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Semi-parametric survival analysis via Dirichlet process mixtures of the First Hitting Time model

Author

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  • Jonathan A. Race

    (The Ohio State University)

  • Michael L. Pennell

    (The Ohio State University)

Abstract

Time-to-event data often violate the proportional hazards assumption inherent in the popular Cox regression model. Such violations are especially common in the sphere of biological and medical data where latent heterogeneity due to unmeasured covariates or time varying effects are common. A variety of parametric survival models have been proposed in the literature which make more appropriate assumptions on the hazard function, at least for certain applications. One such model is derived from the First Hitting Time (FHT) paradigm which assumes that a subject’s event time is determined by a latent stochastic process reaching a threshold value. Several random effects specifications of the FHT model have also been proposed which allow for better modeling of data with unmeasured covariates. While often appropriate, these methods often display limited flexibility due to their inability to model a wide range of heterogeneities. To address this issue, we propose a Bayesian model which loosens assumptions on the mixing distribution inherent in the random effects FHT models currently in use. We demonstrate via simulation study that the proposed model greatly improves both survival and parameter estimation in the presence of latent heterogeneity. We also apply the proposed methodology to data from a toxicology/carcinogenicity study which exhibits nonproportional hazards and contrast the results with both the Cox model and two popular FHT models.

Suggested Citation

  • Jonathan A. Race & Michael L. Pennell, 2021. "Semi-parametric survival analysis via Dirichlet process mixtures of the First Hitting Time model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 177-194, January.
  • Handle: RePEc:spr:lifeda:v:27:y:2021:i:1:d:10.1007_s10985-020-09514-0
    DOI: 10.1007/s10985-020-09514-0
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    References listed on IDEAS

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    1. Jialiang Li & Mei‐Ling Ting Lee, 2011. "Analysis of failure time using threshold regression with semi‐parametric varying coefficients," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(2), pages 164-182, May.
    2. Lu Tian & David Zucker & L.J. Wei, 2005. "On the Cox Model With Time-Varying Regression Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 172-183, March.
    3. Tong Xingwei & He Xin & Sun Jianguo & Lee Mei-Ling T, 2008. "Joint Analysis of Current Status and Marker Data: An Extension of a Bivariate Threshold Model," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-14, October.
    4. P. Economou & S. Malefaki & C. Caroni, 2015. "Bayesian Threshold Regression Model with Random Effects for Recurrent Events," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 871-898, December.
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    Cited by:

    1. Mei-Ling Ting Lee & G. A. Whitmore, 2023. "Semiparametric predictive inference for failure data using first-hitting-time threshold regression," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 508-536, July.
    2. Chrys Caroni, 2022. "Regression Models for Lifetime Data: An Overview," Stats, MDPI, vol. 5(4), pages 1-11, December.

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