# Misdiagnosis quantification

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Cryo
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04 Sep 2016, 8:13 am

I've seen a few discussions on mis- and overdiagnosis of ASD recently. Thought it would be interesting to try quantifying it.

Let the true rate of ASD be A. Of those with ASD, Sa seek diagnosis and of those Da are correctly diagnosed as having ASD. The true rate of NTism (everyone not autistic, not necessarily normal) is 1-A. Of those Sn seek diagnosis and Dn are appropriately not diagnosed with ASD. All parameters represent fractions and are in the range 0-1 inclusive.

The ratio (R) of misdiagnosed NTs to true autistics is the rate of NTs seeking diagnosis (Sn) times the rate they get misdiagnosed as autistic (1-Dn) times the population ratio of NTs to autistics ((1-A)/A).

R = Sn(1-Dn) x (1-A)/A

Sn and (1-Dn) will be small and R will correspondingly be small, but the inverse relationship of R to A means that the smaller A is the larger R is. Because of this I think R in the real world might be larger than most people suspect.

I can only guess at real world values for the parameters. The latest reported autism rate is 1/68, so say 2/68 NTs seek professional help for something similar to autism: Sn=0.029. Psychology isn't an exact science, so say (for the 2.9% of NTs that have something autism-like) the pros get it right 95% of the time: (1-Dn)=0.05. Say the true rate of autism is 1%: A=0.01. Using these numbers,

R = 0.029 x 0.05 x (1-0.01)/0.01 = 0.144

That's roughly 1 NT misdiagnosed as autistic for every 6 true autistics.

I think I've been fair and conservative with my numbers. Real world factors incentivise NTs seeking diagnosis, eg. parents with difficult or genuinely ill but not autistic children might push for a diagnosis either because they believe it or to get access to support services, college-going NTs might fake autism to get extra exam time. Professional psychologists do make mistakes and are likely to with those at the milder end of the spectrum that can pass for normal, stories of misdiagnosis (confusion between ASD, anxiety, OCD...) are relatively common.

Now including self-diagnosing NTs (which will be more common than those that seek professional evaluation and have more diagnostic mistakes) and excluding undiagnosed true autistics, the ratio becomes even larger.

R = (Sn(1-Dn) + Sn_self(1-Dn_self)) x (1-A) / (A x (Sa x Da + Sa_self x Da_self))

Say NT self-diagnosis is twice as common and twice as inaccurate as professional diagnosis (Sn_self = 0.058, 1-Dn_self=0.1). Say most autistics seek (Sa=0.8 ) and get (Da=0.95) professional diagnosis, and of the remainder some self-diagnose with the same accuracy as NTs (Sa_self=0.1, Da_self=0.9).

R = (0.029 x 0.05 + 0.058 x 0.1) x (1-0.01) / (0.01 x (0.8 x 0.95 + 0.1 x 0.9))
R = 0.844

Using these numbers someone reporting a (pro or self) diagnosis of ASD is only slightly more likely to really have ASD (54%) than not (46%). Roughly 8 misdiagnosed NTs for every 10 diagnosed autistics.

Again I think I've been fair with the numbers. If NTs attempt self-diagnosis at rate 0.058 and only get it wrong 10% of the time, only 5.8 out of 1000 NTs will claim to be self-diagnosed with ASD. Only 1.4 out of 1000 NTs will be professionally misdiagnosed. So I'm not suggesting there's a plague of misdiagnosed NTs, just that the number of misdiagnosed NTs is (by my estimate) a significant fraction of the number of autistics, particularly if you count the self-diagnosed.

It'd be interesting if the ratio really is as high as I think it is. Have I wildly over or underestimated anything or made some terrible algebraic error? Are there other factors I should consider in my calculations? How common is misdiagnosis really?

foxfield
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04 Sep 2016, 9:23 am

Wow thanks for the interesting analysis, it made me think a lot! (I tried to find a mistake in your logic but I coulddn't )

One aspect that I wanted to think about more was a notion that some of number of "true autistics" may be unquestionably autistic, i.e. for a certain subset of the autistic population the rates of misdiagnosis and self-diagnosis are effectively zero, because the fact that those people have autism is just clear cut and obvious.

I wanted to experiment and plug some numbers to see how this changes things but I don't have time right now.... Cool post though.

Uncle
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04 Sep 2016, 9:38 am

How about those that have not self diagnosed, but psychologists and behavioral therapists have highly suspected as been on the spectrum without the written formal diagnosis of that of a psychiatrist? There certainly is a percentage of those too

Cryo
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04 Sep 2016, 10:05 am

foxfield wrote:
some of number of "true autistics" may be unquestionably autistic, i.e. for a certain subset of the autistic population the rates of misdiagnosis and self-diagnosis are effectively zero

This isn't too hard to factor in. Give subgroups their own frequencies and misdiagnosis rates - of all autistics, C are classic, H are high functioning... associated seek/correct diagnosis rates Sc, Sh, Dc, Dh... The numbers I've used would represent the overall average. If my number was 95% accuracy you can assume the 5% error would mostly be contributed by the high functioning subgroups.

Uncle wrote:
How about those that have not self diagnosed, but psychologists and behavioral therapists have highly suspected as been on the spectrum without the written formal diagnosis of that of a psychiatrist?

I guess I'm counting them as undiagnosed. But like above it's not hard to factor in (though it does make the equations messy). Some fraction have been to a psychologist/therapist who offers a preliminary diagnosis with whatever error rate, some other fraction have been to a psychiatrist and have gotten a formal diagnosis with a different error rate.

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04 Sep 2016, 10:14 am

Cryo wrote:
I can only guess at real world values for the parameters.

Right.
Cryo wrote:
I think I've been fair and conservative with my numbers. Real world factors incentivise NTs seeking diagnosis, eg. parents with difficult or genuinely ill but not autistic children might push for a diagnosis either because they believe it or to get access to support services, college-going NTs might fake autism to get extra exam time.

I don't think this speculation is consistent with the world that I have observed.

It may be that there are a tiny number of people who have such motives, but I suspect they are statistically insignificant in these calculations. Like you, I can only guess, but only here have I have heard that autism is supposed to be cool, or it's a help in getting access to services or extra exam time. Every place but here and GRASP that I have ever heard autism discussed, it has carried a huge stigma.

It's a thing almost nobody wants to have and almost nobody wants their child to carry the stigmatizing label. I suspect that people who have the kinds of motivation you describe are mentally ill in some unusual way.

Cryo wrote:
Again I think I've been fair with the numbers.

I don't think fairness has anything to do with it. You don't have data and these numbers are made up.

Cryo wrote:
How common is misdiagnosis really?

One day we may have real tests that can conclusively reveal this data. In the meantime, this is nothing more than speculation.

Why is this of interest to you? What purpose do you have for seeking this information and asserting your guesses about it?

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Uncle
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04 Sep 2016, 10:19 am

yup, there are a number of variables, including those misdiagnosed schizophrenia etc as would be seen in the reverse. Would be a hard one to prove what percentage would be to each, These are just a couple of extra variables not including those that haven't been aired.... I like your approach but at present with so many extra variables the present conclusion would be somewhat negligible... I could be totally wrong, just my not so great input! lol

ASPartOfMe
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04 Sep 2016, 10:59 am

That is an interesting brain exercise. Brain exercise is arguably more important then physical exercise. It is also good that you recognize the "data" going in is guesswork. I am afraid until there is basic agreement as to what autism is the accusations, suspicions of "you are not autistic" will continue.

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goatfish57
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04 Sep 2016, 11:03 am

Just sticking to the math, a false positive is a conditional probability. I think you are missing a multiplication.

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Cryo
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04 Sep 2016, 11:34 am

tiny number of people who have such motives, but I suspect they are statistically insignificant in these calculations

Aside from the misdiagnosis estimate, part of what makes this interesting is the perhaps counterintuitive effect on the numbers that seemingly statistically insignificant groups have, eg. 5/1000 NTs self-misdiagnosing doesn't sound like a lot, but it turns out to be comparable to the number of true autistics.

What purpose do you have for seeking this information and asserting your guesses about it?

Numbers are fun, this was on my mind, wanted to work it out.

Sure it's all speculative. I think my estimates are decent. They can be revised and improved once data becomes available.

ASPartOfMe wrote:
suspicions of "you are not autistic" will continue.

Getting some data would help either validating or invalidating such suspicions. As is I think my guesses are reasonable so there's some ground for suspicion. Even if the diagnostic process is relatively accurate the disparity between NT and autistic population sizes makes (by my estimate) false positives in NTs about as common as true autistics. A few percent difference in tested population and test accuracy turns out to be potentially a pretty big deal.

goatfish57 wrote:
Just sticking to the math, a false positive is a conditional probability. I think you are missing a multiplication.

If I am I'll fix it. Where at?

False positives are NTs seeking and getting diagnosed: (1-A) x Sn x (1-Dn). I think the conditional (not autistic) for false positive is already incorporated - becomes the (1-A)/A ratio if that's what you mean. I just wrote it out of order.

goatfish57
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04 Sep 2016, 12:35 pm

Let me try again.

The total number of people with autism in the USA is roughly 350 million times 1/68.

I think that large number dwarfs the total number of Americans self diagnosing incorrectly.

Now, I will make up some numbers as well.

Let us say that 1 in 10 Americans take an autism self test, 1 in 10 Americans who take the self test get a positive diagnosis and 1 in 10 American who self test positive are not autistic.

That would mean 350 millions * 1/10 * 1/10 *1/10 equals 350,000 posers versus 5 million austies

The only real numbers here are 350 million and 1/68.

You seem to enjoy math and statistics. Maybe you take some advanced courses

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Last edited by goatfish57 on 04 Sep 2016, 1:33 pm, edited 2 times in total.

League_Girl
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04 Sep 2016, 12:46 pm

Speaking of misdiagnoses, I wonder what are the numbers of people who are intentionally diagnosed as having it but they really don't quite have it? It could be because the doctor didn't know what is wrong with them so that was the best they could do for a diagnoses or because they needed the same services as autistic people so they are given that label or because they do have symptoms but the amount of support they needed is of someone with autism.

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DevilKisses
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