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45
Accounting for Model Uncertainty in Survival Analysis Improves Predictive Performance
 In Bayesian Statistics 5
, 1995
"... Survival analysis is concerned with finding models to predict the survival of patients or to assess the efficacy of a clinical treatment. A key part of the modelbuilding process is the selection of the predictor variables. It is standard to use a stepwise procedure guided by a series of significanc ..."
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Cited by 39 (12 self)
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Survival analysis is concerned with finding models to predict the survival of patients or to assess the efficacy of a clinical treatment. A key part of the modelbuilding process is the selection of the predictor variables. It is standard to use a stepwise procedure guided by a series of significance tests to select a single model, and then to make inference conditionally on the selected model. However, this ignores model uncertainty, which can be substantial. We review the standard Bayesian model averaging solution to this problem and extend it to survival analysis, introducing partial Bayes factors to do so for the Cox proportional hazards model. In two examples, taking account of model uncertainty enhances predictive performance, to an extent that could be clinically useful. 1 Introduction From 1974 to 1984 the Mayo Clinic conducted a doubleblinded randomized clinical trial involving 312 patients to compare the drug DPCA with a placebo in the treatment of primary biliary cirrhosis...
Semiparametric Bayesian Analysis Of Survival Data
 Journal of the American Statistical Association
, 1996
"... this paper are motivated and aimed at analyzing some common types of survival data from different medical studies. We will center our attention to the following topics. ..."
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Cited by 23 (0 self)
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this paper are motivated and aimed at analyzing some common types of survival data from different medical studies. We will center our attention to the following topics.
Bayesian Variable Selection for Proportional Hazards Models
, 1996
"... The authors consider the problem of Bayesian variable selection for proportional hazards regression models with right censored data. They propose a semiparametric approach in which a nonparametric prior is specified for the baseline hazard rate and a fully parametric prior is specified for the regr ..."
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Cited by 15 (1 self)
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The authors consider the problem of Bayesian variable selection for proportional hazards regression models with right censored data. They propose a semiparametric approach in which a nonparametric prior is specified for the baseline hazard rate and a fully parametric prior is specified for the regression coe#cients. For the baseline hazard, they use a discrete gamma process prior, and for the regression coe#cients and the model space, they propose a semiautomatic parametric informative prior specification that focuses on the observables rather than the parameters. To implement the methodology, they propose a Markov chain Monte Carlo method to compute the posterior model probabilities. Examples using simulated and real data are given to demonstrate the methodology. R ESUM E Les auteurs abordent d'un point de vue bayesien le problemedelaselection de variables dans les modeles de regression des risques proportionnels en presence de censure a droite. Ils proposent une approche semip...
Bayesian information criterion for censored survival models
 Biometrics
"... We investigate the Bayesian Information Criterion (BIC) for variable selection in models for censored survival data. Kass and Wasserman (1995) showed that BIC provides a close approximation to the Bayes factor when a unitinformation prior on the parameter space is used. We propose a revision of the ..."
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Cited by 15 (2 self)
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We investigate the Bayesian Information Criterion (BIC) for variable selection in models for censored survival data. Kass and Wasserman (1995) showed that BIC provides a close approximation to the Bayes factor when a unitinformation prior on the parameter space is used. We propose a revision of the penalty term in BIC so that it is de ned in terms of the number of uncensored events instead of the number of observations. For the simplest censored data model, that of exponential distributions of survival times (i.e. a constant hazard rate), this revision results in a better approximation to the exact Bayes factor based on a conjugate unitinformation prior. In the Cox proportional hazards regression model, we propose de ning BIC in terms of the maximized partial likelihood. Using the number of deaths rather than the number of individuals in the BIC penalty term corresponds to a more realistic prior on the parameter space, and is shown to improve predictive performance for assessing stroke risk in the Cardiovascular Health Study.
Bayesian Semiparametric Inference for the Accelerated Failure Time Model
, 1997
"... Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regressio ..."
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Cited by 14 (0 self)
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Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regression coefficients and a mixtureofDirichletprocesses prior on the unknown error distribution. A Markov chain Monte Carlo (MCMC) method is developed to compute the features of the posterior distribution. A model selection method for obtaining a more parsimonious set of predictors is studied. The method adds indicator variables to the regression equation. The set of indicator variables represents all the possible subsets to be considered. A MCMC method is developed to search stochastically for the best subset. These procedures are applied to two examples, one with censored data. Key words and phrases: Censored data; Log linear model; Markov chain Monte Carlo algorithm; Metropolis algori...
Bayesian Analysis of Multivariate Survival Data Using Monte Carlo Methods
 Canadian Journal of Statistics
, 1995
"... This paper deals with the analysis of multivariate survival data from a Bayesian perspective using Markov Chain Monte Carlo methods. Metropolis along with Gibbs algorithm (Metropolis et al., 1953; Muller, 1991) is used to calculate some of the marginal posteriors. Multivariate survival model is prop ..."
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Cited by 10 (4 self)
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This paper deals with the analysis of multivariate survival data from a Bayesian perspective using Markov Chain Monte Carlo methods. Metropolis along with Gibbs algorithm (Metropolis et al., 1953; Muller, 1991) is used to calculate some of the marginal posteriors. Multivariate survival model is proposed since, survival times within the same `group' are correlated as a consequence of a frailty random block effect (Vaupel et al., 1979). The conditional proportional hazards model of Clayton and Cuzick (1985) is used with a martingale structured prior process (Arjas and Gasbarra, 1994) for the discretized baseline hazard. Besides the calculation of the marginal posteriors of the parameters of interest, this paper presents some Bayesian EDA diagnostic techniques to detect model adequacy. The methodology is exemplified with the kidney infection data where the times to infections within the same patients are expected to be correlated. Key Words: Autocorrelated prior process, credible regions,...
On Posterior Consistency of Survival Models
 ANN. STATIST
, 1999
"... Ghosh and Ramamoorthi (1995) studied the posterior consistency for survival models and showed that the posterior was consistent, when the prior on the distribution of survival times was the Dirichlet process prior. In this paper, we study the posterior consistency of survival models with neutral to ..."
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Cited by 10 (1 self)
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Ghosh and Ramamoorthi (1995) studied the posterior consistency for survival models and showed that the posterior was consistent, when the prior on the distribution of survival times was the Dirichlet process prior. In this paper, we study the posterior consistency of survival models with neutral to the right process priors which include Dirichlet process priors. A set of sufficient conditions for the posterior consistency with neutral to the right process priors is given. Interestingly, not all the neutral to the right process priors have consistent posteriors, but most of the popular priors such as Dirichlet processes, beta processes and gamma processes have consistent posteriors. With a class of priors which includes beta processes, a necessary and sufficient condition for the consistency is also established. An interesting counter intuitive phenomenon is found. Suppose there are two priors centered at the true parameter value with finite variances. Surprisingly, the posterior with s...
Bayesian semiparametric dynamic frailty models for multiple event time data
 Biometrics
, 2006
"... Many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly, such as infection, hospitalization, recurrence of disease, or tumor onset. To analyze such data, it is necessary to account for withinsubject dependency in the multiple event times. Motivated ..."
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Cited by 9 (6 self)
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Many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly, such as infection, hospitalization, recurrence of disease, or tumor onset. To analyze such data, it is necessary to account for withinsubject dependency in the multiple event times. Motivated by data from studies of palpable tumors, this article proposes a dynamic frailty model and Bayesian semiparametric approach to inference. The widely used shared frailty proportional hazards model is generalized to allow subjectspecific frailties to change dynamically with age while also accommodating nonproportional hazards. Parametric assumptions on the frailty distribution are avoided by using Dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty. By centering the semiparametric model on a conditionallyconjugate dynamic gamma model, we facilitate posterior computation and lack of fit assessments of the parametric model. Our proposed method is demonstrated using data from a cancer chemoprevention study.
Bayesian Inferences in the Cox Model for Order Restricted Hypotheses
"... ... This article proposes a Bayesian approach for addressing hypotheses of this type. Ve reparameterize the Cox model in terms of a cumulative product of parameters having conjugate prior densities, consisting of mixtures of point masses at one and truncated garnma densities. Due to the structure of ..."
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Cited by 7 (4 self)
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... This article proposes a Bayesian approach for addressing hypotheses of this type. Ve reparameterize the Cox model in terms of a cumulative product of parameters having conjugate prior densities, consisting of mixtures of point masses at one and truncated garnma densities. Due to the structure of the model, posterior computation can proceed via a simple and efficient Gibbs sampling algorithm. Posterior probabilities for the global null hypothesis and subhypotheses coinparing the hazards fbr specific groups eau be calcnlated directly from the output of a single Gibbs ('.hain. The approach allows for level sets across which a predictor has no effect. Generalizations to multiple predictors are described, and the method is applied to a study of emergency medical treatment for stroke.
HIGHER ORDER SEMIPARAMETRIC FREQUENTIST INFERENCE WITH THE PROFILE SAMPLER
 SUBMITTED TO THE ANNALS OF STATISTICS
, 2006
"... We consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution. The first order validity of this procedure established by Lee, Kosorok and Fine (2005) is extended to second order validity in the setting ..."
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Cited by 7 (5 self)
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We consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution. The first order validity of this procedure established by Lee, Kosorok and Fine (2005) is extended to second order validity in the setting where the infinite dimensional nuisance parameter achieves the parametric rate. Specifically, we obtain higher order estimates of the maximum profile likelihood estimator and of the efficient Fisher information. Moreover, we prove that an exact frequentist confidence interval for the parametric component at level alpha can be estimated by the alpha level credible set from the profile sampler with an error of order OP (n −1). As far as we are aware, these results are the first higher order frequentist results obtained for semiparametric estimation. A fully Bayesian interpretation is established under a certain data dependent prior. The theory is verified for three specific examples.