Bayesian analysis of generalized odds-rate hazards models for survival data
31 Mar 2007-Lifetime Data Analysis (Kluwer Academic Publishers-Plenum Publishers)-Vol. 13, Iss: 2, pp 241-260
TL;DR: A class of nonproportional hazards models known as generalized odds-rate class of regression models, which is general enough to include several commonly used models, such as proportional hazards model, proportional odds model, and accelerated life time model are considered.
Abstract: In the analysis of censored survival data Cox proportional hazards model (1972) is extremely popular among the practitioners. However, in many real-life situations the proportionality of the hazard ratios does not seem to be an appropriate assumption. To overcome such a problem, we consider a class of nonproportional hazards models known as generalized odds-rate class of regression models. The class is general enough to include several commonly used models, such as proportional hazards model, proportional odds model, and accelerated life time model. The theoretical and computational properties of these models have been re-examined. The propriety of the posterior has been established under some mild conditions. A simulation study is conducted and a detailed analysis of the data from a prostate cancer study is presented to further illustrate the proposed methodology.
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TL;DR: A semiparametric Bayesian proportional odds model is proposed in which the baseline event time distribution is estimated nonparametrically by using adaptive monotone splines in a logistic regression model and the potential risk factors are included in the parametric part of the mean structure.
Abstract: Current status data are a type of interval-censored event time data in which all the individuals are either left or right censored. For example, our motivation is drawn from a cross-sectional study, which measured whether or not fibroid onset had occurred by the age of an ultrasound exam for each woman. We propose a semiparametric Bayesian proportional odds model in which the baseline event time distribution is estimated nonparametrically by using adaptive monotone splines in a logistic regression model and the potential risk factors are included in the parametric part of the mean structure. The proposed approach has the advantage of being straightforward to implement using a simple and efficient Gibbs sampler, whereas alternative semiparametric Bayes' event time models encounter problems for current status data. The model is generalized to allow systematic underreporting in a subset of the data, and the methods are applied to an epidemiologic study of uterine fibroids.
41 citations
Cites background from "Bayesian analysis of generalized od..."
...Banerjee et al. (2007) proposed a class of generalized odds-rate hazards models, which includes PO models as a special case....
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TL;DR: A novel expectation-maximization (EM) algorithm under the Gamma-frailty PH model to study bivariate current status data and is robust to the misspecification of the frailty distribution.
32 citations
TL;DR: This paper proposes an efficient and easy-to-implement Bayesian estimation approach for analyzing general interval-censored data, which is a mixture of left-, right-, and interval- censored observations.
Abstract: The proportional hazards (PH) model is the most widely used semiparametric regression model for analyzing right-censored survival data based on the partial likelihood method. However, the partial likelihood does not exist for interval-censored data due to the complexity of the data structure. In this paper, we focus on general interval-censored data, which is a mixture of left-, right-, and interval-censored observations. We propose an efficient and easy-to-implement Bayesian estimation approach for analyzing such data under the PH model. The proposed approach adopts monotone splines to model the baseline cumulative hazard function and allows to estimate the regression parameters and the baseline survival function simultaneously. A novel two-stage data augmentation with Poisson latent variables is developed for the efficient computation. The developed Gibbs sampler is easy to execute as it does not require imputing any unobserved failure times or contain any complicated Metropolis-Hastings steps. Our approach is evaluated through extensive simulation studies and illustrated with two real-life data sets.
32 citations
Cites methods from "Bayesian analysis of generalized od..."
...The newly developed Poisson latent variable augmentation can be extended to the PO model and the generalized odds-rate hazards models (Banerjee et al. 2007) by introducing a gamma frailty term....
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...2000) and the generalized odds-rate hazards models (Banerjee et al. 2007) by introducing a gamma frailty term in the frailty PH model....
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...The proposed method can be modified to fit the PO model (Rabinowitz et al. 2000) and the generalized odds-rate hazards models (Banerjee et al. 2007) by introducing a gamma frailty term in the frailty PH model....
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TL;DR: A semiparametric Bayesian approach for analyzing current status data with the proportional odds model, using monotone splines for the baseline odds function and a novel data augmentation with Poisson latent variables to enable simple updating all of the parameters in the posterior computation.
Abstract: Current status data commonly arise in many fields such as epidemiological studies and cross-sectional tumorigenicity studies. In this article, we propose a semiparametric Bayesian approach for analyzing current status data with the proportional odds model. The use of monotone splines for the baseline odds function and a novel data augmentation with Poisson latent variables enable simple updating all of the parameters in the posterior computation. The proposed approach shows good performance and is compared with the approach in Wang and Dunson (2010) in a simulation study. We also generalize the proposed approach to analyze clustered and multivariate current status data under the frailty proportional odds models.
23 citations
TL;DR: A computationally efficient EM algorithm, facilitated by a gamma-Poisson data augmentation, for maximum likelihood estimation in a class of generalized odds rate mixture cure (GORMC) models with interval-censored data.
Abstract: For semiparametric survival models with interval censored data and a cure fraction, it is often difficult to derive nonparametric maximum likelihood estimation due to the challenge in maximizing the complex likelihood function. In this paper, we propose a computationally efficient EM algorithm, facilitated by a gamma-poisson data augmentation, for maximum likelihood estimation in a class of generalized odds rate mixture cure (GORMC) models with interval censored data. The gamma-poisson data augmentation greatly simplifies the EM estimation and enhances the convergence speed of the EM algorithm. The empirical properties of the proposed method are examined through extensive simulation studies and compared with numerical maximum likelihood estimates. An R package "GORCure" is developed to implement the proposed method and its use is illustrated by an application to the Aerobic Center Longitudinal Study dataset.
22 citations
Cites background from "Bayesian analysis of generalized od..."
...The generalized odds rate (GOR) class of regression models (Bickel 1986; Dabrowska andDoksum 1988; Scharfstein, Tsiatis, and Gilbert 1998; Banerjee et al. 2007), which include the PH and PO models as special cases, have attracted much attention recently....
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References
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TL;DR: The analysis of censored failure times is considered in this paper, where the hazard function is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time.
Abstract: The analysis of censored failure times is considered. It is assumed that on each individual arc available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations are outlined.
28,264 citations
"Bayesian analysis of generalized od..." refers methods in this paper
...... the probability of the survival time to exceed t, is assumed to be absolutely continuous in t > 0. We call S(t|x) the survival function of T given the value of the covariate vector x. Suppose now we are interested in making inference about the effect of x on the survival time T. If there are censored observations in the survival time data, a popular approach for examining the covariate effect is to use Cox proportional hazards model ( Cox ......
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Proceedings Article•
01 Jan 1973
TL;DR: The classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion to provide answers to many practical problems of statistical model fitting.
Abstract: In this paper it is shown that the classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion. This observation shows an extension of the principle to provide answers to many practical problems of statistical model fitting.
18,539 citations
01 Jan 1973
TL;DR: In this paper, it is shown that the classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion.
Abstract: In this paper it is shown that the classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion. This observation shows an extension of the principle to provide answers to many practical problems of statistical model fitting.
15,424 citations
Book•
01 Jan 1984
TL;DR: In this article, the authors give a concise account of the analysis of survival data, focusing on new theory on the relationship between survival factors and identified explanatory variables and conclude with bibliographic notes and further results that can be used for student exercises.
Abstract: The objective of this book is to give a concise account of the analysis of survival data. The book is intended both for the applied statistician and for a wider statistical audience wanting an introduction to this field. Particular attention is paid to new theory on the relationship between survival factors and identified explanatory variables. Each chapter concludes with bibliographic notes and outline statements of further results that can be used for student exercises. (ANNOTATION)
6,299 citations
TL;DR: In this paper, the authors proposed a method for rejection sampling from any univariate log-concave probability density function, which is adaptive: as sampling proceeds, the rejection envelope and the squeezing function converge to the density function.
Abstract: We propose a method for rejection sampling from any univariate log‐concave probability density function. The method is adaptive: As sampling proceeds, the rejection envelope and the squeezing function converge to the density function. The rejection envelope and squeezing function are piece‐wise exponential functions, the rejection envelope touching the density at previously sampled points, and the squeezing function forming arcs between those points of contact. The technique is intended for situations where evaluation of the density is computationally expensive, in particular for applications of Gibbs sampling to Bayesian models with non‐conjugacy. We apply the technique to a Gibbs sampling analysis of monoclonal antibody reactivity.
1,538 citations
"Bayesian analysis of generalized od..." refers methods in this paper
...thus we can use the adaptive rejection algorithm of Gilks and Wild (1992) to draw β. Using the prior in (3.6), the conditional distribution of θ is an inverse gamma distribution given by...
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