Leaving out a confounder in longitudinal regression?

[FallenApple]

Say I want to analyze how a relation changes though time. Like usual, I would throw in the potential confounders into the regression model. But what if some of the confounders are not determined at the beginning of the study but at some point within time?

For example, say I want to analyze the relation between creatine doses and sports performance over time. So a basic linear mixed model would be: $Performance_{ij} \sim Dose_{ij}+Time_{ij}+Dose_{ij}*Time_{ij}+PotentialConfounders_{i}+RandomEffects_{i}+error_{ij}$

Where i is the ith subject and j is within that subject. Say Dose and Performance are measure longitudinally. and the rest of covariates are just recorded once and is the same for all levels within the ith subject.

Say I suspect that gender might confound the relation between creatine and performance. Well, a persons gender is fixed throughout the study.

But what about say injury? Say I have an injury indicator variable that's says whether the athlete experiences injury during the study. Where I don't know when it happened in the study. This is different from say gender, where even if the data is collected after, we know it couldn't have changed. Anyways, If I consider Injury Status as potential confounder, should I include it? I mean, it might not be present at all time points. It seems that whatever inference obtained by including it would be invalid. But then again, if injury is a confounder, then not adjusting for it would also result in invalid inferences.

 

[DrDu]

So yes, you can only partially correct for confounding. Better than nothing, isn't it?
Also note that for a confounder to be a confounder, it has to correlate both with the effect and with the parameter of interest. E.g. injury may not correlate with dose (if subjects take the same dose independently of whether injured or not) but certainly correlates with time.

 

[FactChecker]

It seems that whatever inference obtained by including it would be invalid. But then again, if injury is a confounder, then not adjusting for it would also result in invalid inferences.

The inferences to draw from statistical analysis is always entirely the responsibility of the subject matter expert. One should be careful about thinking that statistics will do more than show correlation.

It should be noted that, unless a person has control of the independent variables, most independent variables will be a confounder. When a person puts a variable into a model, it is usually because he suspects some relationship or correlation between it and the dependent variable. It would be unusual for two such independent variables to not also show some correlation among themselves. So that is what procedures like stepwise multiple regression are designed to handle. The exception to this is when an experiment is specifically designed to minimize or even completely eliminate the correlation between the independent variables.