I’m working on a project in which I have been tasked with determining which of four specific variables are most associated with/predictive of a binary outcome variable (after adjusting for a set of confounding variables), which represents whether or not these patients have a specific clinical condition. The four variables reflect two different indexes (index type 1 and 2) of a separate clinical condition, with Xray and MRI versions of both indexes:
var_1 = Xray index type 1 (scale=0.5-2.0)
var_2 = MRI index type 1 (scale=0.5-2.0)
var_3 = Xray index type 2 (scale=0.0-2.5)
var_4 = MRI index type 2 (scale=0.0-2.5)
Basically, the question is: Of the four methods of measuring clinical condition 1, which is most associated with condition 2?
Because all of the indexes are all measuring condition one, they are relatively highly correlated with each other (r = 0.5 - 0.7). My main question is whether all four of these variables should be entered into one model controlling for a set of confounders versus running four individual models for each variable (adjusting for the same confounders), and comparing the individual models using AIC or something of that variety? I know that if they are entered into one model together, the interpretation for each individual variable of interest will be different (i.e., holding the var_2, var_3 and var_4 variables constant, var_1’s specific contribution is X). Is that the best way of answering my question? If so, how should I deal with the multicollinearity issue?
Thanks in advance.