By Mikel Aickin
''Provides present versions, instruments, and examples for the formula and review of medical hypotheses in causal phrases. Introduces a brand new approach to version parametritization. Illustrates structural equations and graphical parts for complicated causal systems.''
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Additional info for Causal Analysis in Biomedicine and Epidemiology: Based on Minimal Sufficient Causation
The idea behind F is that it represents all of the factors whose causal effects I currently would like to consider. It may well contain factors I cannot measure, either because I have no good way of measuring them, or because I don't actually know about their existence. For example, consider a hypothetical study to try to determine the causes of breast cancer. Here is a list of factors I would like to measure: Xi = first-degree female relative had breast cancer x2 = used birth-control pills x3 = had late menses x4 = had late (or no) childbirth x5 = carries BRCA1 gene x6 = has high intake of dietary saturated fat x7 = age above 50 x7* = age at or below 50 x8 = age above 60 x9 = age above 70 x1() — was exposed to pesticide during puberty 39 6.
I and bi are new factors in vriFj. i is fairly clear - it consists of the causes of y generated by F!. i cannot make any explicit reference to x,, because Xi was removed from F to make FI. 41 6. Nontrivial Implication There is a subtle point here that is worth the digression. Suppose that Xj€ VHP). This means that we can represent Xj exactly with a disjunction of pathways, none of which use xi. In this case C[y|Fi] = C[y|F]. On the left side we have what we would like to interpret as the causes that do not involve x b and on the right we have the causes that can involve x t .
Another version of the lack of distribution is w(uvv) = wu v (w\wu)v Although this may seem a bit bizarre, it turns out that in causal models there is a very precise reason for this equation. For binary u, v, w it is true that v distributes over multiplication, uvvw = (uvv)(uvw) but in general in unitary algebra we only have uvvw = (uvv)((u/uvv)vw) Unitary Probability Models. An important reason for employing unitary algebra concerns the parametrization of probability models. For example, let y and \i be two factors.
Causal Analysis in Biomedicine and Epidemiology: Based on Minimal Sufficient Causation by Mikel Aickin