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A dependent Dirichlet process model for survival data with competing risks

Author

Listed:
  • Yushu Shi

    (University of Missouri, Columbia)

  • Purushottam Laud

    (Medical College of Wisconsin, CAPS)

  • Joan Neuner

    (Medical College of Wisconsin, CAPS)

Abstract

In this paper, we first propose a dependent Dirichlet process (DDP) model using a mixture of Weibull models with each mixture component resembling a Cox model for survival data. We then build a Dirichlet process mixture model for competing risks data without regression covariates. Next we extend this model to a DDP model for competing risks regression data by using a multiplicative covariate effect on subdistribution hazards in the mixture components. Though built on proportional hazards (or subdistribution hazards) models, the proposed nonparametric Bayesian regression models do not require the assumption of constant hazard (or subdistribution hazard) ratio. An external time-dependent covariate is also considered in the survival model. After describing the model, we discuss how both cause-specific and subdistribution hazard ratios can be estimated from the same nonparametric Bayesian model for competing risks regression. For use with the regression models proposed, we introduce an omnibus prior that is suitable when little external information is available about covariate effects. Finally we compare the models’ performance with existing methods through simulations. We also illustrate the proposed competing risks regression model with data from a breast cancer study. An R package “DPWeibull” implementing all of the proposed methods is available at CRAN.

Suggested Citation

  • Yushu Shi & Purushottam Laud & Joan Neuner, 2021. "A dependent Dirichlet process model for survival data with competing risks," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 156-176, January.
    • Handle: RePEc:spr:lifeda:v:27:y:2021:i:1:d:10.1007_s10985-020-09506-0
    DOI: 10.1007/s10985-020-09506-0
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    References listed on IDEAS

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    1. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
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    3. Malay Naskar & Kalyan Das & Joseph G. Ibrahim, 2005. "A Semiparametric Mixture Model for Analyzing Clustered Competing Risks Data," Biometrics, The International Biometric Society, vol. 61(3), pages 729-737, September.
    4. Maria De Iorio & Wesley O. Johnson & Peter Müller & Gary L. Rosner, 2009. "Bayesian Nonparametric Nonproportional Hazards Survival Modeling," Biometrics, The International Biometric Society, vol. 65(3), pages 762-771, September.
    5. Mário de Castro & Ming‐Hui Chen & Yuanye Zhang, 2015. "Bayesian path specific frailty models for multi‐state survival data with applications," Biometrics, The International Biometric Society, vol. 71(3), pages 760-771, September.
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