# multicollinearity between confounders logistic regression

Im going to investigate if a disease have an negative impact on a binary response variable. The disease is the independent variable with additionally confounders.

I want to do a manual stepwise regression where I subtraction the confounder with highest p-value, and I wonder if i first have to check for multicollinearity between the confounders and response variable?

Can I use the glm in r with the response variable against confounders, then use the vif() function? Do I also have to check the confounder against each other and the disease variable?

I would really appreciate an answer!

• This type of stepwise selection is extremely unreliable. Please look at this page for reasons why. Also, note that multicollinearity usually refers to relations among predictor variables, not relations of predictor variables to outcome variables. If you provide more details about your study (number of cases, proportions in the 2 response categories, number of predictors you are considering, the purpose of your modeling) you could get useful advice on better ways to reach your goal.
– EdM
Apr 14, 2019 at 21:30
• Thank you for your answer! I want to test if RDS(Respiratory Distress Syndrome ) has an negative effect on the development of preterm infants, by tests made at 7 years old. The test result are the response variables and RDS with confounders like birthweight are explanatory variables. I want to find out what confounders to include in the logistic regression together with RDS.
– F K
Apr 15, 2019 at 14:11
• So I first was going to check for multicollinearity between the confounders. I compared the vif of all independent variables by first doing a logistic regression with all variables and then look at the vif values (vif(glm(result ~., family = "binomial", data = data))), i took away one by one the variables with vif over 5. Is this correct?
– F K
Apr 15, 2019 at 14:19
• How many cases do you have, and how many potential "confounders" are you evaluating in total? And what exactly is the binary response variable? I thought that RDS was an issue around birth, but you are examining results of tests at 7 years old. Do you have multiple response variables? If so, how many?
– EdM
Apr 15, 2019 at 14:20
• I have 32 preterm with RDS and 28 without RDS, so 60 in total. I have 11 confounders right now. The response variables is the result in ABC movement at 7 years old, percentile ranking between 1-5 normal, 6-15 borderline and 16-96 poor. I have instead of having a ordinal response variables made it a binary with percentile ranking between 1-5 normal and 6-96 poor motor funciton, because I dont know how to check multicollinearity in a ordinal logistic regression. It is 3 test, made into a total score. It is a multiple response variable but in this case the response variables are the 3 tests.
– F K
Apr 15, 2019 at 14:41

Although multicollinearity gets a lot of attention, it is seldom the biggest problem facing studies like yours. My sense it that a lot of the attention to multicollinearity comes from data sets with tens to hundreds to thousands of predictors. That's not your situation.

What's most important is first to set up the model in a way that is best able to answer your question, without overfitting, in ways that deal with multicollinearity. A few thoughts on how you might proceed:

First, you seem to have a total score for the response variable that could reasonably be considered continuous (values from 1 to 96). Try modeling the response as a continuous variable instead of with binary or ordinal cutoffs. You would probably have to do some transformation of the scores (and perhaps of the confounders, too) to meet the requirements of a linear regression model, but I suspect that approach would give you a much better way to evaluate the +/- RDS differences. You could then present results as the coefficient (estimate and standard error) for +/- RDS in the regression model, with the confounders accounted for directly in the regression. That doesn't, however, deal with potential multicollinearity.

Second, you could use your understanding of the clinical issues to choose which of multiple correlated confounders to incorporate into the regression. With a continuous outcome in a standard linear regression model you can reasonably consider 1 predictor per 10 or so cases without overfitting, so you might be able to include RDS along with 4 or 5 thoughtfully chosen confounders and avoid multicollinearity issues that way.

Third, you could use methods that are designed to deal with multicollinearity. Penalized methods like ridge regression could even be considered to take advantage of multicollinearity by including all the variables into the model while lowering the magnitudes of their regression coefficients to prevent overfitting. In your situation you might consider leaving the RDS coefficient as unpenalized while penalizing the coefficients of the confounders.

Fourth, you could try using propensity scores to correct for the confounders. Although propensity scores are typically considered in the context of comparing treatment effects, they might provide a way to correct for the confounders in this +/- RDS context, for example with inverse probability weighting. One approach would use logistic regression to model the probability of having RDS as a function of the confounders, then to weight each case inversely proportional to its estimated probability of RDS given the values of its confounders.

For any of these approaches, however, I would recommend getting some local informed statistical help and using this as an opportunity to extend your knowledge about statistical analysis of clinical data.