## How long does it take to get pregnant?

My girlfriend’s biological clock is ticking, and so we’ve started trying to spawn. Since I’m impatient, that has naturally lead to questions like “how long will it take?”. If I were to believe everything on TV, the answer would be easy: have unprotected sex once and pregnancy is guaranteed.

A more cynical me suggests that this isn’t the case. Unfortunately, it is surpisingly difficult to find out the monthly chance of getting pregnant (technical jargon: the “monthly fecundity rate”, or MFR), given that you are having regular sex in the days leading up to ovulation. Everyone agrees that age has a big effect, with women’s peak fertility occuring somewhere around the age of 25. Beyond that point, the internet is filled with near-useless summary statistics like the chance of conceiving after one year. For example, the usually reliable NHS site says

Women become less fertile as they get older. For women aged 35, about 94 out of every 100

who have regular unprotected sex will get pregnant after three years of trying. However, for

women aged 38, only 77 out of every 100 will do so.

I found a couple of reasonably sciency links(George and Kamath, Socal Fertility) that suggest that the MFR is about 25% for a women aged 25, and 10% at age 35. The Scoal link also gives rates of 15% at age 30, 5% at age 40 and less than 1% at age 45. If the woman is too fat, too thin, a smoker, or has hormone problems, or is stressed, then the rate needs reducing.

Given the MFR, the probability of getting pregnant after a given number of months can be calculated with a negative binomial distribution.

months <- 0:60 p_preg_per_month <- c("25" = 0.25, "30" = 0.15, "35" = 0.1, "40" = 0.05, "45" = 0.01) p_success <- unlist(lapply( p_preg_per_month, function(p) pnbinom(months, 1, p) ))

Now we just create a data frame suitable for passing to ggplot2 …

mfr_group <- paste( "MFR =", format(p_preg_per_month, digits = 2), "at age", names(p_preg_per_month) ) mfr_group <- factor(mfr_group, levels = mfr_group) preg_data <- data.frame( months = rep.int(months, length(mfr_group)) , mfr_group = rep(mfr_group, each = length(months)), p_success = p_success )

and draw the plot.

library(ggplot2) (p <- ggplot(preg_data, aes(months, p_success, colour = mfr_group)) + geom_point() + scale_x_continuous(breaks = seq.int(0, 60, 12)) + scale_y_continuous(breaks = seq.int(0, 1, 0.1), limits = c(0, 1)) + scale_colour_discrete("Monthly fecundity rate") + xlab("Months") + ylab("Probability of conception") + opts(panel.grid.major = theme_line(colour = "grey60")) )

So almost half of the (healthy) 25 year olds get pregnant in the first ~~month~~two months, and after two years (the point when doctors start considering you to have fertility problems) more than 90% of 35 year olds should conceive. By contrast, just over 20% of 45 year old women will. In fact, even this statistic is over-optimistic: at this age, fertility is rapidly decreasing, and a 1% MFR at age 45 will mean a much lower MFR at age 47 and the negative binomial model breaks down.

Of course, from a male point of view, conception is an embarrassingly parallel problem: you can dramatically reduce the time to conceive a child by sleeping with lots of women at once. (DISCLAIMER: Janette, if you’re reading this, I’m not practising or advocating this technique!)

This is the argument I used with my husband to get him to start trying immediately (i was 36 at the time and i told him it would take at LEAST a year to get pregnant). We got knocked up our first try. With twins (women in their 30’s have more fragile eggs and they can break into two much easier than the eggs of a woman in her 20’s).

Congratulations! It must have been quite a shock to get pregnant so quickly (though I’m sure it’s always a shock, no matter how long it takes.) I hope you are enjoying motherhood.

Add to this curve that male fertility shows a 21-23% annual decrease starting at the age of 39 and male fertility is believed to be falling at a rate of 2% every year due to environmental pollutants. Occupation and lifestyle also have significant impact on male sperm count (lower in persons exposed to heat and solvents, office workers, taxi drivers, etc.). Woman MFR is just a part of the overall picture.

Wow, taxi drivers can affect your sperm count? I must be more careful next time I take a cab.

Agreed that reality is more complex than my very simple model. I just wanted to get a rough idea of how long I’m going to have to wait.

Three things:

1) COOL(!) post.

2) Good luck!

3) You totally made me laugh, thanks

p.s: useR2012 was fun, too bad you couldn’t make it (next year it will be in Spain, I hope we’ll both get to be there)

Yours,

Tal

Thanks.

I really wanted to go to useR but since I’m now self employed, a return ticket to the USA + conference fees seemed a little bit frivolous while saving for a wedding and a potential baby.

Hopefully I’ll make it to Spain though next year.

Love using R to do this, but methinks you’re neglecting fall-off of sperm counts, innit?

Yes, the model is way too simple compared to reality, but it’s good enough for a ballpark estimate.

Anyway, I’m 32, so I hope my sperm count hasn’t dropped too dramatically yet.

You should take into account that woman get older during next attempts to become pregnant, so MFR will decrease.

Yeah, I thought about that, then decided it was too difficult to model for a quick blog post.

Feel free to improve the model and write a post about it. (You can guest post here if you like.)

You do know that reproductive science has come to the conclusion that the male factor contributes to roughly 60% in cases of failed contraception?😉

Greets,

Andrej (a “molecular andrologist”)

Andrej, have you got some good links to peer reviewed work on this? Not doubting you, just curious to read more about it [child health researcher of prime reproductive age].

This analysis seems generally optimistic, especially because most of the age groups show a 100% of getting pregnant eventually. It seems to me that the curves for the younger ages shouldn’t go to 100%, since some people never get pregnant. Perhaps that’s the complication of getting older and jumping age groups though….

Nice work and graphs though. Also, nice point about the “getting pregnant is unavoidable with unprotected sex” propaganda that we’re fed as youths.

Like I said in the text, health problems mean that you need to reduce the monthly fecundity rate. In the case of extreme infertility problems (for example, you’ve had a hysterectomy and thus have no womb), the MFR is zero, and the chance is getting pregnant is zero over any time period.

I think the problem raised by geneorama is interesting and deserves investigations. Clearly the curves should not converge to 100%.

The problem is that MFR is unknown. It depends on the age (and you provide average results), but also on hidden parameters. So you have to take into account that there is a probability that your MFR is 0 (not necessarily with medical evidence).

Let’s say whatever your age is, you have a 10% probability that your MFR is 0. The curve should converge to 90%.

Even if you don’t consider this extreme case where MFR=0, this uncertainty on the MFR clearly has a strong influence on the curve and on how to interpret it.

On your curve, with MFR=0.05, a woman has 85% chance to be pregnant after 3 years and 95% after 5 years. Clearly, to be interpreted in an intuitive way for a single woman, it does not work, it should be much flatter after 3 years (sorry for that…). Because if it did not work during 3 years, it could be just bad luck, but most likely the MFR is lower than the expected one knowing only the age.

I should perhaps have stressed more that this model is based upon women of average fertility for an age group.

Using this (simple, dumb) model if a woman’s MFR is greater than zero, the chance of conception will eventually converge on 100%. If it is zero, then it will stay zero no matter how long you try.

I tried to make it clear that the model break down over a long period of time (more than two or three years) since it assumes constant MCR, whereas in reality it will change as the woman gets older/fatter or thinner/quits smoking, etc.

Feel free to come up with a more sophisticated model that takes into account health (or any other) factors.

It’s hard to communicate the results of something that’s changing with time, like fertility (or recidivism). If someone takes a long time to get pregnant, you don’t know that until they’re already close to moving into another age group. For example, if it takes someone who’s 29 two years to get pregnant, then half of her waiting time is spent in a different category. It’s confusing to handle, and it’s confusing to communicate.

Another confusing issue is how to handle subjects who become pregnant multiple times in the data. if you’re a woman looking at this chart then you’re probably interested in the results from the perspective of someone getting pregnant for the first time, since subsequent pregnancies are more probable. As an analyst you may not know if the reported data is for first time or subsequent pregnancies.

I am not sure you got my point.My point was not to take other factor into account, or to discuss the fact that MCR is decreasing with time (which is true, but that’s not the point).

My point is that your model is very far away from reality (the real curves would not look at all like that, it would be way flatter after one year) because you take MCR as an input, whereas your only input is the age, from which you make an initial estimation of MCR.

The first month, your estimate your MCR from the only information you have: the age, which is what you did.

But then, month after month, you have an additional information: it did not work so far. MCR expected value for a 25 years old woman is 0.25, but how much is the MCR expected value for a 25 years old knowing that she unsuccessfully tried to get pregnant during 2 years?

You do not need additional factors to build such model. A distribution function for MCR, some data to fit it (as apparently provided by Shamus Husheer below), and that’s it.

Nice post. As someone working in the field, it’s great to see emphasis on the statistics behind conception rather than the usual bland stats or scare tactics.

One minor point, and one major one: First, your model appears to show people starting off 25% pregnant if they’re 25 years old – by definition “almost half of the (healthy) 25 year olds get pregnant in the first month” is impossible. What you mean is “almost half of the (healthy) 25 year olds get pregnant by the end of the second month”.

Now the more significant point, alluded to above. Some constant fraction of the population who are trying to conceive are sterile, so you can make a vastly more accurate model by assuming that you start with e.g. 100 people, of whom X% are sterile, and the remainder have a Y% monthly fecundity rate. Suddenly those “this many women get pregnant by this time” stats become useful, because any set of at least 3 time points and cumulative pregnancy rates gives you enough data to model both background sterility and monthly fecundity rate.

For example, in the UK, NICE quote the following: “In the general population (which includes people with fertility problems), it is estimated that 84% of women would conceive within one year of regular unprotected sexual intercourse. This rises cumulatively to 92% after two years and 93% after three years.” – fitting to this model, you get a remarkably good fit by assuming that about 7.5% of the population is sterile, with a monthly fecundity rate of 17.7% for the remainder. This suggests that by 12 months, 90% of those who will ever get pregnant naturally, already have.

Of course this model is also far too simplistic – in reality, there are separate populations with different natural fecundity rates (think of a woman with one blocked fallopian tube – her monthly fecundity rate is simply half of the norm – blocked tubes affect about 20% of cases of infertility). And then there’s the fact that fecundity rate changes, not least because baby-making intercourse becomes a real drag, so happens less over time. However, it becomes possible to statistically assign couples to one of these groups based on time trying and a little bit of medical history, and then provide a much more realistic assessment of the chances of natural pregnancy.

For the ultimate (R-powered!) tool to help out with all of this, check out http://www.duofertility.com

> First, your model appears to show people starting off 25% pregnant if they’re 25 years old

Yeah, the graph was drawn as though you start trying around ovulation time, so the first month is month zero. I’ve tweaked the text, but one month either way is the least of the worries with the model.

> Some constant fraction of the population who are trying to conceive are sterile

You’re right that the model can be vatly improved by considering sterility. I had enough trouble finding reasonable estimates for the MFR in healthly women, so I decided not to bother hunting for data on infertility or trying to quantify how health factors might affect the probabilities.

How is duofertility R powered? I went to the website and didn’t see any mention of R… but I didn’t see a good way to search for it either!

Aaah, that would be the non-consumer-facing geekery that we do in the back-end. DuoFertility is basically a big data collection and numbercrunching exercise, with the aim of understanding fertility for various population segments and the specific case for each individual woman.

The woman wears an under-arm sensor that logs physiology (temperature, heat-flow, movement) from which we can extract models of various fertility related hormones (particularly progesterone). We then combine this with other user-entered data (medical history, self-exams, home test kits) from both her and all the other women in the database, and generate predictions for future fertility as well as flagging up a range of other issues. Much of the back-end number-crunching is done in R, though we also do a lot of Java and C (and even some number-crunching in assembly on the sensor itself to maximise sensor lifetime).

Unfortunately, talking about how we use R to work out what’s going on in your body does not exactly inspire the vast majority of the population (present company excluded) – the closest you’ll find to a public explanation of the inner workings is in the various publications on clinical trials etc, e.g. R is mentioned as a foot-note in:

http://www.touchobgyn.com/articles/pregnancy-prognosis-infertile-couples-duofertility-programme-compared-vitro-fertilisationin

An MFR of 0.25 means that one quarter of 25-year olds will get pregnant in the first month. The first month is month zero.

Cool idea, and I appreciate the r code. Is it appropriate to run the graphs out to 60 months, though? By then, the probability for the next age class would apply, right?

On a more practical note, my wife got pregnant within two cycles of starting to use an electronic ovulation tester. She was 39 at the time and we’d been “not-not trying” for 6-8 months before that.

Congratulations on your (wife’s) pregnancy!

You’re right that 60 months is pushing the boundaries of appropriateness. I did consider reducing the timespan, but I thought that a 5 year horizon is still interesting to see, even if the model ia bi nonsensical over such a long period.

Nice! But instead of writing code, get busy!

I’m on the case! Writing code is a very niche kind of foreplay.

The situation is grimmer than this, because of fetal loss, which, I think, increases with the age of the mother. Louis Henry published data on all this back in the 1950s. Lots of good modelling and research on fertility back in the heyday of population control programs (Perrin and Sheps, Potter, …).

IANAM, but I don’t know that true “infertility” in the sense most of us imagine it (a physical incapability to get pregnant) is as common, at least before age 40, as one might think. First of all, it surprised me to learn that the medical definition of “infertile” is (as noted in the OP) simply an inability to achieve pregnancy within two years–it has nothing to do with any precise biological condition. I was further surprised to read a study (sorry, no cite, just going by memory) that found that of couples who met this medical definition, but simply kept on trying the natural way (no medical intervention), half of them achieved pregnancy after a third year of trying. And of those who still had not achieved pregnancy after that third year but kept on trying, half of *them* had success in the fourth year.

Thus, only 25% of “infertile” couples were still infertile after two additional years, even with the impact of increasing age and of the factor you mention (which could be described as increasingly skewing the sample population toward the less fertile). So this suggests to me that the factor you are looking to account for is likely not to be as significant as you think.

I’ve been thinking about this problem for some time now. But I am not

a statistician and it’s been 40 years since I took a statistics course.

The problem I wanted to solve was:

Let’s start with some assumptions:

Woman is 45 years old.

70% of 45 year old women are non-fertile.

45 year old women who are fertile have a 5% chance

of pregnancy each month.

Given 50 months of failure, what is the probability that

the woman is in fact non-fertile, if you know for certain

that the man is (or was!) fertile.

I converted it to the classic urns with white and black balls:

Given 100 urns, 70 of them are filled with all black balls,

representing the assumption that 70% of women at that age are

not fertile.

The remaining 30 urns are 95% black balls, saying that each

month there’s only a 5% chance of getting pregnant for the

fertile women.

Now, assuming monagamy, select one urn. Draw 50 balls. All

are black. What’s the probability that the particular urn

has only black balls?

My attempt at a solution:

If you have one of the black/white urns, the probability of

50 black draws is:

.95^50 = .08 approx

So the conclusion is there’s an 8% chance the woman is fertile,

and if she is, based on the assumption above, each month there’s

a 5% chance of getting pregnant.

Love the stats and chart, but just a slight correction. The point most doctors consider there to be a problem is after 12 months of unprotected sex without conception for under 35 year olds and just 6 months of unprotected sex without conception for the 35 + up crowd… often couples move into ART treatments like IUI and IVF based on that, not stats like these (which would be helpful for them to know). The book Making Babies talks a lot about this… getting in shape, making some adjustments to optimize fertility and then having patience (which I know is waaay easier said than done!) is REALLY great if it can happen and THEN ART where it’s really still needed is a great thing. I’m a fertility educator and holistic practitioner (blog.lifehealinglife.co and lifehealinglife.com) and highly recommend makingbabiesprogram.com Happy conceiving!