How do you test for independence of k binomial variables?

Question

I am analyzing some orthopedic data and our outcome is union vs. non-union of a fracture. One of our independent variables is whether or not the initial fracture was closed (skin intact) vs. open. Such an evaluation could be conducted by doing a Fisher exact test. In R one would simply create a 2*2 contingency table and make that the argument of a fisher.test. However, what happens when one adds a 3rd binomial variable: was any bacterial organism cultured (yes or no)? Now we have a 2*2*2 table. Can a fisher.exact handle 3 factors (or dimensions)?

I can think of another way to handle this. One could do logistic regression where culture and closed vs. open were simply two independent variables. Would that work? The advantage of multiple logistic regression may be that one could get odds ratio estimates and even interaction terms.

Answer 1

Logistic regression may be the easiest way to do it, if you want the idea of the full 3 dimensional table then include teh interaction term between your predictor variables.

There is also the loglin function that will analyze multidimensional contingency tables (though it is more like the chi-squared test than Fisher's exact test).

Fisher's Exact test could be extended to 3 dimensions if you really need it (but for large sample sizes the other techniques would give equivalent results). But I think a Fisher's exact test for a 3 dimensional table would be an all or nothing test where the logistic regression would let you test each of the 2 predictors. So I would recommend the logistic regression approach.