Regression analysis of competing risks data via semi-parametric additive hazard model

When the subjects in a study possess different demographic and disease characteristics and are exposed to more than one types of failure, a practical problem is to assess the covariate effects on each type of failure as well as on all-cause failure. The most widely used method is to employ the Cox models on each cause-specific hazard and the all-cause hazard. It has been pointed out that this method causes the problem of internal inconsistency. To solve such a problem, the additive hazard models have been advocated. In this paper, we model each cause-specific hazard with the additive hazard model that includes both constant and time-varying covariate effects. We illustrate that the covariate effect on all-cause failure can be estimated by the sum of the effects on all competing risks. Using data from a longitudinal study on breast cancer patients, we show that the proposed method gives simple interpretation of the final results, when the primary covariate effect is constant in the additive manner on each cause-specific hazard. Based on the given additive models on the cause-specific hazards, we derive the inferences for the adjusted survival and cumulative incidence functions.

[1]  T. Scheike,et al.  Dynamic regression hazards models for relative survival , 2008, Statistics in medicine.

[2]  John P Klein,et al.  Regression Modeling of Competing Risks Data Based on Pseudovalues of the Cumulative Incidence Function , 2005, Biometrics.

[3]  John P. Klein,et al.  Additive hazards Markov regression models illustrated with bone marrow transplant data , 2005 .

[4]  Torben Martinussen,et al.  Dynamic Regression Models for Survival Data , 2006 .

[5]  Margaret S. Pepe,et al.  Inference for Events with Dependent Risks in Multiple Endpoint Studies , 1991 .

[6]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[7]  Ian W. McKeague,et al.  A partly parametric additive risk model , 1994 .

[8]  Torben Martinussen,et al.  Maximum Likelihood Estimation for Cox's Regression Model Under Case–Cohort Sampling , 2004 .

[9]  Sangita Kulathinal,et al.  Bayesian Inference from Case–cohort Data with Multiple End‐points , 2006 .

[10]  Martin Schumacher,et al.  Time-dependent covariates in the proportional subdistribution hazards model for competing risks. , 2008, Biostatistics.

[11]  S. Cheng,et al.  Confidence Bands for Cumulative Incidence Curves Under the Additive Risk Model , 1999, Biometrics.

[12]  Mei-Jie Zhang,et al.  Predicting cumulative incidence probability by direct binomial regression , 2008 .

[13]  Per Kragh Andersen,et al.  Competing Risks and Time‐Dependent Covariates , 2009, Biometrical journal. Biometrische Zeitschrift.

[14]  D. Schaubel,et al.  Fitting Semiparametric Additive Hazards Models using Standard Statistical Software , 2007, Biometrical journal. Biometrische Zeitschrift.

[15]  Ping K Ruan,et al.  Analyses of cumulative incidence functions via non‐parametric multiple imputation , 2008, Statistics in medicine.

[16]  Lee-Jen Wei,et al.  Prediction of cumulative incidence function under the proportional hazards model. , 1998, Biometrics.

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

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

[19]  P. Andersen.  Time‐Dependent Covariate , 2005 .

[20]  S Chevret,et al.  Misspecified regression model for the subdistribution hazard of a competing risk , 2007, Statistics in medicine.

[21]  Zhiliang Ying,et al.  Semiparametric analysis of the additive risk model , 1994 .

[22]  Mei-Jie Zhang,et al.  MODELING THE SUBDISTRIBUTION OF A COMPETING RISK , 2006 .

[23]  O. Aalen.  A linear regression model for the analysis of life times. , 1989, Statistics in medicine.

[24]  Martin Schumacher,et al.  Misspecified regression model for the subdistribution hazard of a competing risk by Latouche A, Boisson V, Chevret S and Porcher R. Statistics in Medicine 2006; DOI: 10.2002/sim.2600 , 2007, Statistics in medicine.

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

[26]  John P Klein,et al.  Modelling competing risks in cancer studies , 2006, Statistics in medicine.

[27]  Mei-Jie Zhang,et al.  Extensions and Applications of the Cox‐Aalen Survival Model , 2003, Biometrics.