We are studying a disease. Let’s call it k. Let’s also say we have an island of 1,000 humans. All of them are healthy right now; no one has k. We decide to watch them for exactly 365 days. Also, we are in “god-mode”; that means if any of them get sick, we know right away. No tests, no doctors, no diagnosis needed. Over the course of 365 days, we see that 200 of them got sick with k. What is the incidence?
= (200 cases ÷ 1,000 humans) / 1 year = 0.20 cases of k per human per year
Now, if I ask you, “What is the prevalence of k?”, that is a much trickier question.
As god, if you reached down from the heavens, and picked from the island a human, what is the likelihood (or “probability”) you grabbed a sick one?
The answer is not straightforward.
What if I told you our disease, k, only lasts thirty seconds? Once someone gets k, the body clears it after 30 seconds. Or I could tell you k lasts 1 year. It takes 1 year for the body to clear the disease.
See how the prevalence will be wildly different in the two scenarios?
When k lasts only 30 seconds, the prevalence will be very low; the probability of reaching down from heaven and grabbing a sick human is virtually zero. (Since humans get but somehow clear the disease in thirty seconds.)
When k lasts 1 year, on the other hand, well, now we have a different story: when you reach down and grab a human it is much more likely you are going to grab a sick one.
The formula in question is trying to express this idea. It is saying, “the greater the incidence, and the longer-lasting the disease, the more likely you are to grab a sick person from your island than a non-sick person.”
Also note that prevalence is just another way of saying:
probability of grabbing a sick person from the island;
whereas 1 – prevalence is another way of saying:
probability of grabbing a non-sick person from the island.
submitted by drdoom(1206), 2020-01-01T03:27:45Z
We are studying a disease. Let’s call it k. Let’s also say we have an island of 1,000 humans. All of them are healthy right now; no one has k. We decide to watch them for exactly 365 days. Also, we are in “god-mode”; that means if any of them get sick, we know right away. No tests, no doctors, no diagnosis needed. Over the course of 365 days, we see that 200 of them got sick with k. What is the
incidence?= (200 cases ÷ 1,000 humans) / 1 year= 0.20 cases of k per human per yearNow, if I ask you, “What is the
prevalenceof k?”, that is a much trickier question.As god, if you reached down from the heavens, and picked from the island a human, what is the likelihood (or “probability”) you grabbed a sick one?
The answer is not straightforward.
What if I told you our disease, k, only lasts thirty seconds? Once someone gets k, the body clears it after 30 seconds. Or I could tell you k lasts 1 year. It takes 1 year for the body to clear the disease.
See how the
prevalencewill be wildly different in the two scenarios?When k lasts only 30 seconds, the prevalence will be very low; the probability of reaching down from heaven and grabbing a sick human is virtually zero. (Since humans get but somehow clear the disease in thirty seconds.)
When k lasts 1 year, on the other hand, well, now we have a different story: when you reach down and grab a human it is much more likely you are going to grab a sick one.
The formula in question is trying to express this idea. It is saying, “the greater the incidence, and the longer-lasting the disease, the more likely you are to grab a sick person from your island than a non-sick person.”
Also note that
prevalenceis just another way of saying:probability of grabbing a sick person from the island;whereas
1 – prevalenceis another way of saying:probability of grabbing a non-sick person from the island.