title: Predicted probabilities' relationship to inclusion probabilities.
abstract: It has been shown that under a general multiplicative intercept model for risk, case-control (retrospective) data can be analyzed by maximum likelihood as if they had arisen prospectively, up to an unknown multiplicative constant, which depends on the relative sampling fraction. (1) With suitable auxiliary information, retrospective data can also be used to estimate response probabilities. (2) In other words, predictive probabilities obtained without adjustments from retrospective data will likely be different from those obtained from prospective data. We highlighted this using binary data from Medicare to determine the probability of readmission into the hospital within 30 days of discharge, which is particularly timely because Medicare has begun penalizing hospitals for certain readmissions. (3).
authors: Di Fang is with the Morrison School of Agribusiness, Arizona State University, Mesa. Jenny Chong is with the Department of Neurology, College of Medicine, University of Arizona, Tucson. Jeffrey R. Wilson is with the Department of Economics, W. P. Carey School of Business, Arizona State University, Tempe.
authors: Di
authors: D
authors: Fang
authors: Jenny
authors: J
authors: Chong
authors: Jeffrey R
authors: JR
authors: Wilson
mesh_terms: D016021:Epidemiologic Studies; D006801:Humans; D006278:Medicare / Q000706:statistics & numerical data; D010359:Patient Readmission / Q000706:statistics & numerical data; D011336:Probability; D011446:Prospective Studies; D012107:Research Design; D012189:Retrospective Studies; D014481:United States