Wuhan Corona Virus Coming Soon? (Now Here)

[PaulW]

Let me explain, since it seems some people just don't get it.
If the prevalence is 3% then what you do is wherever you see the "x" you replace it with a "3".

0.95 * 3 + 0.05 * (100 - 3)

There's your math lesson for today. Yes, you can mix decimals with whole numbers, who knew?

[ironyak]

So if the disease prevalence (the thing you're trying to measure) is already ASSUMED to be 3% then the likelihood of a tested positive being a true positive by your formula is:
0.95 * 3 + 0.05 * (100 - 3)
= 2.85 + 4.85
= 7.7 (percent?)

Does that seem:
1) A reasonable answer? Your assumed disease prevalence is 3% and the test has a 5% error and yet you end up only 7.7% probability of your positive test result being a true positive?

2) A worthwhile test to run? As many initial antibody tests are in fact showing about 3% of people have already had covid currently, why would there be so much interest in performing such tests if those results have only a 7.7% probability of being accurate?

[Durian Fiend]

.95 X .03=.0285. That's probability that positive result is correct. Then subtract probability the negative result has accidentally been registered as a positive, which would be .05x.03.

.02835, or 2.835%

Edit again: Hmmm, this is not actually answering Tom's initial question, is it?

[kalakoa]

No math can make up for the lack of data.

[HereOnThePrimalEdge]

No math can make up for the lack of data.

No data, or disregard of available data can make up for lack of equipment, when it was needed.

[ironyak]

Hey - weather was too nice, so was out playing hookie. Has teacher Marilyn vos Savant returned yet? No? TomK is still subbing? Ok, cool, cool - cake walk then.

So check it, let's work together before he comes back. He'll never know, right? Yeah, just add this to that vast list of stuff he doesn't know and stuff he doesn't know he doesn't know - he'll be none the wiser...

So you've read your Baysian Conditional Probability, right? Well here's the thing - to actually get an answer you need to know or ASSUME the prevalence x, but we can just work up the algebra and leave those little details for someone else to figure out. How hard can it be to make a test to find the prevalence of a disease that already requires knowing the prevalence of the disease?

So in general, if you have a population tested of D then you know the Total True Positives is D*x (population * prevalence) and the rest of the population is D - D*x. So for the 95% positive test the Test Positives that are True Positives is 0.95(D*x) and the Test Positives that are True Negatives are 0.05(D-D*x).

In this case we're just testing one person so D = 1 which simplifies the equations nicely.

So the overall probability that a Test Positive result is actually a True Positive is the True Positives divided by the Total Test Positives (True Positives and True Negatives), which is 0.95x / (0.95x + 0.05 * (1-x))

Here, someone check my work before teach gets back, I'll keep a look out.
https://ibb.co/6tsPZXM

So then, for 3% ASSUMED prevalence the math is:
0.95*0.03 / (0.95*0.03 +0.05 * (1-0.03))
=0.0285 / (0.0285 + 0.0485)
=0.0285 / 0.077 (hmm that number looks familiar)
=0.37 or 37%

So when you have a test with 5% error, and an ASSUMED 3% disease prevalence, you only have a 37% probability that a positive test result is actually a true positive.

Give it a try with a 5% ASSUMED prevalence while I step back out behind the toolshed for some enlightenment (Marilyn showed the testing is a joke) and flip some more coins.

Oh hey, substitute teacher TomK... Do you like apples? Well I got your number! How do you like them apples?
https://youtu.be/gcZPWkNY6x8?t=75

(with points to Reverend Bayes for figuring this all out centuries ago and apologies to the genius that is Matt Damon)

ETA: snark and spit wads

[HereOnThePrimalEdge]

A third McDonalds restaurant in Kona has reported workers with COVID-19:

The DOH said the 30 confirmed cases are now tied to three McDonald’s restaurants — one at the Kona Commons, another inside a Walmart, and the McDonald’s at 75-5729 Kuakini Hwy.

Officials say this cluster is likely a result of an employee who continued to work despite being sick.
“This so clearly demonstrates how important it is to follow the health advisories of the Department of Health of stay at home if you are sick, sneezing and coughing etiquette, physical distancing, social gatherings and staying healthy. We owe it to our family and the community to do our share. This is a community issue and needs all to do their part,” Kim said in a radio update Saturday.

“The lesson for all of us to learn in this is from very low numbers, you can see how very easily, just one person - just one person - began this chain reaction of families and fellow employees,” Kim added. He said testing in Kona will continue.

https://www.hawaiinewsnow.com/2020/04/18...-infected/

[kander]

n may be as high as 80%
Antibody tests seem to be more important of testing factor.
http://archive.is/9aDP8

[PaulW]

Whoa, you're right, forgot the numerator:

0.95 * x /
(0.95 * x + 0.05 * (100 - x))

Sorry for the mistake!

Yes, so a 37% chance it's a true positive while at first glance one would think it's 95%. Quite the paradox.

[kalakoa]

https://www.sfgate.com/news/article/Anti...211475.php

In Laredo, officials discovered the tests they received were woefully inadequate. The local health department found them to have a reliability of about 20%, far from the 93% to 97% the company had claimed. A police investigation led to a federal seizure of the tests.

For example, Britain recently said the millions of rapid tests it had ordered from China were not sensitive enough to detect antibodies except in people who were severely ill. In Spain, the testing push turned into a fiasco last month after the initial batch of kits it received had an accuracy of 30% rather than the advertised 80%. In Italy, local officials have begun testing even before national authorities have validated the tests.