title: Ornstein-Uhlenbeck threshold regression for time-to-event data with and without a cure fraction.
abstract: In this paper we propose a threshold regression (TR) model for time to event data related to subject health using a latent Ornstein-Uhlenbeck (OU) process that fails once it hits a boundary value for the first time. Baseline covariates are incorporated into the analysis using a log-link function for the initial state of the health process. The model provides clinically meaningful covariate effects and does not require the proportional hazards assumption of the commonly used Cox model. Unlike TR models based on the Wiener process, the OU model allows increments in the health process to depend on previous values and drifts toward a state of equilibrium or homeostasis, which are present in many biological applications. We also extend our model to incorporate a cure rate for applications with improper survival functions, such as time to tumor recurrence in a cancer clinical trial. Our models are applied to overall and relapse-free survival data of melanoma patients undergoing definitive surgery.
authors.affiliation: U.S. Air Force Institute of Technology, Wright-Patterson Air Force Base, OH, 45433, USA.
authors.forename: Roger
authors.initials: R
authors.lastname: Erich
authors.forename: Michael L
authors.initials: ML
authors.lastname: Pennell
mesh_terms: D002986:Clinical Trials as Topic / Q000706:statistics & numerical data; D018572:Disease-Free Survival; D006801:Humans; D015993:Life Tables; D055641:Mathematical Concepts; D008545:Melanoma / Q000401:mortality / Q000601:surgery; D016016:Proportional Hazards Models; D012044:Regression Analysis; D013269:Stochastic Processes; D016019:Survival Analysis; D013997:Time Factors
references.citation: Lifetime Data Anal. 2004 Sep;10(3):213-27
references.pmid: 15456104
references.citation: Stat Med. 2010 Mar 30;29(7-8):896-905
references.pmid: 20213704
references.citation: Lifetime Data Anal. 2009 Jun;15(2):147-76
references.pmid: 19123058
references.citation: Theor Popul Biol. 1977 Feb;11(1):37-48
references.pmid: 854860
references.citation: Biometrics. 1982 Dec;38(4):1041-6
references.pmid: 7168793
references.citation: Math Biosci. 2007 Aug;208(2):538-51
references.pmid: 17300818
references.citation: Stat Med. 1998 Oct 30;17(20):2381-94
references.pmid: 9819834
references.citation: Lifetime Data Anal. 2004 Dec;10(4):407-23
references.pmid: 15690993
references.citation: Lifetime Data Anal. 2004 Mar;10(1):29-49
references.pmid: 15130049
references.citation: Lifetime Data Anal. 2005 Dec;11(4):511-27
references.pmid: 16328574
references.citation: Stat Med. 1999 Sep 15-30;18(17-18):2529-45
references.pmid: 10474158
references.citation: Biometrics. 1995 Sep;51(3):899-907
references.pmid: 7548707
references.citation: Stat Med. 2007 Aug 30;26(19):3591-611
references.pmid: 17252524
references.citation: J Clin Oncol. 2000 Jun;18(12):2444-58
references.pmid: 10856105
references.citation: Environmetrics. 2004 Aug;15(5):501-512
references.pmid: 16741563
references.citation: Biostatistics. 2010 Jan;11(1):111-26
references.pmid: 19828558