A dependent Dirichlet process model for survival data with competing risks
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A dependent Dirichlet process model for survival data with competing risks Yushu Shi1
· Purushottam Laud2 · Joan Neuner2
Received: 5 February 2019 / Accepted: 12 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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.
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10985020-09506-0) contains supplementary material, which is available to authorized users.
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Yushu Shi [email protected] Purushottam Laud [email protected] Joan Neuner [email protected]
1
University of Missouri, Columbia, Middlebush Hall, Columbia, MO 65201, USA
2
Medical College of Wisconsin, CAPS, 8701 Watertown Plank Rd, Milwaukee, WI 53226, USA
123
Y. Shi et al.
Keywords Survival analysis · Competing risks · Nonparametric Bayesian model · Time-dependent covariate
1 Introduction Among survival regression models, Cox model is used most frequently (Cox 1972). Taking the multiplicative covariate effect assumption from the Cox model, Fine and Gray (1999) proposed a model based on the subdistribution hazards for competing risks data. As both models are valid only when the proportional hazards (subdistribution hazards) assumption is not strongly violated, it is desirable to have a model without such an assumption that provides robust yet interpretable results. To provide such a flexible model, De Iorio et al. (2004) proposed a nonparametric Bayesian ANOVA method employing a dependent Dirichlet process (DDP). They then adapted their model for continuous covariates in De Iorio et al. (2009). Inspired by the latter DDP model based on mixture of normal distributions and Kottas (2006)’s mixture of Weibull distributions mo
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