Proportional hazards models: a latent competing risk approach

We propose a novel semiparametric version of the widely used proportional hazards survival model. Features include an arbitrarily rich class of continuous base-line hazards, an attractive epidemiological interpretation of the hazard as a latent competing risk model and trivial handling of censoring. Models are fitted by using a data augmentation scheme. The methodology is applied to a data set recording times to first hospitalization following clinical diagnosis of acquired immune deficiency syndrome for a sample of 169 patients.

[1]  B. Efron.  Logistic Regression, Survival Analysis, and the Kaplan-Meier Curve , 1988 .

[2]  W. Gilks,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 1992 .

[3]  B. Carlin,et al.  Bayesian Model Choice Via Markov Chain Monte Carlo Methods , 1995 .

[4]  J. Kalbfleisch.  Non‐Parametric Bayesian Analysis of Survival Time Data , 1978 .

[5]  A. Gelfand,et al.  Bayesian analysis of proportional hazards models built from monotone functions. , 1995, Biometrics.

[6]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

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

[8]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[9]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[10]  M Gail,et al.  A review and critique of some models used in competing risk analysis. , 1975, Biometrics.

[11]  N. Hjort.  Nonparametric Bayes Estimators Based on Beta Processes in Models for Life History Data , 1990 .

[12]  Adrian F. M. Smith,et al.  Bayesian Inference for Generalized Linear and Proportional Hazards Models Via Gibbs Sampling , 1993 .

[13]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[14]  Purushottam W. Laud,et al.  A Bayesian Nonparametric Approach to Reliability , 1981 .

[15]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[16]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[17]  D. Cox,et al.  Analysis of Survival Data. , 1985 .

[18]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[19]  James J. Heckman,et al.  The identifiability of the competing risks model , 1989 .

[20]  D P Byar,et al.  Dependent competing risks and the latent-failure model. , 1988, Biometrics.

[21]  John Hinde,et al.  Statistical Modelling in GLIM. , 1989 .

[22]  N. Breslow.  Covariance analysis of censored survival data. , 1974, Biometrics.

[23]  V T Farewell,et al.  The analysis of failure times in the presence of competing risks. , 1978, Biometrics.