Ive always wondered about this: Lets say there is a chance of 1 in 23.000 to get a certain disease. But we know that there Are a lot more diseases with those odds Aprox of apearing, would that make the ods lets say 1 in 2.300 of geting a rare disease? Or is it 1 per 23.000 healthy person.
Sorry for bad grammar.
In: Mathematics
Let’s say there are 10 000 diseases in the world, each of which you have a 1 on 10 000 chance of having (meaning that for any one of those diseases, about one person in 10 000 has it). That only gives us information about the probabilities for *each disease individually*. To work out probabilities involving several diseases, we need to know information about the *correlation between* the diseases. Without that information, we can’t know anything about the probability of something like “having any disease” or “having no diseases”.
The probability of having a specific disease is what’s called the *marginal distribution* of that disease. The probabilities governing questions involving several diseases together is called the *joint distribution* for those diseases. So in technical language, what I’m saying is that knowing the marginal distributions does not tell you the joint distribution.
To illustrate this, let’s consider three different possible scenarios. In each of these cases, it’s still true that the chances of having any one of our hypothetical 10k diseases is 1 in 10k. However, in each case the probability of having *some* disease is different.
1. Maybe the way diseases work is that everyone always gets exactly one, and it’s just chosen at random. So for a specific disease, your chances of having it are one in ten thousand, but the chances of having *a* disease are 100%.
2. Maybe all diseases occur together: you either have all of them (which happens one in 10000 times) or none of them. In that case, the chances of having a diseases are 1 in 10000.
3. Maybe (this is the most realistic scenario) the diseases are *independent*. What this means is that having or not having disease A never changes your odds of having disease B (this is unrealistic – e.g. having sickle cell precludes having malaria, and having diabetes increases your odds of having various other health problems). In this case, the easiest way to do the calculation is by considering the odds of having *no* disease. About 9999 out of 10k people (99.99%) *don’t* have disease A. About 9999 out of 10k of *those* people *don’t* have disease B, so overall about 99.98% of people. About 9999 of 19k of that 99.98% also don’t have disease C, which is a bout 99.97%. And so on. By the end of it, you have the proportion of the population which has *no* diseases, and 100% minus that is the proportion with at least one disease.
To get a real answer, you would need information about the co-dependencies between all the different diseases: how does having leprosy affect your odds of having rabies, etc.
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