Ways to handle multiple independent variables

Question

I have a hypothetical question regarding the way to handle a study's independent exposure variables.(English is not my first language, so excuse any issues of clarity).

Say I design a study to assess the effect of three somewhat related chemicals (like three cleaning agents often used in jobs) on the risk of disease (X); the means to analyze this would be estimating ORs using logistic regression analysis. I would want to assess the independent effect of each chemical. Say in the dataset each person would have a separate variable for each chemical, with a value assigned either a 1-=exposed to chemical or 0= not exposed to chemical- so a separate variable for chemical 1, chemical 2 and chemical 3. However, say it is not uncommon that these chemicals are used simultaneously, e.g. chemical 1 and chemical 2 are often used at the same time, chemical 2 and chemical 3 at the same time, etc. so there is a lot of overlap-so perhaps there are an equal number of people using chemical 1 alone as there are using a combination of chemical 1 and chemical 2 simultaneously.
To handle this overlap of chemicals, I see two options:

option 1) In a logistic regression model, include each of the three chemical variables, to essentially adjust for the other two chemicals as possible confounders. However, with regard to the large overlap, if these variables are correlated or often used simultaneously, would this be a possible multicollinearity problem?

option 2) the data set could be set up so that one could assess the effect chemical 1 alone (create a variable that would code those with only chemical 1 exposure =1, those with exposure to no chemicals=0, and those with any other chemical exposure(s) as missing), chemical 2 alone, and chemical 3 alone and use each of those variables to calculate separate ORs for each exposure in separate logistic regression models. I believe this would remove the effect of the other exposure variables, and reduce the multicollinearity issue, however reduce the total sample size.

Is this correct? Are there other strengths and weaknesses or other options I am not thinking of.

Answer 1

The answer must to some extent depend on the exact scientific question. If you create the three dummy variables as you suggests and then put them all into a regression model you will get the effect of each controlling for the others. If in fact some of them co-occur quite frequently then it can be difficult statistically or conceptually to separate their effects. You could always fit a model with interactions first and check for them to see whether the joint effect of your predictors is more or less than the sum of their separate effects. When you are satisfied that a model with just the main effects of the three predictors is OK then you could examine the variance-covariance matrix of the coefficients to see whether the estimates are indeed correlated. I would not worry too much about numerical problems of co-linearity, modern software will fit the model or at least give up gracefully with a warning message. Your option 2 answers a different question and I am not sure whether it is a very helpful question. If the effects of two of the predictors are very different depending on the third you might, having established that in your earlier models (and reported them) go on to stratify by the third and fit separate models. But I would start with an attempt to model all the data.