What I have is a medical data set with several variables, all 0-1 variables. I want to make inference about them with logistic regression. I have a few problems:
I have location variables for the disease. I was advised by my statistic advisor to put them in bins as follows: If it was solely in the right part of the organ then I would mark 1 in the column for right and similarily for left. However if it were in both places I marked in neither of the left and right column but marked one in column both. Using this approach I get error in R, numeric 0 1 error when I use glm in R and I think it is due to how these variables are constructed. Shouldn't I rather have just left and right variables and when we have the disease in both sides I should mark in left and right column and skip the both column and maybe introduce interaction term between left and right (that I would at least do in a linear model).
Using glm (family binomial for logistic regression) in R I was thinking how to find the best model describing some variable. I started with one usual approach with finding univarietly which variables had p-value less than $0.1$ in Fischer exact test. Then I included those variables in my model and started to delete them after which had the highest p-value. In most medical reasearches I have read when applying multivariate regression I see the usage of p-value $0.05$ but I have a feeling that it might be because of lack of understanding of the subject. When I ranked the model according to AIC and explored the best model I usually got variable with p-value around $0.1$. Which approach is preferably, is it justifyable to just cut of at p-value $0.05$ or should use AIC as an estimator of the best multivariate model? AIC does punish for extra variables and so it shouldnt give one too many variables.