title: On the uncertainty of individual prediction because of sampling predictors.
abstract: 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.
authors.affiliation: Department of Biostatistics, School of Medicine, Richard M. Fairbanks School of Public Health, Indiana University, Indianapolis, IN, 46202, U.S.A.
authors.forename: Changyu
authors.initials: C
authors.lastname: Shen
authors.affiliation: Department of Biostatistics, School of Medicine, Richard M. Fairbanks School of Public Health, Indiana University, Indianapolis, IN, 46202, U.S.A.
authors.forename: Xiaochun
authors.initials: X
authors.lastname: Li
mesh_terms: D035843:Biomedical Research / Q000379:methods; D005544:Forecasting; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D008962:Models, Theoretical; D011336:Probability; D016016:Proportional Hazards Models; D012107:Research Design; D012494:Sampling Studies; D035501:Uncertainty
keywords: conditional distribution; frequentist principle; prediction uncertainty; predictor-sampling variation; subject-sampling variation