Controlling the Local False Discovery Rate in the Adaptive Lasso

• Activity Number: 319
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Joshua Sampson*+ and Nilanjan Chatterjee and Raymond J. Carroll and Samuel Mueller
• Companies: DCEG, National Cancer Institute and National Cancer Institute and Texas A&M University and University of Sydney
• Keywords: adaptive lasso ; local false discovery rate ; fdr ; variable selection ; smoothing

Abstract

The Lasso shrinkage procedure achieved its popularity, in part, by its tendency to shrink estimated coefficients to zero, and its ability to serve as a variable selection procedure. Using data-adaptive weights, the adaptive Lasso modified the original procedure to increase the penalty terms for those variables estimated to be less important by ordinary least squares. Although this modified procedure attained the oracle properties, the resulting models tend to include a large number of ``false positives" in practice. Here, we adapt the concept of local False Discovery Rates (lFDR) so that it applies to the sequence, $\lambda_n$, of smoothing parameters for the adaptive Lasso. We define the lFDR for a given $\lambda_n$ to be the probability that the variable added to the model by decreasing $\lambda_n$ to $\lambda_n -\delta$ is not associated with the outcome, where $\delta$ is a small value. We derive the relationship between lFDR and $\lambda_n$, show lFDR=1 for traditional smoothing parameters, and show how to select $\lambda_n$ so as to achieve a desired lFDR. We then use this method to identify SNPs associated with Prostate Specific Antigen.