# “The Pregnant Mathematician” Drinks Glucola

Glucose Challenge Screen for Gestational Diabetes
As I posted about a few days ago, this week I had a one-hour glucose challenge test to screen for Gestational Diabetes (GDM). Today I received a phone call from my OB’s office informing me that my results were back and they were within the “normal” levels. Getting a negative result is comforting, but then I went back to hunting for statistical data on what this result really means.

According to an article I found in Obstetrics & Gynaecology, a 1994 study (“Poor sensitivity of the fifty-gram one-hour glucose screening test for hyperglycemia“) by van Turnhout HELotgering FKWallenburg HC reported the sensitivity and specificity of the 1-hour glucose challenge test were 27% and 89%, respectively, with a prevalence rate of 5%.

In statistics, sensitivity and specificity are markers of how good of a test you’re considering. The sensitivity of a test tells you, “Out of all the people who have the condition, what percent of them will test positive?” Similarly, the specificity of a test tells you, “Out of all the people who don’t have the condition, what percent of them will test negative?”

If a test were perfect, we would expect both of these to be 100%. This would mean that 100% of people who have the condition really test positive, and 100% of the people who don’t have the condition really test negative. Of course, in the real world, this never really happens.

What Can I Conclude?
Another way we can gauge the performance of a test is to find its positive predictive value and its negative predictive value. I’m going to assume the sensitivity and specificity in the study cited above are correct. The same study above also gives a positive predictive value of 11% and a negative predictive value of 96%, but what do these numbers mean?

Let’s assume we give the same 1-hour glucose challenge test to 10,000 pregnant women. With a prevalence rate of 5%, we would expect 500 women to have GDM and 9500 not to have GDM. Of the 500 with GDM, since the sensitivity is 27%, we know 27% of 500 would screen positive, for a total of 135 women. These are women who have GDM and whose screening will come back positive. Meanwhile, of the 9500 women without GDM, since the specificity is 89%, we would expect 89% of 9500 or 8455 women to have a true negative result. The status of all of our 10,000 participants is displayed in the table below:

Women with GDM Women without GDM Women who test positive 135 1045 365 8455 Total 500 9500

According to this table, a total of 135+1045=1180 women would test positive. Of the women who get a positive result, only 135 of them really have GDM; this is the positive predictive value and, in this case, it’s 135/1180 = 11.44%.

What about the women who, like me, get a negative result? There are 8820 of us, and 8455 of us don’t have GDM. This gives a negative predictive value of 8455/8820 = 95.86%.

My results were negative, so I am one of the women with a negative result. The values above tell me that since I got a negative result on my glucose screening, I can assume there’s about a 96% chance I don’t have GDM. I’m waiting to be billed for this screening, but I’ll go with my initial \$40 estimate. Even after this analysis, I’m still wondering if the knowledge I gained was worth the \$40 I paid for it. (“Everything is worth what its purchaser will pay for it,” so I suppose this must be too.)

I feel unqualified to answer the “Worth it?” question because I don’t know a way to quantify the importance of this test. It seems clear that if a condition is really, really awful, then finding out you’ve got it is probably worth \$40, and so is finding out you’re home free.

Is GDM really, really awful? It certainly has the potential to affect both my health and the health of my unborn child, so it seems better to know about it than not. But there are lots and lots of things that could affect our health that I don’t know about, and won’t be screened for, and probably won’t ever hear about.

One thing I wish I did have, for this screening and all of the others I have been (or will be) offered, is data ahead of time. I want to know the false positive and false negative rates. I want to know the sensitivity and the specificity and the predictive values. And I want to know how much money it’s going to cost me, and how much of a hassle it’s going to be. Lastly, I would like to know more about the medical significance of the condition, and since I’m not a medical doctor, I need it in some kind of quantifiable metric for when I do these kinds of calculations.

## 19 thoughts on ““The Pregnant Mathematician” Drinks Glucola”

1. I’m really enjoying this series, and I hope you’ll keep doing it! I do not anticipate being a pregnant mathematician anytime in the near future, but I plan on sharing your posts with pregnant friends.

• Thanks, Evelyn! These statistical issues bugged me the first time I was pregnant, so I’m trying to use the second time around as a chance to ponder them more thoroughly!

2. Don’t read this comment if you want to feel like the test was worth it, but I just realized that before you took the test, you could assume you had a 95% chance of not having GDM, and now you can assume you have a 95.86% chance of not having GDM. I hope they have improved the test since 1994.

• Yes, I did that same comparison, too. I wonder, though, what my chance really was (pre-screening) and what it really is now (post-screening), given that I’m in a low-risk category: No family history of GDM, low BMI, etc. I’d assume that my pre-screening risk was below 5%, and then the fact I got a negative result means my risk is really below 5%*n%, but I don’t know what n would be. So maybe it was m%, and now it’s m%*n%, but again — the lack of specific statistical info on the values of m and n is my major complaint about all these things!

Postscript: I suppose I should be more careful. Obviously, my risk now is the same as my risk before, and I don’t know what either really is. What I mean to say is about a betting game. If I had to bet \$100 on my risk for GDM before I had the screening, I would have chosen 5%, since that’s what I’m taking to be the overall incidence rate in the population. Now that my screening has come back negative, I would now bet my \$100 that my risk is really something below 5%, maybe 100-95.86%=4.14%. This would be a good starting place for my wagers. So what I said above is that my original \$100 bet would have been m% (which I don’t know), and now it’d be m%*n% (which I don’t know).

3. Let’s define a “placebo test” as one for which the odds of your having the condition given you have a negative test result are equal to the odds of your having the condition given you haven’t taken the test (or, at any rate, given you don’t know whether you’ve tested positive or negative). I think what Evelyn is saying is that the GDM test you took is very close to a placebo test. Why “placebo”? Because a random test (say, based on your horoscope) would yield as much information — but your having taken the test gives you some peace of mind. Question is, how close does a real test have to come to an actual Placebo Test before it is totally useless? I suggest the answer is inversely related to the seriousness of the condition being tested for — a medical answer being required, rather than “just” a mathematical one.

4. Greetings from a fellow pregnant mathematician!

Thanks for posting on flawed statistics during pregnancy exams. Unfortunately, it doesn’t improve after birth. My previous experience was that they would measure the baby’s growth and get obsessed about it as well… even when the baby is measuring in the highly error percentile zone of the curve (too big or too small).

• Interesting point. Do you have data about the error rates versus percentile measurements based on child’s measurements? Our 2.5-year-old has measured in the 95th-99th percentile for all measurements since birth (weight, head circumference, height) and now you’ve got me wondering what these values really mean!

A friend of mine has twins (one girl, one boy) who are about 3 now. She told me that her pediatrician said the boy twin is so tall, “he’s above the 100th percentile.” What does that even mean?!

• I don’t have data but I also have a boy who used to be above the 100 percentile during his first year of life! The pediatrician was very happy with this. On the other hand, I’ve heard of perfectly normal babies following curves under 10 percentile and the pediatricians were unhappy and did a lot of tests only to conclude that the kids were normal. Extreme percentiles must have a lot of error…

5. This is fascinating stuff, and something I’ve wondered about for 23 years. My children are 20 & 22 years old, and back then maternal serum alpha fetoprotein was used as a screening test for neural tube defects. Mine was elevated in both pregnancies, and since I was an elderly pregnancy/advanced maternal age, I followed my OB’s practice of following up with amniocentesis. The amnio. results were normal, but I’ve wondered about predictive value ever since then because I didn’t have data ahead of time, was making decisions based more on emotion than data, and the amnios. were a huge hassle and >\$1500/each. My degree is in medical technology and I have over 25 years experience working in clinical labs., but my knowledge of false positives/negatives went out the window when I was making decisions about my children with too little data.

For many laboratory tests, the lab performing your test should be able to provide some data about sensitivity, specificity, and false negatives/positives (most likely from the manufacturer of the reagents/instrumentation), but that data may or may not be useful. For some laboratory tests, the reported false positive rate range can be 5-80%. They definitely should be able to tell you how much of a hassle (time, pain, risk of fetal/maternal complications) the tests will be, but it may also be a hassle obtaining the information. As for cost, that is something your insurance company should be able to tell you, but again, it may be quite a hassle getting the information. For medical significance, your doctor should be providing you with that information, but many physicians don’t have enough time to provide complete information ahead of time. Even if patients have good reasons to not have a test performed, their drs. (especially OBs) and insurance companies may be concerned enough about medico-legal issues that the patients are forced to sign waivers to not have the test performed.

My apologies for the far-too-long comment, but your approach is very interesting, reasonable, and worthy of further consideration. I hope you continue your mathematical/gestational ponderings; I would really enjoy reading more.

• I like far-too-long comments 🙂 No apology necessary. Got any ideas about future topics for gestational posts? I would love to hear them.

Re: Sensitivity/Specificity data
You bring up a good point — the lab probably does have these numbers. Unfortunately, I’m not sure exactly who I would ask. For my glucose screen, the blood draw was done by one of the nurses at my OB office, and then the blood was sent out to the lab. Once the results were returned (probably electronically), I was phoned by another nurse who told me the results. I could probably track down exactly where my blood went & get the information from the lab itself, but I honestly don’t know how long it would take to get said information. Example: I go to my OB office visit, they suggest a blood test this week for whatever; how long will it take me to track down the lab and have a quick phone conversation with someone at the lab who has access to this information? It seems that on some of these tests, you have to have it “between week X and week X+2” and I could foresee that it would take me more than 2 weeks to discover these answers…

I was also concerned about the high cost & high risk of the amnio, having crunched the conditional probabilities on that, too. My OB told me that there is a new test, called “MaterniT21 PLUS LDT” that is non-invasive: Fetal DNA is isolated via the mother’s bloodstream; i.e., a maternal blood draw gives access to fetal chromosomes, and thus relatively certain knowledge about all the Trisomy conditions. See http://www.non-invasivetesting.com/ about the test. Right now, I believe the test itself is in the \$2500 range. Insurance companies only cover it if a mother is in the “high risk” category for a Trisomy disorder. This includes: having a family history of Down Syndrome; having a previous child with a Trisomy disorder; being over age 35; etc. Since I am currently 32 and didn’t want to fork over \$2k, I didn’t have this test. But it seems likely that (a) the cost of the test will decline over the next several years and (b) I could be 35 during my next pregnancy.

I do wish I knew more about the “medico-legal issues” you mention above and how much they really are contributing to my care (unbeknownst to me).

6. I just had my glucose test and was wondering many of the same things. The OB-GYN practice I use no longer uses the glucose challenge. The midwife said they get too many false positives. Instead, we all get to do the glucose tolerance test. That’s the 3-hour version where you fast from midnight the night before, and have to sit in the doctor’s office while watch you drink the horrible-glucose-drink, and take blood several times over 3 hours. As someone who did fine with the glucose challenge the first time, I wasn’t so happy about this more annoying and time-consuming test. I did manage to do a bit of refereeing during the first hour, but by the second I was tired, hungry and a bit cranky, so refrained from taking it out on some poor authors.

The glucose tolerance test is supposed to have better predictive value, but that’s the most I got out of the midwife. I presume it’s much more expensive. I should do the analysis you have done for this one, but I had really better finish that referee report!

• After eventually getting my EOB from my insurance company, they paid \$21 for my glucose screen; since I have now met my deductible for the year, my test was “free.”

The 3-hour version does not sound fun. There was a 1999 study about using jelly beans (instead of the awful glucola!) to do the 1-hour screen; see http://www.ncbi.nlm.nih.gov/pubmed/10561636 for information. That sounds more delicious.

Having a “high predictive value” is good, especially from my OB’s perspective. Being relatively inexpensive is good, especially from my insurance company’s perspective. Meanwhile, having to sit for three hours in the waiting room is a major inconvenience only to *me*. Somehow, doesn’t the value of my time have to weigh in the “Is it worth it?” question? First, I bet my calculus students would rather have my help for three hours than to know I’m sitting around reading the Nov 2012 issue of “People” magazine. Second, since I’m trying to save all of my sick leave to have paid time during FMLA, if I need three or four hours away from work this week, it means three or four hours I won’t get paid while recovering post-delivery.

I earn 9.38 hours of sick leave per month for 9-months per year. So to take about four hours off from work to have the 3-hr glucose test is about 3.6% of my annual amount of sick leave. Is the glucose test sufficiently important and necessary to justify this? In other words, if I have to work for two full weeks in order to accrue enough sick leave to take the time off work to have the 3-hour glucola test, is it really worth it?

7. Thank you for doing the math for us. The percentages and verbiage mean nothing to me, but when I see your numbers, I have hope that my 1-hour test was a false positive. I’ve never failed a 1-hour screen before, and this is my fourth go-round. I’ve decided to do the 3-hour test, because I truly want to know if I had GDM. I’m praying I do not, but either way, I need to know! Thank you again for your insight!

• Thanks for your comment, Jen! I hope that your 3-hour screen goes well. GDM is pretty rare (way more rare than the false positive rate!) so take comfort in that 🙂 And, on the flip side, one of the effects of GDM is large babies. Both my babies were big (8lb 12oz & 9lb 1oz, both at 39-weeks) and I didn’t get a GDM diagnosis either time! Wishing you a really healthy pregnancy & positive delivery experience.

8. Thank you so much for this post. I recently read EXPECTING BETTER and really appreciate the pespective that staticians, economists, and mathematicians can bring to this topic.

My doctor recently recommended the ogtt 2-hour test, and i guess that this is becoming the new gold standard (did the one hour with my first). The ADA and WHO have different recommendations for results. WHO is more stringent. I am having trouble reading the science on this, but it appears the The false neg rate for this test apprears to be higher (3%?) but the false neg still seems astronomical to me (20%?). But it is really hard to get numbers on this. (Try googling “gestational diabetes test” and “false positive” and you will see what i mean. “Ogtt” and “specificity” does a little better). But i also want to know the false positives given various risk factors. For example, it seems to me that the false positive rate for those with risk factors related to obesity and family history would be lower than for those who, say, only have age (>35) going against them. Most doctors say that there is less harm in treating all those that test positive than in not catching, but as a patient, i have to disagree. Treatment is burdensome, and i think treatment and further testing may extend to both mother AND baby after birth. In fact, it appears that the label GDM could follow you and your child, affecting testing and treatment decisions, for the rest of your life?

• I meant to say that the false positive (not neg) rate may be as high as 20%…

• Yes, I agree, it is definitely difficult to track down these numbers! This was one of the frustrations I had when I was writing my initial “Pregnant Mathematician” posts.

What I took from the GDM testing was the following (your mileage may vary): The false positive rate is quite high. This tells me that getting a positive test result doesn’t necessarily mean I have GDM; instead, getting a positive test result means I need to re-do the test. Because as you point out, if I get a positive, there’s a ~20% chance it’s false. But if I get two positives in a row, the chance they’re BOTH a false positive is (0.20)*(0.20)=0.04=4%. And if I get three positives in a row, then the chance they’re all just false positives is 0.008=0.8% < 1%. So, three positives all of the sudden means we're more than 99% sure I really have GDM. So, in all of these prenatal testing situations, I took any "positive" result to mean "get tested again."

9. Is \$40 worth it for a negative screening test? I look at it differently. If the screening test is positive and I turn out to have GDM, \$40 is a small price to pay for the health of the mother and the precious baby. If the patient knows the consequences of unrecognized GDM, then she will know the cost far outweighs the untoward outcomes. Not to mention the long term health of the patient since we know patients with GDM have an increased risk of DM later on in life and it is potentially preventable if the GDM patient can change her lifestyle for the better.