Intro to assisted fertility

Any successful pregnancy is viable with just one egg. As an increasing number of women delay pregnancy until their 30s and 40s, getting pregnant is increasingly a sociotechnical process. Assisted reproductive technologies can force women’s ovaries to produce a clutch of eggs at once…but it cannot force women to produce high quality, viable eggs. Quality still depends on age, with a higher rate of chromosomal abnormalities present in any given egg, the older mom is. The question becomes: what quantity of mixed quality eggs is enough to get to a live birth? Is the likelihood of getting a live birth correlated with the number of eggs retrieved? Yes. But how many eggs does it take?

As with almost all fertility issues, that question rests on the age of the egg. Usually, the age of the egg is the same as the age of the mom-to-be. Now that eggs can be frozen (in time and in the freezer), the age of the egg can be younger than the age of the mom-to-be.

A study by Sunkara, Rittenberg, Raine-Fenning et al. looked at data from 400,135 IVF cycles performed in the UK from 1991 to 2008. They found that 15 eggs is basically the magic number. No matter her age, a woman’s chance of getting a live birth increases up to ~15 eggs. Less than that OR more than 20, her chances for live birth are lower. Notably, most women did not make 15 eggs: “The median number of eggs retrieved was 9 [inter-quartile range (IQR) 6–13] and the median number of embryos created was 5 (IQR 3–8).”

For those freezing eggs, it is especially productive to wonder how the number of frozen eggs impacts the chance of a live birth because egg freezers could opt for more than one cycle (if they can afford it). The study I am quoting does NOT look at egg freezers, it only looks at IVF patients. There are not enough egg freezers who have gone on to try to become moms to produce data nearly this robust. Biologically, the stimulation protocol for egg freezers and IVF patients is largely the same so the number of eggs harvested should be decently reliable across populations. Egg freezers may produce more eggs than IVF patients, because egg freezers aren’t reporting infertility. On the other hand, IVF patients in this study were infertile for a number of reasons, the largest percentage had male-factor infertility. Pregnancy rates may vary between IVF and egg freezing patients. IVF patients usually get pregnant using fresh embryos. If they do freeze material before implantation, they usually freeze embryos which survive the thawing process better than a single egg does.

What Works

The nomogram above is able to display chances of live birth by age group using a U-turn in the trend line for each age cohort. This demonstrates that the chance of live birth rises until 15 and then drops for egg counts higher than ~20 no matter how old the woman.

This graphic has a number of key characteristics. First, it is legible in black and white, which is key for printing in academic journals. Academic journals rarely print in color. Second, the nomogram allows each age cohort to be visualized without overlap. If this were presented with a million lines – one for each age cohort – there would be overlap or bunching and it would be harder to understand each age cohort clearly. Third, the U-turn shape allows us to see that there is an optimal number of eggs, above and below which sub-optimal outcomes arise. Fourth, the authors do not try to hide the fact that these types of assisted fertility are low probability events. The maximum probability of a live birth is just over 40% for the youngest cohort of women who produce the optimal number of eggs for retrieval.

Overall, the two key strengths of the nomograph type are that it is able to show each age cohort without overlap and that it allows for the data to U-turn in cases where there is an inflection point.

What needs work

Many of us are accustomed to comparing slopes in trend lines. This format does not allow for any kind of slope, making it difficult to visualize the shape of the trend. From looking at other plots, live-by-birth by eggs retrieved appears to be a Poisson distribution. In other words, it is a lot better to have, say, 8 eggs retrieved than 7, but only a little bit better to have 15 eggs retrieved than 14 because the slope rises faster for smaller numbers. The nomogram *does* visualize this. Look at all the space between 1 and 2 eggs retrieved and the small amount of space between 14 and 15 eggs retrieved. I happen to think it is easier to understand the changes in relative marginal impact with slopes than distances. That could simply be because I am more used to seeing histograms and line charts than nomograms, but I see no reason to pretend that visual habits don’t matter. Because people are used to making inferences based on slopes, using slopes to visualize data makes sense.

What does this mean for fertility

Women who are undergoing IVF – meaning that they are aiming to end up with a baby ASAP – cannot do much more than what they are already doing to increase their egg count. Women who are planning to freeze their eggs for later use may be able to use this information to determine how many cycles of stimulation they undergo. One cycle may not be enough, especially if they are expecting to have more than one child. Eggs from two or more stimulation cycles can be added up to get to the 15-20 egg sweet spot per live birth.

Of course, egg freezing is still an elective procedure not covered by insurance. The cost is likely to prohibit many women from pursuing even one round of egg freezing, let alone multiple rounds.


Sesh Kamal Sunkara, Vivian Rittenberg, Nick Raine-Fenning, Siladitya Bhattacharya, Javier Zamora, Arri Coomarasamy; Association between the number of eggs and live birth in IVF treatment: an analysis of 400 135 treatment cycles. Hum Reprod 2011; 26 (7): 1768-1774. doi: 10.1093/humrep/der106

Visualization of outbreak pathways in a hospital
Visualization of outbreak pathways in a hospital | Scientific American, Graphic by Jan Willem Tulp

What works

Using RFID tags worn by hospital staff and patients at the Bambino Ges&#uacute; pediatric hospital in Rome, researchers with the SocioPatterns group tracked interaction patterns to help understand how nosocomial illnesses spread. Nosocomial infections are infections patients and hospital staff contract while they are in the hospital. According to wikipedia, about 10% of patients in hospitals in the US contract some kind of nosocomial infection every year; the most common infection is the urinary tract infection (36%).

The RFID tags were distributed to 119 individuals to tally up each person’s encounters with anyone who came within 1.5 meters for a minute or more. Of course, this generated a great deal of data. The graphic above does a good job of condensing the data into a single image – well, actually, there is one image for each category of person in the hospital and it is important to look at all five images for full analytical impact. Click on the graphic to go to Scientific American and see them all.

Legend for reading the radial graph of outbreak pathways in a hospital
Legend for reading the radial graph of outbreak pathways in a hospital | Scientific American, Jan Willem Tulp [graphic]

Somewhat unsurprisingly, nurses proved to be the most well-connected people in the hospital. They interact frequently with each other and with every other category of person: patients, ward assistants, doctors, and care givers. Even though I said this finding was “unsurprising” it is extremely important to have solid data supporting what seem to be obvious findings. For instance, imagine you had not read the previous paragraphs or looked at the graphics and I had written: “Unsurprisingly, doctors proved to be the most well-connected people in the hospital, interacting frequently with patients, care givers, nurses, and ward assistants”. It sounds almost as logical as what I wrote about nurses (quite frankly, I would have found it hard to believe that doctors interact frequently with ward assistants). The point is, before data exists, it is easy to convince ourselves that a variety of different logical scenarios are playing out. The RFID methodology was a wise choice because it did not rely on self-reports. Self-reports are tough because they ask responders to remember all their contacts AND to be unbiased about reporting them. Some encounters in hospitals are more valued than others. Contacts with patients are valuable because patient care is the manifest purpose of a hospital and would thus be more likely to be reported than, say, standing next to another nurse at the bathroom sink or urinal for a minute.

What needs work

Radial graphs, to me, are difficult to read. The science of networks is still what I would call an emerging field in the sense that both the methodologies and the techniques for analyzing data are not yet fixed. New strategies are still being developed at a relatively rapid rate. I think there might be a better way to present the data than the above radial graph, but the radial graph is a huge step ahead of the messy network nests that used to dominate the presentations/analysis of network research.

Messy nest network visualization
Nest visualization technique. Even with the colors it’s hard to make sense of the cluster on the left.

Here’s where I am having a hard time making sense of the radial graph. First of all, I didn’t get the immediate impression that nurses were the network hubs holding this whole situation together. I had to click through each of the five graphics twice to ‘see’ the finding that nurses are more well-connected than others in the network. Even then, it would have been relatively easy to make a mistake and think that ward assistants were just about equally important (and maybe they are!) because the dots representing their total contacts are just as large and somewhat more tightly clustered than the dots representing the nurses total contacts. However, the size of the dots records only total contacts and it seems that ward assistants have a great deal of contacts with each other (perhaps they work in teams?), but relatively little contact with patients or physicians. But the lines representing that data are faint compared to the weight of the dots making that part of the data analysis seem secondary, which is not the case.

I don’t have a great solution to the radial graph visualization of networks situation. To me, it seems like it is a huge step beyond the messy nests that used to be the go-to for network visualization but not yet fully baked as the gold standard.


Matson, John. (November 2012) RFID tags track possible outbreak pathways in the hospital Scientific American.
Note: The official date on the above source is 15 November 2012 but since it is only 4 November 2012, I left the day out of the date field.

Graphic by Jan Willem Tulp; Source: “Close Encounters in a Pediatric Ward: Measuring Face-to-Face Proximity and Mixing Patterns with Wearable Sensors,” by Lorenzo Isella et al., in PLoS ONE, vol. 6, No. 2, article e17144; 2011