Demystifying the bias from selective inference: A revisit to Dawid’s treatment selection problem

High-dimensional prediction of binary outcomes in the presence of between-study heterogeneity

Many prediction methods have been proposed in the literature, but most of them ignore heterogeneity between populations. Either only data from a single study or population is available for model building and evaluation, or when data from multiple studies make up the training dataset, studies are pooled before model building. As a result, prediction models might perform less than expected when applied to new subjects from new study populations. We propose a linear method for building prediction models with high-dimensional data from multiple studies. Our method explicitly addresses between-population variability and tends to select predictors that are predictive in most of the study populations. We employ empirical Bayes estimators and hence avoid selection bias during the variable selection process. Simulation results demonstrate that the new method works better than other linear prediction methods that ignore the between-study variability. Our method is developed for classification into two groups.