Stepwise regression to screen for covariates

Steve Simon


[StATS]: Stepwise regression to screen for covariates (November 25, 2005).

Someone wrote asking about how best to use stepwise regression in a research problem where there were a lot of potential covariates. A covariate is a variable which may affect your outcome but which is not of direct interest. You are interested in the covariate only to assure that it does not interfere with your ability to discern a relationship between your outcome and your primary independent variable (usually your treatment or exposure variable).

The writer offered up a couple of approaches. First, include all the covariates (but not the primary independent variable) in a stepwise regression model and then adjust your primary independent variable for those covariates which survive the stepwise regression. Second, include all the covariates and the primary independent variable in a stepwise regression model and then report the final model. If the final model fails to include your primary independent variable, that is just evidence that your primary hypothesis is negative.

The person who wrote in was well aware of the weaknesses of stepwise regression, but for those of you who are not familiar with those weaknesses, please read

which is a summary I made of comments about stepwise regression by Ira Bernstein, Ronan Conroy and Frank Harrell that were published on the email discussion list, stat-l.

The research community is gradually moving away from stepwise regression to other more sophisticated methods, but for now you can probably get a stepwise regression model published in most medical journals. Furthermore, there is no established method for how to use stepwise regression, so you are free to use any approach that is not totally outrageous. Here are some general comments, though.

First, if your goal is to assure that no confounding variables produce an incorrect relation between exercise and breast cancer, then the safest thing to do is to include all the potential covariates in the model and not worry about which ones pass some threshold for inclusion in the model. The drawback to this approach, of course, is that you lose a lot of degrees of freedom.

Second, never let a stepwise regression model violate your notion of common sense. If a particular covariate is known to be important (e.g., cigarette smoking in a cancer study) then exclusion of this covariate on the basis of a stepwise regression approach is a mistake. I like to think of stepwise regression as an intelligent assistant. It offers some help and guidance, but don’t let it dictate the form of your final statistical model.

Third, never let stepwise regression bypass your primary research hypothesis. If a stepwise approach tosses out your primary independent variable, force it back into the equation anyway at the end, because you need to see the confidence interval and p-value associated with this variable.

Finally, as noted above, there are some new approaches that compete very well against stepwise regression in this particular situation. You should examine the use of propensity scores (which I hope to write an example for soon), as these offer all the advantages of including all possible covariates and none of the disadvantages. There is also a book by Frank Harrell on regression modeling approaches that is well worth reading.

You can also browse for pages similar to this one at Category: Covariate adjustment.

You can find an earlier version of this page on my website.