A Flexible Approach to Time-varying Coefficients in the Cox Regression Setting

Daniel J. Sargent

doi:10.1023/A:1009612117342

A Flexible Approach to Time-varying Coefficients in the Cox Regression Setting

Daniel J. Sargent

Quantitative Health Sciences

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

Research on methods for studying time-to-event data (survival analysis) has been extensive in recent years. The basic model in use today represents the hazard function for an individual through a proportional hazards model (Cox, 1972). Typically, it is assumed that a covariate's effect on the hazard function is constant throughout the course of the study. In this paper we propose a method to allow for possible deviations from the standard Cox model, by allowing the effect of a covariate to vary over time. This method is based on a dynamic linear model. We present our method in terms of a Bayesian hierarchical model. We fit the model to the data using Markov chain Monte Carlo methods. Finally, we illustrate the approach with several examples.

Original language	English (US)
Pages (from-to)	13-25
Number of pages	13
Journal	Lifetime Data Analysis
Volume	3
Issue number	1
DOIs	https://doi.org/10.1023/A:1009612117342
State	Published - 1997

Keywords

Dynamic linear model
Hierarchical models
Markov chain Monte Carlo
Smoothing
Survival analysis

ASJC Scopus subject areas

Applied Mathematics

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10.1023/A:1009612117342

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title = "A Flexible Approach to Time-varying Coefficients in the Cox Regression Setting",

abstract = "Research on methods for studying time-to-event data (survival analysis) has been extensive in recent years. The basic model in use today represents the hazard function for an individual through a proportional hazards model (Cox, 1972). Typically, it is assumed that a covariate's effect on the hazard function is constant throughout the course of the study. In this paper we propose a method to allow for possible deviations from the standard Cox model, by allowing the effect of a covariate to vary over time. This method is based on a dynamic linear model. We present our method in terms of a Bayesian hierarchical model. We fit the model to the data using Markov chain Monte Carlo methods. Finally, we illustrate the approach with several examples.",

keywords = "Dynamic linear model, Hierarchical models, Markov chain Monte Carlo, Smoothing, Survival analysis",

author = "Sargent, {Daniel J.}",

note = "Funding Information: This work was supported in part by National Institute of Allergy and Infectious Diseases (NIAID) Contract NO1-AI05073 and NIAID Graduate Training in Biostatistics Grant # 1-T32-A107432-01A1. The author would like to thank Jim Hodges, Brad Carlin, and Patricia Grambsch for helpful discussions and two anonymous referees for comments that greatly improved the manuscript.",

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PY - 1997

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N2 - Research on methods for studying time-to-event data (survival analysis) has been extensive in recent years. The basic model in use today represents the hazard function for an individual through a proportional hazards model (Cox, 1972). Typically, it is assumed that a covariate's effect on the hazard function is constant throughout the course of the study. In this paper we propose a method to allow for possible deviations from the standard Cox model, by allowing the effect of a covariate to vary over time. This method is based on a dynamic linear model. We present our method in terms of a Bayesian hierarchical model. We fit the model to the data using Markov chain Monte Carlo methods. Finally, we illustrate the approach with several examples.

AB - Research on methods for studying time-to-event data (survival analysis) has been extensive in recent years. The basic model in use today represents the hazard function for an individual through a proportional hazards model (Cox, 1972). Typically, it is assumed that a covariate's effect on the hazard function is constant throughout the course of the study. In this paper we propose a method to allow for possible deviations from the standard Cox model, by allowing the effect of a covariate to vary over time. This method is based on a dynamic linear model. We present our method in terms of a Bayesian hierarchical model. We fit the model to the data using Markov chain Monte Carlo methods. Finally, we illustrate the approach with several examples.

KW - Dynamic linear model

KW - Hierarchical models

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KW - Smoothing

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A Flexible Approach to Time-varying Coefficients in the Cox Regression Setting

Abstract

Keywords

ASJC Scopus subject areas

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