Bayesian inference of the fully specified subdistribution model for survival data with competing risks

Competing risks data are routinely encountered in various medical applications due to the fact that patients may die from different causes. Recently, several models have been proposed for fitting such survival data. In this paper, we develop a fully specified subdistribution model for survival data in the presence of competing risks via a subdistribution model for the primary cause of death and conditional distributions for other causes of death. Various properties of this fully specified subdistribution model have been examined. An efficient Gibbs sampling algorithm via latent variables is developed to carry out posterior computations. Deviance information criterion (DIC) and logarithm of the pseudomarginal likelihood (LPML) are used for model comparison. An extensive simulation study is carried out to examine the performance of DIC and LPML in comparing the cause-specific hazards model, the mixture model, and the fully specified subdistribution model. The proposed methodology is applied to analyze a real dataset from a prostate cancer study in detail.

[1]  A. D'Amico,et al.  Impact of postoperative prostate‐specific antigen disease recurrence and the use of salvage therapy on the risk of death , 2010, Cancer.

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

[3]  Gregg E. Dinse,et al.  A mixture model for the regression analysis of competing risks data , 1985 .

[4]  D. Clayton.  A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence , 1978 .

[5]  R. Gray.  A Class of $K$-Sample Tests for Comparing the Cumulative Incidence of a Competing Risk , 1988 .

[6]  Ming-Hui Chen,et al.  Bayesian Inference of Interval-Censored Survival Data , 2012 .

[7]  Robert Gray,et al.  A Proportional Hazards Model for the Subdistribution of a Competing Risk , 1999 .

[8]  Joseph G. Ibrahim,et al.  A Bayesian justification of Cox's partial likelihood , 2003 .

[9]  Ning Li,et al.  A Joint Model for Longitudinal Measurements and Survival Data in the Presence of Multiple Failure Types , 2008, Biometrics.

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

[11]  Jun S. Liu,et al.  The Collapsed Gibbs Sampler in Bayesian Computations with Applications to a Gene Regulation Problem , 1994 .

[12]  Joseph G. Ibrahim,et al.  Monte Carlo Methods in Bayesian Computation , 2000 .

[13]  A. Gelfand,et al.  Bayesian Model Choice: Asymptotics and Exact Calculations , 1994 .

[14]  Jeffrey J. Gaynor,et al.  On the Use of Cause-Specific Failure and Conditional Failure Probabilities: Examples from Clinical Oncology Data , 1993 .

[15]  Xin Huang,et al.  A general joint model for longitudinal measurements and competing risks survival data with heterogeneous random effects , 2011, Lifetime data analysis.

[16]  A A Tsiatis,et al.  Multiple Imputation Methods for Estimating Regression Coefficients in the Competing Risks Model with Missing Cause of Failure , 2001, Biometrics.

[17]  Ming-Hui Chen,et al.  Monte Carlo Estimation of Bayesian Credible and HPD Intervals , 1999 .

[18]  Joseph G. Ibrahim,et al.  Bayesian Survival Analysis , 2004 .

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

[20]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[21]  C. Mann,et al.  A Practical Treatise on Diseases of the Skin , 1889, Atlanta Medical and Surgical Journal (1884).

[22]  J. Vaupel,et al.  The impact of heterogeneity in individual frailty on the dynamics of mortality , 1979, Demography.

[23]  Gang Li,et al.  A Bayesian approach to joint analysis of longitudinal measurements and competing risks failure time data , 2007, Statistics in medicine.

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

[25]  Stephanie N Dixon,et al.  A competing risks model for correlated data based on the subdistribution hazard , 2011, Lifetime data analysis.

[26]  R. Elashoff,et al.  An approach to joint analysis of longitudinal measurements and competing risks failure time data , 2007, Statistics in medicine.

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

[28]  Joseph G. Ibrahim,et al.  Posterior propriety and computation for the Cox regression model with applications to missing covariates , 2006 .