Estimating a positive false discovery rate for variable selection in pharmacogenetic studies

Selecting predictors to optimize the outcome prediction is an important statistical method. However, it usually ignores the false positives in the selected predictors. In this paper, we develop a positive false discovery rate (pFDR) estimate for a conventional step-wise forward variable selection procedure. We propose two views of a variable selection process, an overall and an individual test. An interesting feature of the overall test is that its power of selecting non-null predictors increases with the proportion of non-null predictors among all candidate predictors. Data analysis is illustrated with a pharmacogenetics example.