Variable Selection for Qualitative Interactions in Personalized Medicine While Controlling the Family-Wise Error Rate

Abstract

For many years, subset analysis has been a popular topic for the biostatistics and clinical trials literature. In more recent years, the discussion has focused on finding subsets of genomes which play a role in the effect of treatment, often referred to as stratified or personalized medicine. Though highly sought after, methods for detecting subsets with altering treatment effects are limited and lacking in power. In this article we discuss variable selection for qualitative interactions with the aim to discover these critical patient subsets. We propose a new technique designed specifically to find these interaction variables among a large set of variables while still controlling for the number of false discoveries. We compare this new method against standard qualitative interaction tests using simulations and give an example of its use on data from a randomized controlled trial for the treatment of depression.

Key Words:

• Lasso
• Personalized medicine
• Qualitative interactions
• Variable selection

ACKNOWLEDGMENTS

We thank Martin Keller and the investigators who conducted the trial “A Comparison of Nefazodone, the Cognitive Behavioral-analysis System of Psychotherapy, and Their Combination for Treatment of Chronic Depression” for use of their data, and gratefully acknowledge Bristol-Myers Squibb for helping fund the study. We also acknowledge financial support from NIDA grant P50 DA10075, NIMH grant R01 MH080015, and NSF grants DMS 0505432 and DMS 0705532, and technical support from the Vice-Dean, Prof. A. John Rush, MD, at Duke-NUS Graduate Medical School, Singapore.

Notes

Note. The first two columns list the desired significance level and the method. AGVL stands for AGV Lasso, LRT stands for the Gail–Simon likelihood ratio test, SVE for the Shuster–Van Eys test, Bonferroni stands for a Bonferroni correction, and permute stands for the permutation-based multiplicity correction. The last eight columns give the percentage of time one or more spurious qualitative interactions was selected over the 200 repetitions for each generative model. Stared percentages fall outside the 95% confidence interval for the desired significance level.

Note. The first two columns list the desired significance level and the method. AGVL stands for AGV Lasso, LRT stands for the Gail–Simon likelihood ratio test, SVE for the Shuster–Van Eys test, Bonferroni stands for a Bonferroni correction, and permute stands for the permutation-based multiplicity correction. The last four columns give the percentage of time the true qualitative interaction was selected over the 200 repetitions for each generative model. Bolded percentages correlate with settings where the desired significance level was maintained.