I& #39;ve seen a few papers describing the characteristics of people who tested positive for COVID-19 and this is sometimes being interpreted as describing people with certain characteristic& #39;s the *probability of infection*. Let& #39;s talk about why that& #39;s likely not true https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ‘‡" title="Down pointing backhand index" aria-label="Emoji: Down pointing backhand index">https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧡" title="Thread" aria-label="Emoji: Thread">

1/22
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ‘‰" title="Right pointing backhand index" aria-label="Emoji: Right pointing backhand index"> Usually when thinking about estimating the prevalence of a disease, we use the *sensitivity* and *specificity* of the test to help us
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ‘‰" title="Right pointing backhand index" aria-label="Emoji: Right pointing backhand index"> The calculations assume that everyone is equally likely to get tested, and with COVID-19 that is likely not the case

2/22
Let& #39;s do some https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> thought experiments. For these, my goal is to estimate the probability of being infected with https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">COVID-19 given you have https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">Disease X

For example,https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> Disease X could be:
https://abs.twimg.com/emoji/v2/... draggable="false" alt="β™₯️" title="Heart suit" aria-label="Emoji: Heart suit"> heart disease
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🩸" title="Drop of blood" aria-label="Emoji: Drop of blood"> hypertension
https://abs.twimg.com/emoji/v2/... draggable="false" alt="βž•" title="Heavy plus sign" aria-label="Emoji: Heavy plus sign"> it could also be any subgroup (for example age, etc)

3/22
In these https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> thought experiments, we don& #39;t actually have perfect information about who is infected with https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> COVID-19, we just know among those who are https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> *tested* who has been infected with https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> COVID-19. This is really the crux of the matter.

4/22
For these https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> thought experiments, assume that the current tests are *perfect* (that is there are 0 false positives and 0 false negatives)

https://abs.twimg.com/emoji/v2/... draggable="false" alt="☝️" title="Up pointing index" aria-label="Emoji: Up pointing index">note that this is likely not the case, with the current testing framework false (+) are unlikely but false (-) may be occurring

5/22
We want the probability of being infected with COVID-19 given you have disease X
P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">)

To get this, we need P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) because based on Bayes& #39; Theorem we know:

P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">)P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) / P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">)

6/22
BUT, instead of P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">), we actually have P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">, https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube">) - the probability of having disease X given you have COVID-19 AND you were tested. So the crux of these thought experiments will be trying to get an accurate estimate of P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) so that we can get back to P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">)

7/22
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="1️⃣" title="Keycap digit one" aria-label="Emoji: Keycap digit one">: Best case scenario

https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20%¹ of the population has disease X
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 50%¹ have COVID-19
https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> There is no relationship between disease X and COVID-19
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are just as likely to get tested than people without disease X

-
ΒΉ all numbers are made up
8/22
https://abs.twimg.com/emoji/v2/... draggable= experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="1️⃣" title="Keycap digit one" aria-label="Emoji: Keycap digit one">: Best case scenariohttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20%ΒΉ of the population has disease Xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 50%ΒΉ have COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> There is no relationship between disease X and COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are just as likely to get tested than people without disease X-ΒΉ all numbers are made up8/22" title="https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="1️⃣" title="Keycap digit one" aria-label="Emoji: Keycap digit one">: Best case scenariohttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20%ΒΉ of the population has disease Xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 50%ΒΉ have COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> There is no relationship between disease X and COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are just as likely to get tested than people without disease X-ΒΉ all numbers are made up8/22" class="img-responsive" style="max-width:100%;"/>
Why is https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="1️⃣" title="Keycap digit one" aria-label="Emoji: Keycap digit one"> a best case scenario?

It looks like:
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube">50% have COVID-19 among those tested
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive, the prevalence of disease X is 20%
P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 50%

https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> Reality (no relationship between disease X and COVID-19) matches what we see

9/22
Why is https://abs.twimg.com/emoji/v2/... draggable= experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="1️⃣" title="Keycap digit one" aria-label="Emoji: Keycap digit one"> a best case scenario?It looks like:https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube">50% have COVID-19 among those testedhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive, the prevalence of disease X is 20%P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 50%https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> Reality (no relationship between disease X and COVID-19) matches what we see9/22" title="Why is https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="1️⃣" title="Keycap digit one" aria-label="Emoji: Keycap digit one"> a best case scenario?It looks like:https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube">50% have COVID-19 among those testedhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive, the prevalence of disease X is 20%P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 50%https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> Reality (no relationship between disease X and COVID-19) matches what we see9/22" class="img-responsive" style="max-width:100%;"/>
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="2️⃣" title="Keycap digit two" aria-label="Emoji: Keycap digit two">: Oversampling scenario

https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20% of the population has disease X
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 50% have COVID-19
https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> There is no relationship between disease X and COVID-19
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles">2xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles"> more likely to get tested than people without disease X

10/22
https://abs.twimg.com/emoji/v2/... draggable= experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="2️⃣" title="Keycap digit two" aria-label="Emoji: Keycap digit two">: Oversampling scenariohttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20% of the population has disease Xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 50% have COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> There is no relationship between disease X and COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles">2xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles"> more likely to get tested than people without disease X10/22" title="https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="2️⃣" title="Keycap digit two" aria-label="Emoji: Keycap digit two">: Oversampling scenariohttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20% of the population has disease Xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 50% have COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> There is no relationship between disease X and COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles">2xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles"> more likely to get tested than people without disease X10/22" class="img-responsive" style="max-width:100%;"/>
Why is https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="2️⃣" title="Keycap digit two" aria-label="Emoji: Keycap digit two"> bad?

It looks like:
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> 50% have COVID-19 among those tested
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive for COVID-19, the prevalence of disease X is 33% https://abs.twimg.com/emoji/v2/... draggable="false" alt="😱" title="Face screaming in fear" aria-label="Emoji: Face screaming in fear">

https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> If we plug in what we see P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">, https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube">) for P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">), it looks like P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) is 82.5%, reality is 50%

11/22
Why is https://abs.twimg.com/emoji/v2/... draggable= experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="2️⃣" title="Keycap digit two" aria-label="Emoji: Keycap digit two"> bad?It looks like:https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> 50% have COVID-19 among those testedhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive for COVID-19, the prevalence of disease X is 33% https://abs.twimg.com/emoji/v2/... draggable="false" alt="😱" title="Face screaming in fear" aria-label="Emoji: Face screaming in fear">https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> If we plug in what we see P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">, https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube">) for P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">), it looks like P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) is 82.5%, reality is 50%11/22" title="Why is https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="2️⃣" title="Keycap digit two" aria-label="Emoji: Keycap digit two"> bad?It looks like:https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> 50% have COVID-19 among those testedhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive for COVID-19, the prevalence of disease X is 33% https://abs.twimg.com/emoji/v2/... draggable="false" alt="😱" title="Face screaming in fear" aria-label="Emoji: Face screaming in fear">https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> If we plug in what we see P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">, https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube">) for P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">), it looks like P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) is 82.5%, reality is 50%11/22" class="img-responsive" style="max-width:100%;"/>
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="3️⃣" title="Keycap digit three" aria-label="Emoji: Keycap digit three">: Undersampling scenario

https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20% of the population has disease X
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 50% have COVID-19
https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> There is no relationship between disease X and COVID-19
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles">1/2https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles"> as likely to get tested than people without disease X

12/22
https://abs.twimg.com/emoji/v2/... draggable= experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="3️⃣" title="Keycap digit three" aria-label="Emoji: Keycap digit three">: Undersampling scenariohttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20% of the population has disease Xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 50% have COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> There is no relationship between disease X and COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles">1/2https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles"> as likely to get tested than people without disease X12/22" title="https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="3️⃣" title="Keycap digit three" aria-label="Emoji: Keycap digit three">: Undersampling scenariohttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20% of the population has disease Xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 50% have COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> There is no relationship between disease X and COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles">1/2https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles"> as likely to get tested than people without disease X12/22" class="img-responsive" style="max-width:100%;"/>
Why is https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="3️⃣" title="Keycap digit three" aria-label="Emoji: Keycap digit three"> bad?

It looks like:
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> 50% have COVID-19 among those tested
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive for COVID-19, the prevalence of disease X is 11%

https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> If we plug in what we see (P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">, https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube">)) for P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">), it looks like P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) is 27.5%, reality is 50%

13/22
Why is https://abs.twimg.com/emoji/v2/... draggable= experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="3️⃣" title="Keycap digit three" aria-label="Emoji: Keycap digit three"> bad?It looks like:https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> 50% have COVID-19 among those testedhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive for COVID-19, the prevalence of disease X is 11% https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> If we plug in what we see (P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">, https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube">)) for P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">), it looks like P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) is 27.5%, reality is 50%13/22" title="Why is https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="3️⃣" title="Keycap digit three" aria-label="Emoji: Keycap digit three"> bad?It looks like:https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> 50% have COVID-19 among those testedhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive for COVID-19, the prevalence of disease X is 11% https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> If we plug in what we see (P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">, https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube">)) for P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">), it looks like P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) is 27.5%, reality is 50%13/22" class="img-responsive" style="max-width:100%;"/>
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="4️⃣" title="Keycap digit four" aria-label="Emoji: Keycap digit four">: two problems scenario

https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20% of the population has disease X
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 56% have COVID-19
https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> people with disease X are 1.6 times more likely to have COVID-19, P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 80%
https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles">5https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles"> as likely to get tested than people without disease X
14/22
https://abs.twimg.com/emoji/v2/... draggable= experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="4️⃣" title="Keycap digit four" aria-label="Emoji: Keycap digit four">: two problems scenariohttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20% of the population has disease Xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 56% have COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> people with disease X are 1.6 times more likely to have COVID-19, P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 80%https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles">5https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles"> as likely to get tested than people without disease X14/22" title="https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="4️⃣" title="Keycap digit four" aria-label="Emoji: Keycap digit four">: two problems scenariohttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> 20% of the population has disease Xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> 56% have COVID-19https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> people with disease X are 1.6 times more likely to have COVID-19, P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 80%https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> People with disease X are https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles">5https://abs.twimg.com/emoji/v2/... draggable="false" alt="✨" title="Sparkles" aria-label="Emoji: Sparkles"> as likely to get tested than people without disease X14/22" class="img-responsive" style="max-width:100%;"/>
Why is https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="4️⃣" title="Keycap digit four" aria-label="Emoji: Keycap digit four"> bad?

It looks like:
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> 66% have COVID-19 among those tested
https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive for COVID-19, the prevalence of disease X is 66%

https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> We& #39;re getting both the prevalence of COVID-19 *and* the it& #39;s association with Disease X wrong

15/22
Why is https://abs.twimg.com/emoji/v2/... draggable= experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="4️⃣" title="Keycap digit four" aria-label="Emoji: Keycap digit four"> bad?It looks like:https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> 66% have COVID-19 among those testedhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive for COVID-19, the prevalence of disease X is 66%https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> We& #39;re getting both the prevalence of COVID-19 *and* the it& #39;s association with Disease X wrong15/22" title="Why is https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ’­" title="Thought balloon" aria-label="Emoji: Thought balloon"> experiment https://abs.twimg.com/emoji/v2/... draggable="false" alt="4️⃣" title="Keycap digit four" aria-label="Emoji: Keycap digit four"> bad?It looks like:https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> 66% have COVID-19 among those testedhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ§ͺ" title="Test tube" aria-label="Emoji: Test tube"> Of those who tested positive for COVID-19, the prevalence of disease X is 66%https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark"> We& #39;re getting both the prevalence of COVID-19 *and* the it& #39;s association with Disease X wrong15/22" class="img-responsive" style="max-width:100%;"/>
OKAY, scenarios finished, so hopefully this highlights why we can& #39;t take the prevalence of characteristics in the *tested positive* population as the prevalence of characteristics in the overall COVID-19 population. Now, here are tips for how we can correct the numbers https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ‘‡" title="Down pointing backhand index" aria-label="Emoji: Down pointing backhand index">

16/22
Scenario https://abs.twimg.com/emoji/v2/... draggable="false" alt="2️⃣" title="Keycap digit two" aria-label="Emoji: Keycap digit two">: Oversampling by 2x

https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ‘‰" title="Right pointing backhand index" aria-label="Emoji: Right pointing backhand index"> take those with disease X that tested positive for COVID-19 and downweight them by a factor of 2.
https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> the adjusted prevalence of Disease X among those that tested positive for COVID-19 (0.5 / 2.5) = 0.2 (20%)
P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 50%

17/22
Scenario https://abs.twimg.com/emoji/v2/... draggable=: Oversampling by 2xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ‘‰" title="Right pointing backhand index" aria-label="Emoji: Right pointing backhand index"> take those with disease X that tested positive for COVID-19 and downweight them by a factor of 2.https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> the adjusted prevalence of Disease X among those that tested positive for COVID-19 (0.5 / 2.5) = 0.2 (20%)P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 50%17/22" title="Scenario https://abs.twimg.com/emoji/v2/... draggable="false" alt="2️⃣" title="Keycap digit two" aria-label="Emoji: Keycap digit two">: Oversampling by 2xhttps://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ‘‰" title="Right pointing backhand index" aria-label="Emoji: Right pointing backhand index"> take those with disease X that tested positive for COVID-19 and downweight them by a factor of 2.https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> the adjusted prevalence of Disease X among those that tested positive for COVID-19 (0.5 / 2.5) = 0.2 (20%)P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 50%17/22" class="img-responsive" style="max-width:100%;"/>
Scenario https://abs.twimg.com/emoji/v2/... draggable="false" alt="3️⃣" title="Keycap digit three" aria-label="Emoji: Keycap digit three">: Undersampling by 1/2

https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ‘‰" title="Right pointing backhand index" aria-label="Emoji: Right pointing backhand index"> take those with disease X that tested positive for COVID-19 and upweight them by a factor of 2.
https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> the adjusted prevalence of Disease X among those that tested positive for COVID-19 (2/ 10) = 0.2 (20%)
P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 50%

18/22
Scenario https://abs.twimg.com/emoji/v2/... draggable=: Undersampling by 1/2https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ‘‰" title="Right pointing backhand index" aria-label="Emoji: Right pointing backhand index"> take those with disease X that tested positive for COVID-19 and upweight them by a factor of 2.https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> the adjusted prevalence of Disease X among those that tested positive for COVID-19 (2/ 10) = 0.2 (20%)P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 50%18/22" title="Scenario https://abs.twimg.com/emoji/v2/... draggable="false" alt="3️⃣" title="Keycap digit three" aria-label="Emoji: Keycap digit three">: Undersampling by 1/2https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ‘‰" title="Right pointing backhand index" aria-label="Emoji: Right pointing backhand index"> take those with disease X that tested positive for COVID-19 and upweight them by a factor of 2.https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> the adjusted prevalence of Disease X among those that tested positive for COVID-19 (2/ 10) = 0.2 (20%)P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 50%18/22" class="img-responsive" style="max-width:100%;"/>
Scenario https://abs.twimg.com/emoji/v2/... draggable="false" alt="4️⃣" title="Keycap digit four" aria-label="Emoji: Keycap digit four">: Two problems

For the prevalence of COVID-19, correct by weighing by the probability of being tested in each subgroup (https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> = disease X, https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark">https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> = No disease X)

P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) + P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark">https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark">https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">)

https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark">P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = β…˜ * 0.2 + Β½ * 0.8 = 56%

19/22
Scenario https://abs.twimg.com/emoji/v2/... draggable=: Two problemsFor the prevalence of COVID-19, correct by weighing by the probability of being tested in each subgroup (https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> = disease X, https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark">https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> = No disease X)P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) + P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark">https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark">https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark">P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = β…˜ * 0.2 + Β½ * 0.8 = 56%19/22" title="Scenario https://abs.twimg.com/emoji/v2/... draggable="false" alt="4️⃣" title="Keycap digit four" aria-label="Emoji: Keycap digit four">: Two problemsFor the prevalence of COVID-19, correct by weighing by the probability of being tested in each subgroup (https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> = disease X, https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark">https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> = No disease X)P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) + P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark">https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="❌" title="Cross mark" aria-label="Emoji: Cross mark">https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark">P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = β…˜ * 0.2 + Β½ * 0.8 = 56%19/22" class="img-responsive" style="max-width:100%;"/>
Scenario https://abs.twimg.com/emoji/v2/... draggable="false" alt="4️⃣" title="Keycap digit four" aria-label="Emoji: Keycap digit four">: Two problems

For calculating the prevalence of disease X among COVID-19 patients
https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) / P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = β…˜ * 0.2 / 0.56 = 0.285
Again, downweight the oversampled Disease X population (divide by 5).
https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> β…˜ / (β…˜ + 2) = 0.285

P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 80%
21/22
Scenario https://abs.twimg.com/emoji/v2/... draggable=: Two problemsFor calculating the prevalence of disease X among COVID-19 patientshttps://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) / P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = β…˜ * 0.2 / 0.56 = 0.285Again, downweight the oversampled Disease X population (divide by 5).https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> β…˜ / (β…˜ + 2) = 0.285P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 80%21/22" title="Scenario https://abs.twimg.com/emoji/v2/... draggable="false" alt="4️⃣" title="Keycap digit four" aria-label="Emoji: Keycap digit four">: Two problemsFor calculating the prevalence of disease X among COVID-19 patientshttps://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe"> | https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) / P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">) = β…˜ * 0.2 / 0.56 = 0.285Again, downweight the oversampled Disease X population (divide by 5).https://abs.twimg.com/emoji/v2/... draggable="false" alt="βœ…" title="White heavy check mark" aria-label="Emoji: White heavy check mark"> β…˜ / (β…˜ + 2) = 0.285P(https://abs.twimg.com/emoji/v2/... draggable="false" alt="🦠" title="Microbe" aria-label="Emoji: Microbe">|https://abs.twimg.com/emoji/v2/... draggable="false" alt="🧩" title="Jigsaw" aria-label="Emoji: Jigsaw">) = 80%21/22" class="img-responsive" style="max-width:100%;"/>
Hopefully this is somewhat helpful when reading about characteristics of those who are currently testing positive for COVID-19. As always, please let me know if there is something I& #39;ve missed! https://abs.twimg.com/emoji/v2/... draggable="false" alt="πŸ™" title="Folded hands" aria-label="Emoji: Folded hands">

22/22
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