When do you stratify an analysis versus including an interaction term?

Question

I’m not very familiar with when and why you would stratify on a variable or set of variables in a regression analysis generally and would like to know what the issues are particularly in contrast to including the variable (by itself or as an interaction term) in the model without stratifying.

I’m somewhat familiar with the example in Cox regression where you would stratify when the baseline hazard functions differ across levels of a variable, the variable is discrete and you don’t care if you have an estimate of it. In this case stratifying may be preferable to including an interaction with time term. But I’ve never really considered it in other regression contexts. What am I missing and what do I need to pay attention to?

Also, I’m only talking about the analysis side of things, not in the design phase or sampling. I am only working with secondary analysis on observational data that hasn’t been taken from a stratified sample or design if that helps narrow the focus.

And a specific question within this – would I really check each predictor in my model on whether to stratify? I understand with interactions that you wouldn’t necessarily check for interactions if you didn’t have an a priori reason to and they are not of primary interest. Thanks.

Answer 1

Stratified approach does not provide a test of statistical significance of the difference between the stratified parameter estimates.

A more serious statistical shortcoming arises when a model has numerous covariates in addition to the modifier. Stratification unnecessarily attenuates multicollinearity among the covariates because it allows for no statistical interrelationships between data items segregated into the stratified models.

The stratified models would provide slightly different and less satisfactory results than a model that includes all your data and tests for modification using an interaction term. Thus, interpretations of measures of association for stratified models are also subtly different: statistical inferences can be generalized only to the population from which the sample stratum was drawn and not to the entire original sample.

Finally the most serious problem is that if the sampling design did not account for that same stratification, you might end up with a very different associated risk distribution in each strata invalidating the comparison of estimates across strata. Use interactions to test for modification, even if the seem difficult to understand, any other analysis is INCORRECT.

Answer 2

One practical difference is that stratified analysis is usually easier for non-statisticians to understand, but analysis with interactions allows more comparisons to be done - in particular, it gives a parameter estimate, p value and confidence interval for the difference.