Interactions between categorical and continuous independent variables

Question

Im going to investigate if a disease have a negative impact on the development of children. The disease is the independent variable with additionally 10 confounders. Do I have to check for interactions between the confounders? And interactions between the disease and the confounders? I have both categorical and continuous independent variables, how do I check them in that case before the logistic regression?

Answer 1

If the interactions among confounders affect the development of children and they are imbalanced prior to your effect estimation, then your effect estimate will be biased. You can easily assess whether the interactions are imbalanced by simply computing the means of products of the confounders with each other between those who have the disease and those who don't. It may be more challenging to know whether the interactions affect development. You can try to rely on theory (although theory is probably incomplete here), or you can attempt to investigate whether this is so in your data. If you do that latter, it's very important to split your sample into an exploratory subsample and an analysis subsample, do the exploration of interactions in the exploratory subsample, and finally estimate the treatment effect in your analysis sample using the best model from your exploratory sample. This method is called "sample splitting". I'll discuss another solution below.

The presence of interactions between the disease and confounders on development can bias your effect estimate if you don't clearly specify the population you want to generalize to and if you use a method that doesn't account for those interactions. For example, if you want to generalize the effect of disease on development to a population that resembles your sample, you can use regression or inverse probability weighting, but not matching. If you use regression, it's important to include the relevant interactions in your model. It's better to include more interactions than fewer if your data can support such a model. If you use inverse probability weighting, you don't have to be concerned about interactions between disease and the confounders.

Finally, you should probably use a state-of-the-art method that flexibly models the relationships among the disease, the confounders, and development. These methods do the work for you of figuring out whether you need to account for interactions or not. They don't tell you the answer to that question, but they will give you a (likely) valid estimate of the treatment effect without relying on you to specify the correct model. I outline a few such methods here with references in the linked post. I tend to recommend Bayesian Additive Regression Trees (BART) because the bartCause R package makes it so easy to use them, and they tend to have excellent performance in many arbitrary simulations (including in the presence of interactions).

Whatever you do, do not interpret the coefficient on the disease variable in a logistic regression as a treatment effect! Not only are odds ratios essentially uninterpretable scientifically, but effect estimates from logistic regression models also have a variety of interpretational difficulties statistically. If you're using R or Stata, use the marginal effects procedure to estimate a risk difference (using the margins function in either software), and if you're using SAS, use PROC CAUSALTRT. Seek the help of a biostatistician or epidemiologist trained in causal inference if these concepts are unfamiliar to you.