Inference for outcome probabilities in multi-state models

In bone marrow transplantation studies, patients are followed over time and a number of events may be observed. These include both ultimate events like death and relapse and transient events like graft versus host disease and graft recovery. Such studies, therefore, lend themselves for using an analytic approach based on multi-state models. We will give a review of such methods with emphasis on regression models for both transition intensities and transition- and state occupation probabilities. Both semi-parametric models, like the Cox regression model, and parametric models based on piecewise constant intensities will be discussed.

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

[2]  Halina Frydman,et al.  A Nonparametric Estimation Procedure for a Periodically Observed Three‐State Markov Process, with Application to Aids , 1992 .

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

[4]  Niels Keiding,et al.  Non- and semi-parametric estimation of transition probabilities from censored observation of a non-homogeneous Markov process , 1991 .

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

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

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

[8]  P Hougaard,et al.  Multi-state Models: A Review , 1999, Lifetime data analysis.

[9]  Zhiliang Ying,et al.  Semiparametric regression for the mean and rate functions of recurrent events , 2000 .

[10]  Carmen Cadarso-Suárez,et al.  Multi-state models for the analysis of time-to-event data , 2009, Statistical methods in medical research.

[11]  H Putter,et al.  Tutorial in biostatistics: competing risks and multi‐state models , 2007, Statistics in medicine.

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

[13]  Somnath Datta,et al.  Validity of the Aalen–Johansen estimators of stage occupation probabilities and Nelson–Aalen estimators of integrated transition hazards for non-Markov models , 2001 .

[14]  D Commenges,et al.  Inference for multi-state models from interval-censored data , 2002, Statistical methods in medical research.

[15]  M. Schumacher,et al.  On pseudo-values for regression analysis in competing risks models , 2009, Lifetime data analysis.

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

[17]  Niels Keiding,et al.  Event history analysis and the cross‐section , 2006, Statistics in medicine.

[18]  Mei-Jie Zhang,et al.  Direct Modelling of Regression Effects for Transition Probabilities in Multistate Models , 2007 .

[19]  N. Keiding,et al.  Multi-state models for event history analysis , 2002, Statistical methods in medical research.

[20]  D Commenges,et al.  Multi-state Models in Epidemiology , 1999, Lifetime data analysis.

[21]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[22]  J. Klein,et al.  Asymptotic theory for the Cox semi-Markov illness-death model , 2007, Lifetime data analysis.

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

[24]  Per Kragh Andersen,et al.  Regression Analysis for Multistate Models Based on a Pseudo‐value Approach, with Applications to Bone Marrow Transplantation Studies , 2007 .

[25]  Carmen Cadarso-Suárez,et al.  Nonparametric estimation of transition probabilities in a non-Markov illness–death model , 2006, Lifetime data analysis.

[26]  J. Fine,et al.  Regression modeling of competing crude failure probabilities. , 2001, Biostatistics.

[27]  R Kay,et al.  A Markov model for analysing cancer markers and disease states in survival studies. , 1986, Biometrics.

[28]  Halina Frydman,et al.  Nonparametric estimation of a Markov ‘illness-death’ process from interval-censored observations, with application to diabetes survival data , 1995 .

[29]  John P Klein,et al.  Multi-state models for bone marrow transplantation studies , 2002, Statistical methods in medical research.

[30]  Richard J. Cook,et al.  The Statistical Analysis of Recurrent Events , 2007 .