The Conditional Prediction Function: A Novel Technique to Control False Discovery Rate for Complex Models

In modern scientific research, the objective is often to identify which variables are associated with an outcome among a large class of potential predictors. This goal can be achieved by selecting variables in a manner that controls the the false discovery rate (FDR), the proportion of irrelevant predictors among the selections. Knockoff filtering is a cutting-edge approach to variable selection that provides FDR control. Existing knockoff statistics frequently employ linear models to assess relationships between features and the response, but the linearity assumption is often violated in real world applications. This may result in poor power to detect truly prognostic variables. We introduce a knockoff statistic based on the conditional prediction function (CPF), which can pair with state-of-art machine learning predictive models, such as deep neural networks. The CPF statistics can capture the nonlinear relationships between predictors and outcomes while also accounting for correlation between features. We illustrate the capability of the CPF statistics to provide superior power over common knockoff statistics with continuous, categorical, and survival outcomes using repeated simulations. Knockoff filtering with the CPF statistics is demonstrated using (1) a residential building dataset to select predictors for the actual sales prices and (2) the TCGA dataset to select genes that are correlated with disease staging in lung cancer patients.