How I learned to stop worrying and love Bayes’ Theorem

My daughter is turning 1 this week (ahhh time just flies by!) and in honor of her birthday, I want to share my experience with non-invasive prenatal DNA testing (NIPT).

At my 9 week doctor’s appointment, my doctor brought up the option of genetic testing, specifically non-invasive prenatal DNA testing. As a geneticist doing bioinformatics, I thought how cool it is that we can test for chromosomal abnormalities from the blood of the mother. The idea is that there are fetal DNA floating around in the mother’s blood and so inferences about whether there is an excess of a particular chromosome can be made by examining the mother’s blood (It’s pretty technical and I don’t want to get into the details of how NIPT works here, but if anyone is interested, I’m happy to do a literature review on this). Typically, at the prenatal stage, abnormalities on chromosome 21 (if three copies of chromosome 21 are present, it’s Down’s syndrome), chromosome 18 (if three copies of chromosome 18 are present, it’s Edward’s syndrome), chromosome 13 (if three copies of chromosome 13 are present, it’s Patau’s syndrome), and the X chromosome (if the genetic sex of the fetus is female but there is only one X chromosome present, it’s monosomy X or Turner’s syndrome). NIPT is routinely done for mothers who are older than 35 because the risk of chromosomal abnormalities increases with maternal age and typically, insurance will cover the cost. However, I was 26 when I was pregnant with my daughter, so the doctor was asking my opinion on having the test done because I would also have to pay out-of-pocket. Since I’m a nerd (I did 23andme and also sequenced my dog’s DNA), I thought it would be so cool to do this test. Little did I prepare for the results of the test and how it affected my whole pregnancy.

Fast forward 2 weeks, I was at a FedEx store faxing my medical record to the doctor’s office at UCLA (I was in Boston for an internship for a few weeks during my first trimester) when I got a phone call from my doctor in Boston. This was the most difficult phone conversation I have ever had in my life. Over the phone, she told me that the NIPT test came back that my baby was high risk (40% chance) for Trisomy 13 (or Patau’s syndrome). My heart dropped. I called my husband (who was in Los Angeles) but no word could come out of my mouth as I was sobbing uncontrollably. I had no idea how I managed to get on the T and got back to my AirB&B in Central Square when all I wanted to do was to cry (yes, I’m an extremely emotional person, especially when it comes to my baby).

Undoubtedly, having somebody telling me that my baby is at high risk for having a genetic condition where the baby does not survive outside of the uterus and if it does, only for a few days with gross deformities is the hardest thing I have gone through. The next few days and weeks seemed to last forever. What I was going through was made even harder by the fact that my husband was on the other coast and that I was doing an internship and couldn’t tell anyone about what I’m going through
(however, I did tell my direct manager about the news because she was also pregnancy so could relate which I’m so grateful for).

Anyway, today’s post is to partly tell you about why I love Bayes’s theorem. Over the next couple of days, my husband and I (mainly my husband – I was too emotional to think critically) dig into the literature about NIPT and Trisomy 13. The biggest finding was that the number quoted on the result where they predicted that the fetus is having a 40% chance of having Trisomy 13 is based on a study with a totally different age group than I am, so the incidence rate they used to report my results is totally inaccurate. If you have taken a statistics/probability class, you have probably encountered a problem where you are asked to calculate the probability of having a disease if you are tested positive for the disease, which is a function of the incidence of the disease (how many people in the population have the disease), the true positive rate of the test, and the true negative rate of the test). I don’t want to go into the nitty gritty details of Bayes’s theorem, but you can find more details on the wikipedia page here:

As I mentioned before, the risk of chromosomal abnormalities increases drastically with age. So the incidence rate for a mother at 26 is very low. I have written an RShiny app to find out the probability of a true positive given a positive NIPT test here: You can define your own values of the true positive rate, true negative rate, and the incidence rate under the User-defined values tab. If not, I have compiled some pre-defined values from the literature under the Predefined values tab. For example, at my age of 26, given that the NIPT test is positive for Trisomy 13, there is actually only about 7% chance that it’s a true positive (that the fetus has Trisomy 13). However, this probability increases drastically with age. For a mother at 35, the probability is 15%. For a mother at 46, the probability increases to 60%. From these numbers, you can see that the probability of a positive test being true depends a lot on the incidence rate of the disease. Further, I noticed that the true positive rate and the true negative rate of the test reported by the testing company are typically better than what the literature reports, which is not surprising. While I used Taylor-Phillips et al. (2015) ( to record the true positive rate and the true negative rate for NIPT test, I hope to incorporate other values here from other sources. If you know what the true positive rate and the true negative rate for your test, please use the User-defined values on my Rshiny app.

As soon as I got back to Los Angeles after my internship, I went to have my 12-week ultrasound. Even thought Bayes’s theorem did make me feel better and that the test was probably just a false positive, the period from that phone call until my 12-week ultrasound seemed like an eternity. My doctor did a very thorough examination on the ultrasound for any deformities such as cleft palate, club feet, brain deformities, and holes in heart. Fortunately, she didn’t find any defect and everything looked perfect to her. However, she cautioned us that the fetus was still small at that point to say for certain and we would go back at 18 week for another anatomy scan. At the 18 week appointment, thankfully everything was perfect again. And just to put this first-time mom at ease, my doctor referred me to a heart doctor for an ultrasound of baby’s heart to see if there is any defect. Again, the heart doctor who told me that he has seen hundreds of Trisomy 13 cases, did not find anything to be concerned about with the fetus.

Now, I should stress that NIPT is a screening test and not a diagnosis one. In other words, my baby was not diagnosed with Trisomy 13 unless more diagnosis tests were done. One such diagnosis test is called amniocentesis where a small sample of the amniotic fluid is withdrawn for testing. While this procedure is considered generally safe, there is still a considerable risk for a miscarriage with this procedure. Plus, I’m terrified when it comes to needles, so much that I was too afraid to needles to get an epidural during labor (but that could be a story for another time). My husband and I calculated the pros and cons of getting an amniocentesis and decided against it.

Even though Bayes’s theorem suggests that the NIPT test was likely a false positive and with the perfect ultrasounds, the thoughts that my baby could have Trisomy 13 didn’t fully escape my mind until after she was born and I could see her and hold her in my arms. My story does have a happy ending, that the test turned out to be false positive and my baby is perfectly healthy and has hit every milestone (some even early): she can turn over at 4 months, sit without support at 5 months, and walk at 10 months. Here is my daughter at my thesis defense:

It’s hard to believe that a year and a half earlier I was told that she was high risk for Trisomy 13. For families that have actually gone through the experience of having a child with Trisomy 13, or any other diseases, I can’t even imagine what that must feel like. I remember searching for stories or blog posts online everyday to read about people having false positive experience with NIPT, so I hope that this blog post would be useful for someone who is in a similar situation as I was. I also hope that the Rshiny app I created would give you a little bit of insight about what the positive test actually means, given your age, incidence rate, and the accuracy of the test. Disclaimer: I’m by no mean a medical doctor (not that kind of doctor) or a genetic counselor so please always consult the professionals.


3 thoughts on “How I learned to stop worrying and love Bayes’ Theorem

  1. Can relate, my wife fell pregnant aged 38. The OBGYN picked up abnormalities at 16 weeks and we had an amnio. Results came back as Patau’s syndrome. We were heart broken and devastated after trying for many years to have a baby. Very experienced OBGYN said in 30 years of practicing he had never seen this occurrence.

    But 2 years later we were blessed with a healthy boy, now 10 years old and doing very well for himself.

    Age related risks associated with these abnormalities are significant. I was 53 with the 1st pregnancy and 55 with the 2nd one. We had an early amnio with the 2nd pregnancy. I understand the risks are very low if carried out by a competent practitioner so perhaps for people in their mid to late 30’s and certainly in the 40’s this should be considered.


    1. Thank you for sharing your story. I can’t even imagine how heartbroken you were to hear about the Patau’s syndrome news, especially after trying for many years. I am also happy to hear that your boy is healthy and doing well.


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