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Proportional hazards and threshold regression: their theoretical and practical connections.

Authors
Lee-ML; Whitmore-GA
Source
Lifetime Data Anal 2010 Apr; 16(2):196-214
NIOSHTIC No.
20037029
Abstract
Proportional hazards (PH) regression is a standard methodology for analyzing survival and time-to-event data. The proportional hazards assumption of PH regression, however, is not always appropriate. In addition, PH regression focuses mainly on hazard ratios and thus does not offer many insights into underlying determinants of survival. These limitations have led statistical researchers to explore alternative methodologies. Threshold regression (TR) is one of these alternative methodologies (see Lee and Whitmore, Stat Sci 21:501-513, 2006, for a review). The connection between PH regression and TR has been examined in previous published work but the investigations have been limited in scope. In this article, we study the connections between these two regression methodologies in greater depth and show that PH regression is, for most purposes, a special case of TR. We show two methods of construction by which TR models can yield PH functions for survival times, one based on altering the TR time scale and the other based on varying the TR boundary. We discuss how to estimate the TR time scale and boundary, with or without the PH assumption. A case demonstration is used to highlight the greater understanding of scientific foundations that TR can offer in comparison to PH regression. Finally, we discuss the potential benefits of positioning PH regression within the first-hitting-time context of TR regression.
Keywords
Analytical-methods; Analytical-models; Analytical-processes; Exposure-levels; Exposure-methods; Mathematical-models; Statistical-analysis; Workplace-studies; Mathematical-models; Risk-analysis; Author Keywords: Brownian motion; First hitting time; Gamma process; Poisson process; Process time; Renewal process; Stochastic process; Survival time; Time to event
Contact
Mei-Ling Ting Lee, University of Maryland, College Park, MD 20740, USA
CODEN
LDANFI
Publication Date
20100401
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
2
ISSN
1380-7870
Source Name
Lifetime Data Analysis
State
MD
Performing Organization
University of Maryland - College Park
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