Using an Anchor to Improve Linear Predictions with Application to Predicting Disease Progression

Linear models are some of the most straightforward and commonly used modelling approaches. Consider modelling approximately monotonic response data arising from a time-related process. If one has knowledge as to when the process began or ended, then one may be able to leverage additionalassumed data to reduce prediction error. This assumed data, referred to as the anchor, is treated as an additional data-point generated at either the beginning or end of the process. The response value of the anchor is equal to an intelligently selected value of the response (such as the upper bound, lower bound, or 99th percentile of the response, as appropriate). The anchor reduces the variance of prediction at the cost of a possible increase in prediction bias, resulting in a potentially reduced overall mean-square prediction error. This can be extremely eective when few individual data-points are available, allowing one to make linear predictions using as little as a single observed data-point. We develop the mathematics showing the conditions under which an anchor can improve predictions, and also demonstrate using this approach to reduce prediction error when modelling the disease progression of patients with amyotrophic lateral sclerosis.

• Autores: Karanevich, Alex G.; He, Jianghua; Gajewski, Byron
• Tipo de recurso: Article of journal
• Fecha de publicación: 2018
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/66487
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/66487; http://bdigital.unal.edu.co/67515/
• Palabra clave: 51 Matemáticas / Mathematics; 31 Colecciones de estadística general / Statistics; Anclaje; esclerosis lateral amiotrófica; modelos lineales; mínimos cuadrados ordinarios; regresión sesgada; Anchor; Amyotrophic lateral sclerosis; Biased regression; Linear models; Ordinary least squares
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional