A Bayesian semiparametric survival model with longitudinal markers

Song Zhang, Peter Müller, Kim Anh Do

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We consider inference for data from a clinical trial of treatments for metastatic prostate cancer. Patients joined the trial with diverse prior treatment histories. The resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment arms. Inference is further complicated by the need to include a longitudinal marker as a covariate. To address these challenges, we develop a semiparametric model for joint inference of longitudinal data and an event time. The proposed approach includes the possibility of cure for some patients. The event time distribution is based on a nonparametric Pólya tree prior. For the longitudinal data we assume a mixed effects model. Incorporating a regression on covariates in a nonparametric event time model in general, and for a Pólya tree model in particular, is a challenging problem. We exploit the fact that the covariate itself is a random variable. We achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal model for the event time and a regression of the longitudinal outcomes on the event time, i.e., we implicitly model the desired regression by modeling the reverse conditional distribution.

Original languageEnglish (US)
Pages (from-to)435-443
Number of pages9
JournalBiometrics
Volume66
Issue number2
DOIs
StatePublished - Jun 2010

Fingerprint

Survival Model
Semiparametric Model
Survival
Regression
Covariates
Longitudinal Data
Joints
Marginal Model
Mixed Effects Model
Joint Model
Prostate Cancer
Factoring
Conditional Distribution
Statistical Inference
Progression
Random variables
Clinical Trials
prostatic neoplasms
Reverse
Prostatic Neoplasms

Keywords

  • Bayesian nonparametric models
  • Pólya tree
  • Regression
  • Survival

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Medicine(all)

Cite this

A Bayesian semiparametric survival model with longitudinal markers. / Zhang, Song; Müller, Peter; Do, Kim Anh.

In: Biometrics, Vol. 66, No. 2, 06.2010, p. 435-443.

Research output: Contribution to journalArticle

Zhang, Song ; Müller, Peter ; Do, Kim Anh. / A Bayesian semiparametric survival model with longitudinal markers. In: Biometrics. 2010 ; Vol. 66, No. 2. pp. 435-443.
@article{fbdc1bccca3c46468dc60caf0dbcd083,
title = "A Bayesian semiparametric survival model with longitudinal markers",
abstract = "We consider inference for data from a clinical trial of treatments for metastatic prostate cancer. Patients joined the trial with diverse prior treatment histories. The resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment arms. Inference is further complicated by the need to include a longitudinal marker as a covariate. To address these challenges, we develop a semiparametric model for joint inference of longitudinal data and an event time. The proposed approach includes the possibility of cure for some patients. The event time distribution is based on a nonparametric P{\'o}lya tree prior. For the longitudinal data we assume a mixed effects model. Incorporating a regression on covariates in a nonparametric event time model in general, and for a P{\'o}lya tree model in particular, is a challenging problem. We exploit the fact that the covariate itself is a random variable. We achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal model for the event time and a regression of the longitudinal outcomes on the event time, i.e., we implicitly model the desired regression by modeling the reverse conditional distribution.",
keywords = "Bayesian nonparametric models, P{\'o}lya tree, Regression, Survival",
author = "Song Zhang and Peter M{\"u}ller and Do, {Kim Anh}",
year = "2010",
month = "6",
doi = "10.1111/j.1541-0420.2009.01276.x",
language = "English (US)",
volume = "66",
pages = "435--443",
journal = "Biometrics",
issn = "0006-341X",
publisher = "Wiley-Blackwell",
number = "2",

}

TY - JOUR

T1 - A Bayesian semiparametric survival model with longitudinal markers

AU - Zhang, Song

AU - Müller, Peter

AU - Do, Kim Anh

PY - 2010/6

Y1 - 2010/6

N2 - We consider inference for data from a clinical trial of treatments for metastatic prostate cancer. Patients joined the trial with diverse prior treatment histories. The resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment arms. Inference is further complicated by the need to include a longitudinal marker as a covariate. To address these challenges, we develop a semiparametric model for joint inference of longitudinal data and an event time. The proposed approach includes the possibility of cure for some patients. The event time distribution is based on a nonparametric Pólya tree prior. For the longitudinal data we assume a mixed effects model. Incorporating a regression on covariates in a nonparametric event time model in general, and for a Pólya tree model in particular, is a challenging problem. We exploit the fact that the covariate itself is a random variable. We achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal model for the event time and a regression of the longitudinal outcomes on the event time, i.e., we implicitly model the desired regression by modeling the reverse conditional distribution.

AB - We consider inference for data from a clinical trial of treatments for metastatic prostate cancer. Patients joined the trial with diverse prior treatment histories. The resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment arms. Inference is further complicated by the need to include a longitudinal marker as a covariate. To address these challenges, we develop a semiparametric model for joint inference of longitudinal data and an event time. The proposed approach includes the possibility of cure for some patients. The event time distribution is based on a nonparametric Pólya tree prior. For the longitudinal data we assume a mixed effects model. Incorporating a regression on covariates in a nonparametric event time model in general, and for a Pólya tree model in particular, is a challenging problem. We exploit the fact that the covariate itself is a random variable. We achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal model for the event time and a regression of the longitudinal outcomes on the event time, i.e., we implicitly model the desired regression by modeling the reverse conditional distribution.

KW - Bayesian nonparametric models

KW - Pólya tree

KW - Regression

KW - Survival

UR - http://www.scopus.com/inward/record.url?scp=77952992326&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77952992326&partnerID=8YFLogxK

U2 - 10.1111/j.1541-0420.2009.01276.x

DO - 10.1111/j.1541-0420.2009.01276.x

M3 - Article

VL - 66

SP - 435

EP - 443

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 2

ER -