The traditional approach to variable selection is to find variables that contribute the most to predicting a new response. Recently I learned of an alternative to this. In modeling variables that determine the effect of a treatment--as for example in a clinical trial of a pharmaceutical--the variable is said to be qualitatively interacting with treatment if, leaving other things fixed, a change in that variable can create a change in which treatment is most effective. These variables are not always strong predictors of the effect but may be important for a physician when deciding on treatment for individual patients. In her PhD thesis Lacey Gunter developed a method for selecting these qualitatively interacting variables that could be missed by algorithms that base selection on prediction. Recently I have worked with her on extending these methods to other models including logistic regression and Cox proportional hazard regression models.
I have two questions:
- What do you think about the value of these new methods?
- In the case of the traditional methods what approach do you prefer? Criteria such as AIC, BIC, Mallows Cp, F tests for entering or dropping variables in stepwise, forward and backward...
The first paper on this came out in Gunter, L., Zhu, J and Murphy, S. A. (2009). Variable selection for qualitative interactions. Statistical Methodology doi:10, 1016/j.stamet.2009.05.003.
The next paper appeared in Gunter,L., Zhu, J. and Murphy, S. A. (2011). Variable selection of qualitative interactions in personalized medicine while controlling the familywise error rate. Journal of Biopharmaceutical Statistics 21, 1063-1078.
The next one appeared in a special issue on variable selection Gunter, L., Chernick, M. R. and Sun, J. (2011). A simple method for variable selection in regression with respect to treatment selection. Pakistan Journal of Statistics and Operations Research 7: 363-380.
You can find the papers at the journal websites. You may have to purchase the article. I might have the pdf files for these articles. Lacey and I have just completed a monograph on this topic which will be published as a SpringerBrief later this year.