 49 to get just one additional child diagnosed in the autism spectrum. Even for men who are 50 years of age, it would take 82 additional pregnancies from those men to get just one additional autism case. So, as you see, statistics are not always what they seem to be. As you can imagine, there are many, many other things I can go over, such as the chances of getting pregnant based off different ages, how it affects it. But I don't want this podcast to get too long, so we're going to stop here. But what I want you to see is that when you're looking at statistics, you always have to ask these questions. Is this an absolute risk? What's the number needed to occur? And is this an independent percentage, or is it a cumulative percentage? So context is very important. Additionally, it's important to know what the baseline risk is for something. Something can be a thousand times more common, but in reality, if it's a very low risk, it's a very low risk still. And the same token, keep in mind that we aren't used to a lot of these high, big numbers and low numbers. And so you have to keep that in context so that it doesn't seem right. But statistics are a little bit different. It's like I always tell someone, you could flip a quarter five times in a row and get five heads, and yet that quarter is normal. There's nothing wrong with that quarter. The sample size is just too small. You have to flip that quarter a thousand times until you start seeing a 50% chance of heads and tails. And that's assuming there's not another variable affecting it. Maybe the person flipping it isn't doing it the same way every time, and that could change it. So when you look at statistics, you have to look at everything. So that takes us then back to the Monty hall puzzle. So we talked about there's door number one and there's door number two. And I gave you a chance to switch the doors. I said you would your chances go up or would it stay the same? Now, I said you'd be shocked, and you may be, because if you change the door, you would actually increase your chances by 16%. Now, I know you're thinking, but wait, it's only one or two wouldn't be 50%. But the problem is, in this example, they are not independent events. In the very first event, when I gave you three doors, you actually had a 66% chance of picking the wrong door. But when I told you it wasn't one of other doors, at that point it seems 50 50. But it's not. Because remember, you had a 66% chance of picking the wrong door, which means the actual door is more likely to be the other door because you probably picked the wrong door. They're not independent of each other. And that's the thing about cumulative chances and looking at statistics and probability. It's not always just the numbers, but you have to look at the setup. And so in this Monty hall puzzle, it's actually better to switch your door than to stay with the same door. Because although it looks like it's a 50% chance and it wouldn't change, it actually is a 66% chance if you change the door and only a 33% chance if you keep the door. I hope you guys found this episode fun and maybe helpful. I know sometimes a lot of people don't like math or don't enjoy these type of topics, but I love this stuff. I bet you're surprised, but I am a nerd and that's why I like this stuff. Big surprise. But hopefully you enjoy the if you do, let me know when people send me podcast ideas or they tell me they like things and I know they make more of them like this. I really appreciate everyone who listens to podcast and as I always say, thank you so much. If you love us, please tell people about us, give us a five star review on your favorite medium that you listen to. But most of all, keep coming back. I look forward to talking to you again next week on Talk About Fertility Tuesday.