Multistate survival models for partially censored data

Multistate survival models for partially censored data are of great interest for investigating factors attributing to transitions from one state of survival to other states of survival or death. Kay (1982) extended the proportional hazards model for a multistate framework with several transient states. However, in his framework, Kay did not incorporate reverse transitions. This paper discusses an extension of the proportional hazards model for several transient states under a competing risk framework for transitions and reverse transitions. The relationship with the multistate product-limit method is also shown in this paper.

[1]  B. Efron.  The Efficiency of Cox's Likelihood Function for Censored Data , 1977 .

[2]  G. Beck,et al.  Stochastic Survival Models with Competing Risks and Covariates , 1979 .

[3]  J. Neyman,et al.  A simple stochastic model of recovery, relapse, death and loss of patients. , 1951, Human biology.

[4]  Jan M. Hoem,et al.  Point Estimation of Forces of Transition in Demographic Models , 1971 .

[5]  P. Andersen,et al.  Multistate models in survival analysis: a study of nephropathy and mortality in diabetes. , 1988, Statistics in medicine.

[6]  R. Kay.  The analysis of transition times in multistate stochastic processes using proportional hazard regression models , 1982 .

[7]  N. Breslow,et al.  A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship , 1974 .

[8]  A. V. Peterson,et al.  On the regression analysis of multivariate failure time data , 1981 .

[9]  B. Efron.  The two sample problem with censored data , 1967 .

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

[11]  O. Aalen.  Nonparametric Inference for a Family of Counting Processes , 1978 .

[12]  N Keiding,et al.  Assessing the influence of reversible disease indicators on survival. , 1991, Statistics in medicine.

[13]  Andrei Rogers.  Introduction to Multiregional Mathematical Demography , 1975 .

[14]  Gregg E. Dinse,et al.  A note on semi-Markov models for partially censored data , 1986 .

[15]  S. Krishnamoorthy.  Classical approach to increment-decrement life tables: an application to the study of the marital status of United States females 1970 , 1979 .

[16]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[17]  Ørnulf Borgan,et al.  Counting process models for life history data: a review , 1984 .

[18]  J P Klein,et al.  Semiparametric Marshall-Olkin models applied to the occurrence of metastases at multiple sites after breast cancer. , 1989, Biometrics.

[19]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[20]  K. Land,et al.  A general algorithm for estimating a Markov-generated increment-decrement life table with applications to marital-status patterns. , 1979, Journal of the American Statistical Association.

[21]  Paul Meier,et al.  Estimation of a Distribution Function from Incomplete Observations , 1975, Journal of Applied Probability.

[22]  Niels Keiding,et al.  Nonparametric Estimation of Transition Intensities and Transition Probabilities: A Case Study of a Two‐State Markov Process , 1989 .

[23]  A. V. Peterson.  Expressing the Kaplan-Meier estimator as a function of empirical subsurvival functions , 1977 .

[24]  A. Rogers.  The multtregional life table , 1973 .