On the uncertainty of individual prediction because of sampling predictors

Prediction of an outcome for a given unit based on prediction models built on a training sample plays a major role in many research areas. The uncertainty of the prediction is predominantly characterized by the subject sampling variation in current practice, where prediction models built on hypothetically re‐sampled units yield variable predictions for the same unit of interest. It is almost always true that the predictors used to build prediction models are simply a subset of the entirety of factors related to the outcome. Following the frequentist principle, we can account for the variation because of hypothetically re‐sampled predictors used to build the prediction models. This is particularly important in medicine where the prediction has important and sometime life‐death consequences on a patient's health status. In this article, we discuss some rationale along this line in the context of medicine. We propose a simple approach to estimate the standard error of the prediction that accounts for the variation because of sampling both subjects and predictors under logistic and Cox regression models. A simulation study is presented to support our argument and demonstrate the performance of our method. The concept and method are applied to a real data set. Copyright © 2015 John Wiley & Sons, Ltd.