X) does not equal 1; nor does it equal 0. In fact, it could be anything between 0 and 1.
The lower P(Y
X) is the harder it is to find, believe and know the causal association between X and Y. Based on how we test for causal associations, to ever have a chance to identify whether X causes Y when it is a possible cause is for:
X) > P(Y
That is, the probability of Y given X needs to be greater than the probability of Y given not X. Going one step further, to really demonstrate X causes Y we need to consider the probability of Y given X versus the probability of Y given not X, or anything else that causes Y.
For example, to demonstrate that HF causes DOE I need to demonstrate that the P(DOE
HF) is greater than the P(DOE
not HF). But if my sample of people with “not HF” all have COPD, then the P(DOE
HF) may not be larger than the P(DOE
not HF) in that sample which is, quite honestly, a bad representation of the population :)
But none of that is the reason I find possible cause so intriguing (by the way, much of what I wrote up there can be considered for definite cause as well, it is just that with definite cause, since the P(Y
X) = 1 it is easier to identify (lots of signal, less noise)).
The reason I find possible cause so intriguing is that there are reasons for the “possible” state of effect based on a cause. What about the cause makes it only “possibly” create an effect? Or is it something about the effect? Or is it something in whatever force or entity interacts between the cause and the effect? In which case is there another “cause” in the chain that we have been ignoring, what once known would result in a series of definite causes just with several interacting modifying factors. Possible cause is intriguing because whether it is truly a form of cause is questionable. Perhaps there are no possible causes, we just observe possible causes because of our lack of knowledge about the full causal web.
The next 3 types of cause start to get into what happens with a causal web of interacting components. We will keep them simple at first, with one additional causal agent - a “worsening factor”, a “definite correction” or a “possible correction.”
Similiar to this post- I will be keeping new posts below 500 words :)