Infertility math*

This post was primarily inspired by a recent, lovely post by Jane at Mine to Command who confronted the myth that stress causes infertility. She delves into the medical literature on the subject, so I won’t provide my own (undoubtedly less eloquent) rehashing of what she’s said there. Go read it! Then come back, if you like.

The myth that stress causes infertility is a pervasive one. And, its logical consequence – namely, that infertiles should “Just relax, and you’ll get pregnant – has lead to a laundry list of charming little chestnuts of advice including:

  • Just adopt, and you’ll get pregnant.
  • Go on vacation, and you’ll get pregnant.
  • Get drunk, and you’ll get pregnant.
  • Don’t try so hard, and you’ll get pregnant.

and so on…

This myth originated – and continues to be fueled – by the observation that indeed many infertile couples get pregnant when they stop trying.

Although I’m not a medical practitioner and haven’t consulted the scientific literature on this particular topic, my intuition (aided by some basic mathematical understanding) tells me that this observation is probably true: many infertiles do get pregnant when they “aren’t actively trying”.

Before you chase after me with torches and pitchforks, please let me explain…

While I do think that the probability of getting pregnant while not “trying” is significant (in some cases rivaling the probability of getting pregnant through medical intervention), the often-touted “logical consequence” of this observation – that infertiles should stop trying to get pregnant…in order to get pregnant – is complete and total hooey!

I’m a chemist, but I nearly minored in math. I’m particularly grateful that I took statistics (both math stats and biostatistics), which comes in quite handy in situations like this…

So, why do so many couples get pregnant when they aren’t actively trying?

As Jane pointed out, this is kind of a silly question. Anybody who is having sex without birth control is, on some level, trying to get pregnant. So immaculate conception and birth control failures aside, everyone who gets pregnant is technically trying. But any infertile knows that there’s a wide spectrum of “trying”, all the way from “pulling the goalie” (aka unprotected intercourse) to spending tens-of-thousands of dollars for the privilege of being poked with needles, pumped full of hormones, subjected to minor and/or major surgery, and violated on a regular basis by an ultrasound wand, among other things…

Statistics provided by reproductive endocrinologists – the infertility experts – tell us that our odds of conceiving are significantly increased by all these interventions. Consider the following per-cycle odds of conception for several common interventions:

Intervention Per-cycle odds of conceiving** Source
timed intercourse 5% Health.com
natural cycle IUI 5-10% Babycenter.com
medicated IUI Up to 20% Babycenter.com
IVF 46% SART

I couldn’t find any odds for “not trying”, but I think it’s safe to say that they would be less than 5% per cycle.

So, how on earth is it possible that so many infertile couples get pregnant after they’ve stopped trying, even though their odds are so much less – more than 9 times less compared to IVF?

The key words here are per cycle. The odds, per cycle, of success from IVF are nine times that for timed intercourse (and >9 times that for ‘not trying’). But how many cycles of IVF do people actually do? Looking around the blogosphere, I can find lots of examples of people who have done IVF two, three, four times. But at over $10K a pop, few people have the financial means (or an IVF clinic willing to risk hurting its SART stats) to do many more cycles than that.

On the other hand, an infertile couple might have 5-, 10-, 20-years of “not trying” to get pregnant. For a woman who ovulates regularly every 28-days, that corresponds to as many as 65, 130, or 260 cycles of not actively trying to get pregnant.

So, how do we do the math to figure out the odds of getting pregnant by “not trying” versus using a technology such as IVF?

Let’s take an example of a couple that tried IVF three times unsuccessfully, adopted a child, then had unprotected sex for ten years:

First, let’s calculate their odds of a pregnancy resulting from three rounds of IVF. (In statistics, it’s actually slightly easier to calculate the odds of something not happening, and then to convert that to the odds of that thing happening…)

  • According to SART, the average odds of a pregnancy resulting from one cycle of IVF for a woman under 35 are 46%. We can express this value as the decimal 0.46.
  • That means the odds of not getting pregnant from one IVF cycle are 100-46 = 54% or 0.54.
  • The odds of not getting pregnant after two rounds of IVF are 0.54 x 0.54 = 0.29 or 29%.
  • The odds of not getting pregnant after three rounds of IVF are 0.54 x 0.54 x 0.54 (or 0.54 to the third power, 0.54^3), which equals 0.16 or 16%.
  • Now, to get the probability of a pregnancy resulting from three IVF cycles, we just subtract from 100% the probability of not getting pregnant: 100-16 = 84%. (Not bad odds! It seems our hypothetical couple – like many of us – was on the unlucky side of these stats…)

Now let’s calculate the odds of getting pregnant from ten years of unprotected sex.

  • For the sake of argument, I’m going to estimate that the couple’s per-cycle odds of pregnancy are a mere 1% (0.01). (Given that the per cycle odds for infertile couples practicing timed intercourse is estimated at 5%, I think 1% odds for “not trying” is actually pretty conservative…as long as the couple is having sex…) If the odds of a pregnancy are 1%, that means the odds of not getting pregnant are 99% or 0.99 per cycle.
  • The odds of not being pregnant after two cycles are 0.99 x 0.99 = 0.98, or 98%.
  • The odds of not being pregnant after three cycles are 0.99^3 = 0.97. In other words, there is only a 3% chance of a pregnancy resulting from three cycles of “not trying” – not even close to the 84% odds from three cycles of IVF.

Like interest on a long-held bank account, things start to get interesting as these paltry odds compound over large numbers of cycles…

  • The odds of not being pregnant after 13 cycles (one year) are 0.99 to the thirteenth power (0.99^13) or 88%. That means the odds of a pregnancy resulting from those 13 cycles is 12% (100 – 88 = 12). In other words, more than one tenth of “infertile” couples will be pregnant after a year of “not trying”. (Thereby supplying ample anecdotal “evidence” for annoying fertiles to misinterpret and hold up to their infertile friends…)
  • The odds of not being pregnant after 130 cycles (0.99^130) are 0.27, or 27%.

In other words, after ten years of “not trying”, this “infertile” couple had a 73% chance of achieving at least one pregnancy. (And remember, that pregnancy could occur randomly at any time during the ten years of not trying…)

How do you suppose most people interpret this series of events?

The facts: a couple failed to get pregnant from three rounds of IVF, adopted a child, and then got pregnant after a few years of not actively trying to get pregnant.

I can think of a couple of likely interpretations:

“After becoming parents through adoption, they were finally able to “just relax” and get pregnant!”

“In adopting, they were able to resolve the karmic imbalance that had previously interfered with their attempts at pregnancy!”

Nonsense! The real reason is far less romantic:

Over the course of many years of regular unprotected sex (albeit without officially “trying”), chances are that at least once, healthy sperm would meet with healthy egg at the right time to fertilize, and travel through the fallopian tube to find a uterus in just the right condition for implantation.

As Jane would say, “it was just their time.”

For women with diminished ovarian reserve (like me) the odds of conceiving by IVF are far below the 46% average I used in the example above (see this post for the depressing stats). Yet it’s not known how significantly DOR affects our chances of success through natural conception (which only requires one good egg each month…) In such cases, it’s easy for me to believe that the odds of conceiving from 100+ cycles of “not trying” could exceed the odds of conceiving from a handful of IVF cycles!

Am I saying we should all “just relax” and abandon assisted reproductive technologies?

No way! I can think of several good reasons to take a more aggressive approach:

  1. I don’t want to wait ten years to have a decent chance at a pregnancy! (Since I didn’t start until 33, I don’t even have 10 years of trying left in my old lady ovaries anyway…) I want my child yesterday! I want to change her diapers, not ask her to change mine. ART gives me the best odds of a child soon!
  2. Unlike in my simplified example, our odds of success are not static. My odds of pregnancy with my eggs – whether via ART or natural conception – are decreasing every month. With that fact hanging over me, it’s hard to justify waiting around for years for a natural conception. I can always try (or “not try”) for a natural conception after trying other family-building options (IVF, adoption, etc.) But ten years from now, if natural conception doesn’t work, I can’t go backwards and do IVF (at least not with my own eggs, which will have long dried up by then…)
  3. It’s not an either/or situation. If the odds of a pregnancy in my hypothetical example were 84% for three rounds of IVF, or 73% for 130 cycles of “not trying”, the total probability of a pregnancy – given that this hypothetical couple used both methods – was an almost unbelievable 96%! (1 – 0.16 x 0.27 = 0.96). Carefully timing intercourse instead of “not trying” should increase the odds further. Trying a combination of aggressive treatment (using ART) and regular unprotected intercourse will give me the very best odds of a biological child.
  4. There’s comfort in knowing that I’ve “tried everything”. If things don’t work out, and I end up on the unlucky end of all these statistics, at least I won’t wonder whether I might have been a genetic parent, “if only I’d tried X…” I’d rather go ‘all in’ now, and then move on to the next family-building option (or child-free living) without regrets.

As you’ve probably figured out by now, my plan is to continue with high-tech treatment…and to break out the Marvin Gaye around ovulation time every month in between!

It’s a plan that will mean a lot of two-week waits,…

a lot of peeing on sticks,…

and charting temps,…

and reading signs…

You’ll understand if I get tired of all the effort and decide to “take a break” and skip the meticulous timing for a few months…

And if, by chance, I happen to get pregnant that cycle,…

For heaven’s sake, DON’T use me as an example of how you “know this girl who got pregnant as soon as she stopped trying!”

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*I can’t write about Infertility Math without acknowledging this brilliant post by Aramis at It Only Takes One.

**Odds shown are for infertile couples (that is, couples who have been trying unsuccessfully for at least a year) in which the woman is less than 35 years old. Other factors can dramatically change these odds. For example, when fertile couples are included, the per-cycle odds are much higher – as high as 25% per cycle for timed intercourse. For older women, the per-cycle odds are lower in each case. Also, note that these stats show approximate pregnancy rates. The live birth rates are (sadly) lower due to miscarriage…

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Roid Monkey

So, on Monday I started rubbing Androgel on my upper arm each morning…and taking two Estrace (orally…phew!) each night. This is the hormone priming step of my IVF protocol. Add these to the Pulmicort inhaler that I use to keep my asthma under control and the progesterone that my corpus luteum is dutifully excreting, and you’ve got quite a steroid soup warming in my innards… I keep checking in the mirror for facial hair, bacne, or increased muscle mass. Aside from my pesky chin hair (excuse me while I find my tweezers…erm…got it!) I haven’t noticed anything.

ImageA sampling of roids in my system. You can read about progesterone, and what makes a steroid a steroid, here.

 

Speaking of progesterone, I’ve relapsed into another of my pre-IUI TTC habits, namely, charting. I keep track of each morning’s BBT (basal body temp) measurement, my CBFM (ClearBlue Fertilility Monitor) reading, any eggwhite sightings, and sexual encounters on a little paper chart on my nightstand. Recording it on the paper chart has a certain old-school charm about it, but can be a bit tricky to analyze and doesn’t quite satisfy my appetite for data.

Enter FertilityFriend. I type in my data to this website and it uses an algorithm that incorporates the data from my temperature, cervical fluid, fertility monitor, and OPK (when I use it) to determine when I ovulated. Actually, there’s a ridiculous amount of other data I could enter, but even a data junkie like me has to draw the line somewhere…

charts aMy paper chart for this month (left), and the FertilityFriend version, with est. ovulation shown as a red vertical line (right).

If you spring for the VIP membership (or if you are a new member, in which case you get a free ‘teaser’ VIP membership), the website will evaluate how well you timed intercourse. C and I apparently did ‘Good’ this month

ImageAnother feature of the VIP membership is that it will overlay up to 7 charts and show you the average BBT pattern. I’m not sure what this would be useful for, but it looks pretty cool:

Image

The average line (in blue) eliminates some of the noise of individual monthly charts to reveal a general trend of low temps pre-ovulation, followed by progesterone-elevated temps post-ovulation, which drop off just before the next cycle start (bonus benefit of charting – no surprise visits from AF!)

 

And this brings me to my newest dilemma: when to pick up my meds. Obviously, I already have some of them (including the Androgel and Estrace), but there are still ~$1K-worth of meds that Kaiser pharmacy doesn’t carry, which I have to pick up. If it weren’t for traffic, I would have picked them up the day Dr. Y prescribed them. But now that there is a chance – however miniscule – that I might be pregnant, I can’t bring myself to shell out that $1K until I’m sure I’ll need it…

So it’s one more thing on my ‘to do’ list. If FertilityFriend is right about my ovulation date, and if I follow my usual luteal phase of 11 days, then AF should arrive on Monday, and I can swing by the pharmacy after that, with plenty of time before I need those particular stims… On the other hand, maybe I should wait longer – until my baseline ultrasound (next Thursday) to make sure there are any follicles to stimulate with those drugs…yes, I think that makes more sense.

It’s a plan! And thank you, bloggy friends, for inspiring me to think this through, and patiently reading while I do. 🙂 Yet another perk of blogging…it forces me to think before shelling out C’s hard-earned money!

 

p.s. Welcome ICLW visitors! You can read my TTC resume here, but in brief: I’m a 34-year-old chemistry professor with diminished ovarian reserve, who has been TTC for about 15 months, including one missed miscarriage at 9 weeks. After 1 unsuccessful round of IUI, we are moving ahead with our first IVF next month. I use this blog as a form of therapy, and as a repository for interesting chemistry (and biology) that I learn along the way!