Diagnosed with Celiac, but I doubt my diagnosis. The statistics (Bayes theorem) leave a lot of room for doubt.

[DevJac]

My gastroenterologist said I have celiac, but a biopsy came back negative and I don't have the most common symptoms (heartburn is my only symptom). I'm going to follow a gluten-free diet for a year or more and see what happens. I am currently following a gluten free diet as best I can (still new to this), and will not go against my doctors advice without talking to them first, and neither should anyone else.

That said, I'm skeptical and hopeful that I might not actually have celiac disease based on some statistics I've done.

In statistics we write P(A|B) and read it as "the probability of A given B". For example, P(wet ground | it's raining) = 1.00, "the probability that the ground is wet given that it's raining is 100%."

It important to note that P(A|B) does not equal P(B|A). The P(it's raining | wet ground) is not 100%; "the probability that it's raining given that the ground is wet is not 100%".

There's a very important formula in statistics called Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / (P(B|A) * P(A) + P(B|not A) * P(not A)) where * means multiplication.

Here's the number as best I can gather:

P(celiac | positive test) = See below, this is what I'm trying to answer.

P(positive test | celiac) = This is the "sensitivity" [1] of the test, how likely the test is to show positive if a person actually has celiac. It's 92.6% sensitive.

P(no positive test | not celiac) = This is the "specificity" [1], how likely the test is to show negative is a person does not have celiac. It's 97.6% specific.

P(positive test | not celiac) = 1 - P(no positive test | not celiac) = 1 - 0.976 = 0.024

P(celiac) = Probability a random person has celiac. It's about 1%.

P(not celiac) = 1 - P(celiac) = 1 - 0.01 = 0.99

Plug and chug:

P(celiac | positive test) = (P(positive test | celiac) * P(celiac)) / (P(positive test | celiac) * P(celiac) + P(positive test | not celiac) * P(not celiac))

(0.926 * 0.01) / (0.926 * 0.01 + 0.024 * 0.99) = 0.28

If these numbers are right, there's a 28% chance I have celiac disease.

I think the important intuition here is we see the test is right ~95% of the time, and then think there's a 95% chance we have the disease if the test comes back positive. But the truth is the ~5% chance the test might be wrong is a lot bigger than the ~1% chance a random person has celiac disease. Of course, if a person has classic celiac symptoms, and a scope has shown they have villi damage, etc, that is not a random person and they are more likely to have celiac than the entire population on average. That's not me though, my scope / biopsy was negative, I don't have classic celiac symptoms, only heart burn (which is very common).

Another problem is, who knows if these numbers are right? Do 1% of people have celiac? I don't think we know for sure, but that's what I read. How accurate are the tests? We don't know exactly, but, given the numbers, as best I can research them, I don't consider it a conclusive case that I have celiac disease. But, again, I'll stay on the GFD, and maybe in time I'll come to believe otherwise.

Or maybe this is just my denial phase of acceptance.

 

[1] Here's the study with the sensitivity and specificity.

[RMJ]

A lot of people are in denial when they get a diagnosis.

You’re calculating positive predictive value for one test.  You had two positive antibody tests, and two equivocal antibody tests.  I don’t know how to put that into a calculation, but I’d think it would up the chances of your having celiac disease.

[Scott Adams]

Even one positive blood test is enough to mean that you likely do have celiac disease, but with two, the odds are very high indeed.  I believe it is a good idea to go gluten-free, and you should also consider asking your first degree relatives to also get tested. Have you considered genetic testing to see if you carry any of the known celiac genetic markers? 

You could also have non-celiac gluten sensitivity, which is possibly 10x more common than celiac disease, but there is no test yet for it. The treatment is the same, a gluten-free diet.

[DevJac]

34 minutes ago, RMJ said:

A lot of people are in denial when they get a diagnosis.

You’re calculating positive predictive value for one test.  You had two positive antibody tests, and two equivocal antibody tests.  I don’t know how to put that into a calculation, but I’d think it would up the chances of your having celiac disease.

You mean the GLIADIN DP IGA test and the TTG IGA test are completely separate test? I thought they were just two ways of measuring the same thing?

You're probably right that my numbers only account for one of the tests.

[RMJ]

The Gliadin DP IgA test measures IgA antibodies against deamidated gliadin peptides. The peptides are derived from the gliadin portion of gluten.

The Gliadin DP IgG tests measures IgG antibodies, a different class of antibody, against the same peptides.

The TTG IgA test measures IgA antibodies against tissue transglutaminase.  This is the autoimmune part of celiac disease, because tissue transglutaminase is a normal protein in the human body.  The TTG IgG test… well you probably get the idea

Tests for four different types of antibodies.  From your previous post, positive in two (the IgAs) and equivocal in two (the IgGs).

 

[Wheatwacked]

300 Signs and Symptoms of Celiac Disease

Go over this list and see if it changes your calculations. Certain vitamin and mineral deficiencies can also be indicative. celiac disease is a disease of malabsorption.