Causation- Definite cause

Let’s consider cause in greater detail. There are at least 5 different types for us to consider and underlying these 5 we can further consider the mechanisms as a source of insight into the causal relation. After getting some feedback I am going to make the posts shorter and make sure they continue to come out at a regular interval, so I will take each of these 5 with separate posts.

The 5 types to consider cause include: definite cause, possible cause, exacerbating factor, definite elimination and possible elimination. A notational reminder X causes Y can be considered as the probability that Y occurs given X; and the probability of Y given X is P(YX).

P(Y) simply means the the probability of Y, and one of the axioms of probability is that: 0 <= P(Y) <= 1; meaning P(Y) can be equal to 0, or be between 0 and 1, or be equal to 1. Being equal to 0 or 1 is a statement of certainty.

A definite cause: P(YX) = 1; is a statement of certainty, if X then Y. Definite causes are what we refer to when we speak of a “deterministic” system. If all causes within a system are definite then given a set of variables the outcome is definite. If the variables are binary then the rules of logic determine the outcome, if the variables are continuous then we would rely on equations to provide outcome.

If there are a chain of events from “cause” to “effect” and each event is, itself, a cause-effect interaction then for the total chain to be definite each part of the chain must also be definite.

dagitty-modelFor P(EA) = 1 then P(BA) and P(CB) and P(DC) and P(ED) must also all equal 1; and the probability of each of these steps must not be influenced by other factors.

From this quick introduction I am sure you can imagine how complicated cause can become as we consider the mechanisms. I will go so far as to say there are very few clinical references to cause that are definite cause and a major reason is simply the number of interacting variables. As I continue through the different types of cause I will use graphical models (as above). If you are interested, the program I am using to draw these diagrams is “DAGitty” and is freely available here.

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