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Ornstein–Uhlenbeck threshold regression for time-to-event data with and without a cure fraction

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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.

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Acknowledgments

This work was supported by the National Institute of Occupational Safety and Health [OH008649].

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Authors and Affiliations

  1. U.S. Air Force Institute of Technology, Wright-Patterson Air Force Base, OH, 45433, USA

    Roger Erich

  2. Division of Biostatistics, College of Public Health, The Ohio State University, 246 Cunz Hall, 1841 Neil Avenue, Columbus, OH, 43210, USA

    Michael L. Pennell

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  1. Roger Erich
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  2. Michael L. Pennell
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Correspondence to Michael L. Pennell.

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Erich, R., Pennell, M.L. Ornstein–Uhlenbeck threshold regression for time-to-event data with and without a cure fraction. Lifetime Data Anal 21, 1–19 (2015). https://doi.org/10.1007/s10985-014-9306-8

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  • DOI: https://doi.org/10.1007/s10985-014-9306-8

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