Bayesian Analysis of the Proportional Hazards Model with Time‐Varying Coefficients

Kim, Gwangsu; Kim, Yongdai; Choi, Tae-Yong

doi:10.1111/sjos.12263

Cited by 12 publications

(2 citation statements)

References 43 publications

(63 reference statements)

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“…In unreported numerical studies, we have found that these three choices lead to little practical difference in the properties of θ n (x) for x γ and n ≥ 1000. Kim et al (2017) proved that the rate of converge of the posterior distribution of the nonparametric Bayesian estimator proposed by Kim et al ( 2011) is (n/log n) −1/3 , which is the same as the pointwise rate of convergence of our estimator up to a log factor. However, to the best of our knowledge, it is not known whether the posterior distribution of the estimator proposed by Kim et al (2011) yields asymptotically calibrated confidence intervals for θ(x).…”

Section: Convergence In Distributionsupporting

confidence: 67%

Nonparametric inference under a monotone hazard ratio order

Wu¹,

Westling²

2022

Preprint

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The ratio of the hazard functions of two populations or two strata of a single population plays an important role in time-to-event analysis. Cox regression is commonly used to estimate the hazard ratio under the assumption that it is constant in time, which is known as the proportional hazards assumption. However, this assumption is often violated in practice, and when it is violated, the parameter estimated by Cox regression is difficult to interpret. The hazard ratio can be estimated in a nonparametric manner using smoothing, but smoothingbased estimators are sensitive to the selection of tuning parameters, and it is often difficult to perform valid inference with such estimators. In some cases, it is known that the hazard ratio function is monotone. In this article, we demonstrate that monotonicity of the hazard ratio function defines an invariant stochastic order, and we study the properties of this order. Furthermore, we introduce an estimator of the hazard ratio function under a monotonicity constraint. We demonstrate that our estimator converges in distribution to a mean-zero limit, and we use this result to construct asymptotically valid confidence intervals. Finally, we conduct numerical studies to assess the finite-sample behavior of our estimator, and we use our methods to estimate the hazard ratio of progression-free survival in pulmonary adenocarcinoma patients treated with Gefitinib or carboplatin-paclitaxel.

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Section: Convergence In Distributionsupporting

confidence: 67%

Nonparametric inference under a monotone hazard ratio order

Wu¹,

Westling²

2022

Preprint

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“…Second, the proposed Bayesian inference for the PH model is developed based on the full likelihood with data augmentation. A valuable alternative is the partial likelihood‐based Bayesian inference procedure proposed by Kim et al, 40 which is asymptotically equivalent to the full likelihood‐based approach in terms of posterior convergence rate. Developing the partial likelihood approach in the context of the proposed model is worthy of investigation in the future.…”

Section: Discussionmentioning

confidence: 99%

Joint analysis of mixed types of outcomes with latent variables

Pan

Wei

Song

2020

Statistics in Medicine

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We propose a joint modeling approach to investigating the observed and latent risk factors of mixed types of outcomes. The proposed model comprises three parts. The first part is an exploratory factor analysis model that summarizes latent factors through multiple observed variables. The second part is a proportional hazards model that examines the observed and latent risk factors of multivariate time‐to‐event outcomes. The third part is a linear regression model that investigates the determinants of a continuous outcome. We develop a Bayesian approach coupled with MCMC methods to determine the number of latent factors, the association between latent and observed variables, and the important risk factors of different types of outcomes. A modified stochastic search item selection algorithm, which introduces normal‐mixture‐inverse gamma priors to factor loadings and regression coefficients, is developed for simultaneous model selection and parameter estimation. The proposed method is subjected to simulation studies for empirical performance assessment and then applied to a study concerning the risk factors of type 2 diabetes and the associated complications.

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Bayesian analysis under accelerated failure time models with error-prone time-to-event outcomes

Tang

Song

2022

Lifetime Data Anal

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Bayesian Analysis of the Proportional Hazards Model with Time‐Varying Coefficients

Cited by 12 publications

References 43 publications

Nonparametric inference under a monotone hazard ratio order

Nonparametric inference under a monotone hazard ratio order

Joint analysis of mixed types of outcomes with latent variables

Bayesian analysis under accelerated failure time models with error-prone time-to-event outcomes

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