## 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!)