Causal Analysis in Biomedicine and Epidemiology: Based on by Mikel Aickin

By Mikel Aickin

''Provides present versions, instruments, and examples for the formula and evaluate of clinical hypotheses in causal phrases. Introduces a brand new approach to version parametritization. Illustrates structural equations and graphical components for advanced causal systems.''

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Extra info for Causal Analysis in Biomedicine and Epidemiology: Based on Minimal Sufficient Causation

Example text

In particular applications, Q could be quite complex, consisting of elaborate combinations of simpler elements. For the moment, however, we simply assume that it is always defined. Saying that event A happened at opportunity co is denoted "coeA". This latter is mathematics for saying that co is an element of A. " Thus, the idea of a sub-event is essentially the same as implication. In the same way, "A = B" means the same as "coe A <=> coe B", so that set equality is the same as equivalence. In philosophical discussions, events are often taken to be universals that is, no specific Q is assumed.

This concept looms so large in causal theory that some researchers have tried to base the idea of causation itself on conditional probabilities. Events A and B are said to be independent if and only if P[AB] = P[A]P[B]. When P[B]7K) this is equivalent to P[A|B] = P[A], meaning that being informed of the occurrence of B, we have no reason to modify the 25 4. Events and Probabilities probability of A. Note that the definition of independence is symmetric in A and B. Expectation. A chance variable is a function x defined on Q, provided there is an event a-algebra on the range of x such that whenever F is an event in that a-algebra then {co: x(co)eF) is in the a-algebra that P is defined on.

Q and GO are the Greek capital and lower case omega, which we can identify with the word "opportunity". An event is nothing more than a subset of Q. The elements of the set are the opportunities at which the event "happened", and those outside the set are those opportunities where it didn't. There are several reasons for making this definition so formally. The first is Russell's paradox. If you do not specify Q. explicitly, then it seems as though you ought to be able to talk about sets like U = "the set of all sets that are not subsets of themselves".

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