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Threshold regression for survival data with time-varying covariates.

Authors
Lee-ML; Whitmore-GA; Rosner-BA
Source
Stat Med 2010 Mar; 29(7-8):896-905
NIOSHTIC No.
20036958
Abstract
Time-to-event data with time-varying covariates pose an interesting challenge for statistical modeling and inference, especially where the data require a regression structure but are not consistent with the proportional hazard assumption. Threshold regression (TR) is a relatively new methodology based on the concept that degradation or deterioration of a subject's health follows a stochastic process and failure occurs when the process first reaches a failure state or threshold (a first-hitting-time). Survival data with time-varying covariates consist of sequential observations on the level of degradation and/or on covariates of the subject, prior to the occurrence of the failure event. Encounters with this type of data structure abound in practical settings for survival analysis and there is a pressing need for simple regression methods to handle the longitudinal aspect of the data. Using a Markov property to decompose a longitudinal record into a series of single records is one strategy for dealing with this type of data. This study looks at the theoretical conditions for which this Markov approach is valid. The approach is called threshold regression with Markov decomposition or Markov TR for short. A number of important special cases, such as data with unevenly spaced time points and competing risks as stopping modes, are discussed. We show that a proportional hazards regression model with time-varying covariates is consistent with the Markov TR model. The Markov TR procedure is illustrated by a case application to a study of lung cancer risk. The procedure is also shown to be consistent with the use of an alternative time scale. Finally, we present the connection of the procedure to the concept of a collapsible survival model.
Keywords
Accident-analysis; Accident-statistics; Analytical-methods; Analytical-processes; Exposure-assessment; Exposure-levels; Exposure-methods; Mathematical-models; Risk-analysis; Statistical-analysis; Survival-rate; Worker-health; Author Keywords: competing risks; first-hitting-time; latent process; longitudinal data; Markov property; stopping time; unevenly spaced time points; Wiener diffusion process
Contact
Mei-Ling Ting Lee, Department of Epidemiology and Biostatistics, University of Maryland, College Park, MD 20740, USA
CODEN
SMEDDA
Publication Date
20100330
Document Type
Journal Article
Email Address
mltlee@umd.edu
Funding Type
Grant
Fiscal Year
2010
NTIS Accession No.
NTIS Price
Identifying No.
Grant-Number-R01-OH-008649
Issue of Publication
7-8
ISSN
0277-6715
Source Name
Statistics in Medicine
State
MD; MA
Performing Organization
University of Maryland - College Park
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