Repeated Sieving for Prediction Model Building with High-Dimensional Data

Abstract

Background: The prediction of patients’ outcomes is a key component in personalized medicine. Oftentimes, a prediction model is developed using a large number of candidate predictors, called high-dimensional data, including genomic data, lab tests, electronic health records, etc. Variable selection, also called dimension reduction, is a critical step in developing a prediction model using high-dimensional data. Methods: In this paper, we compare the variable selection and prediction performance of popular machine learning (ML) methods with our proposed method. LASSO is a popular ML method that selects variables by imposing an L1-norm penalty to the likelihood. By this approach, LASSO selects features based on the size of regression estimates, rather than their statistical significance. As a result, LASSO can miss significant features while it is known to over-select features. Elastic net (EN), another popular ML method, tends to select even more features than LASSO since it uses a combination of L1- and L2-norm penalties that is less strict than an L1-norm penalty. Insignificant features included in a fitted prediction model act like white noises, so that the fitted model will lose prediction accuracy. Furthermore, for the future use of a fitted prediction model, we have to collect the data of all the features included in the model, which will cost a lot and possibly lower the accuracy of the data if the number of features is too many. Therefore, we propose an ML method, called repeated sieving, extending the standard regression methods with stepwise variable selection. By selecting features based on their statistical significance, it resolves the over-selection issue with high-dimensional data. Results: Through extensive numerical studies and real data examples, our results show that the repeated sieving method selects far fewer features than LASSO and EN, but has higher prediction accuracy than the existing ML methods. Conclusions: We conclude that our repeated sieving method performs well in both variable selection and prediction, and it saves the cost of future investigation on the selected factors.