Fun with Numbers

How to make sense of COVID-19 case & test numbers -- Sensitivity and Specificity

TL;DR: The "accuracy" of a test is NOT just determined by its "Sensitivity". The "Specificity" of the test also determines its accuracy.

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This is something to consider about the daily testing numbers, case numbers etc. 

Here's an example of how to make sense of these numbers. Apply this logic to the current covid scenario and make your own decision. 

Consider this scenario:

You are the head of the tribunal security team.

We are dealing with a baggage scanner used in court/tribunal at the entrance.

The scanner has a sensitivity of 99% and a specificity of 98%. It is known that 99.5% of people attending courts & tribunals do not carry any weapon.

Someone gets flagged by the scanner at the entrance of the tribunal.

Should you, as the head of the security team, rush to intervene, or let your staff deal with it? 

To make this decision, you need to answer the question: What is the likelihood that a person alerted by the scanner is actually carrying a "weapon"? 

Solution:

Sensitivity = 99% 

99% is the probability that the scanner correctly alerts (returns positive) when someone is carrying is a weapon. 

This means that, 1% (that is, 1 in 100 times) is the probability that the scanner fails to detect someone who is carrying a weapon. That is, it fails to alert (returns a negative) when the person is actually carrying a weapon.

Therefore, False Negative = 1%

Specificity = 98%

98% is the probability that the scanner correctly does not alert (returns a negative) when someone is not carrying a weapon. 

This means that, 2% (that is, 2 in 100) is the probability that the scanner falsely alerts (returns a positive) for a person who is not really carrying any weapon. 

Therefore, False positive = 2%

99.5% of the time, people do NOT carry any weapon to courts & tribunals.

So the probability of someone carrying a weapon is 0.5% , that is, 1 in 200.

Let B denote the event that someone carries a weapon.

P(B) = 0.5% = 0.005

P(B') = 0.995 

Let A denote the event that the scanner alerts (returns a positive).

P(A/B) = 99% = 0.99

P(A/B') = 2% = 0.02

We need to find the probability that someone is actually carrying a weapon when the scanner alerts.

P(B/A) =         P(A/B) * P(B)

                —————————

                             P(A)

P(A) = P(A∩B) + P(A∩B') = { P(A/B) * P(B) } + { P(A/B') * P(B') }

Therefore,

P(B/A) =

               P(A/B) * P(B)

———————————————

  { P(A/B) * P(B) } + { P(A/B') * P(B') }

=               0.99 * 0.005

 ———————————————

  {0.99 * 0.005} + { 0.02 * 0.995}

= 19.9195 %

There's only a ~20% chance that someone who is flagged by the scanner is actually carrying a weapon. You, as the head of the security, need not rush each time the scanner flags a person at the entrance of the tribunal.

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Now, apply this to the daily "tests" & "cases" about which you have been hearing for the past ~2 years.

The Australian Government continues to claim that, for the purpose of diagnosing the rona disease, the RTPCR is THE GOLD STANDARD because it has "high accuracy".  (Archived at the time of posting here).

They keep forgetting that the "accuracy" of a test is NOT just determined by the "Sensitivity". The "Specificity" of the test also determines its accuracy.

Remember that the Australian Government declares someone as a "covid case" even when their sample is marked as positive by RTPCR only at a Cycle Threshold of 35-45.

This is despite the fact that, at Ct value of 25, up to 70% of positive results are true positives. At Ct value of 35, this drops to less than 3%.

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P.S.: The example scenario described above is based on a true story. Victorian Tribunal VCAT security lost their sh*t when the scanner went nuts on me. 

The security was convinced that I was a dangerous person capable of carrying a weapon.

Picture this:

A puny disabled girl, who could barely stay awake, let alone walk, rejected hush money & instead spoke up & represented herself at the Human Rights Division of VCAT. She was all alone against a notoriously cruel, intimidating & biased Tribunal Member and a team of big bloke barrister & lawyer thugs who were hired by Swinburne University in their effort to cover up the relentless Disability Abuse & Harassment of this female student by the University’s Professors & Pro Vice Chancellor .

VCAT security, who knew my case number and case division, thought I was a dangerous person. 

All I had was a specs tightener (my glasses were broken & held together by a piece of metal from my ear ring).  It came off often & so I carried the tightener with me. I am literally blind without my glasses. 

The security asked me to do whatever tightening I needed to do right then & there & leave the "weapon" with them. I was faced with a situation where I had to fix my glasses *without* my glasses. I stood there in the dark wearing my prescription sunglasses, clumsily trying to tighten my regular glasses. 

They just watched on. I was late to the hearing. 

Oh, my name & personal details are now on their dangerous persons list. 

Victoria, The Place to Be, eh?

—The Solitary Reaper