Semiparametric Accelerated Failure Time Models for Censored Data

An accelerated failure time (AFT) semiparametric regression model for censored data is analyzed as an alternative to the widely used proportional hazards survival model.The statistical inference is based on a nonparametric Bayesian approach that uses a Dirichlet process prior for the mixing distribution.Consistency of the posterior distribution of the regression parameters in the Euclidean metric is established under certain conditions.Finite sample parameter estimates along with associated measure of un-certainties can be computed by a MCMC method. Simulation studies are presented to provide empirical validation of the new method.Analysis of data from two studies are provided to show the easy applicability of the proposed method.

[1]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[2]  J. Harley,et al.  A step-up procedure for selecting variables associated with survival. , 1975, Biometrics.

[3]  T. Fleming,et al.  Different chemotherapeutic sensitivities and host factors affecting prognosis in advanced ovarian carcinoma versus minimal residual disease. , 1979, Cancer treatment reports.

[4]  J. V. Ryzin,et al.  Regression Analysis with Randomly Right-Censored Data , 1981 .

[5]  T. Ferguson.  BAYESIAN DENSITY ESTIMATION BY MIXTURES OF NORMAL DISTRIBUTIONS , 1983 .

[6]  J. Heckman,et al.  A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data , 1984 .

[7]  D. Freedman,et al.  On the consistency of Bayes estimates , 1986 .

[8]  Geoffrey J. McLachlan,et al.  Mixture models : inference and applications to clustering , 1989 .

[9]  Ronald Christensen,et al.  Modelling accelerated failure time with a Dirichlet process , 1988 .

[10]  Ronald Christensen,et al.  Nonparametric Bayesian analysis of the accelerated failure time model , 1989 .

[11]  Grace L. Yang,et al.  On Bayes Procedures , 1990 .

[12]  Mai Zhou,et al.  Asymptotic Normality of the `Synthetic Data' Regression Estimator for Censored Survival Data , 1992 .

[13]  Lee-Jen Wei,et al.  The accelerated failure time model: a useful alternative to the Cox regression model in survival analysis. , 1992, Statistics in medicine.

[14]  A. Raftery,et al.  Model-based Gaussian and non-Gaussian clustering , 1993 .

[15]  Nancy Reid,et al.  On “A conversation with Sir David Cox” , 1994, Issue 5.2, Spring 2023.

[16]  J. Ghosh,et al.  Consistency of Bayesian inference for survival analysis with or without censoring , 1995 .

[17]  Tze Leung Lai,et al.  Asymptotic Normality of a Class of Adaptive Statistics with Applications to Synthetic Data Methods for Censored Regression , 1995 .

[18]  M. Escobar,et al.  Bayesian Density Estimation and Inference Using Mixtures , 1995 .

[19]  B. Lindsay.  Mixture models : theory, geometry, and applications , 1995 .

[20]  C. Robert.  Mixtures of Distributions: Inference and Estimation , 1996 .

[21]  Uniform rates of estimation in the semiparametric Weibull mixture model , 1996 .

[22]  L. Wasserman,et al.  Practical Bayesian Density Estimation Using Mixtures of Normals , 1997 .

[23]  Hemant Ishwaran.  Exponential posterior consistency via generalized Pólya urn schemes in finite semiparametric mixtures , 1998 .

[24]  L. Wasserman,et al.  The consistency of posterior distributions in nonparametric problems , 1999 .

[25]  J. Ghosh,et al.  POSTERIOR CONSISTENCY OF DIRICHLET MIXTURES IN DENSITY ESTIMATION , 1999 .

[26]  J. Ghosh,et al.  Bayesian analysis of censored data , 1999 .

[27]  B. Mallick,et al.  A Bayesian Semiparametric Accelerated Failure Time Model , 1999, Biometrics.

[28]  M. Campolieti.  Bayesian semiparametric estimation of discrete duration models: an application of the dirichlet process prior , 2001 .

[29]  Yongdai Kim,et al.  On posterior consistency of survival models , 2001 .

[30]  S. Ghosal.  Convergence rates for density estimation with Bernstein polynomials , 2001 .

[31]  A. V. D. Vaart,et al.  Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities , 2001 .

[32]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[33]  L. Wasserman,et al.  Consistency of Bernstein polynomial posteriors , 2002 .

[34]  Michael,et al.  On a Class of Bayesian Nonparametric Estimates : I . Density Estimates , 2008 .

[35]  H. Ishwaran,et al.  DIRICHLET PRIOR SIEVES IN FINITE NORMAL MIXTURES , 2002 .

[36]  Z. Ying,et al.  Rank-based inference for the accelerated failure time model , 2003 .

[37]  W. Johnson,et al.  A Bayesian Semiparametric AFT Model for Interval-Censored Data , 2004 .