Two Methods To Estimate Homogenous Markov Processes

Multi-state Markov processes have been introduced recently in Health Sciences in order to study disease history events. This sort of model have some advantages respect to traditional survival analysis, therefore they are an important line of research into stochastic processes applied to Epidemiology. However these types of models increase the complexity of analysis, even for simpler processes, and standard software is limited. In this paper, two methods for fitting homogene­ ous Markov models are proposed and compared.

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

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

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

[4]  M. Islam,et al.  Multistate survival models for transitions and reverse transitions: an application to contraceptive use data. , 1994, Journal of the Royal Statistical Society. Series A,.

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

[6]  Homogeneous Markov Processes For Breast Cancer Analysis , 2003 .

[7]  J. Kalbfleisch,et al.  The Analysis of Panel Data under a Markov Assumption , 1985 .

[8]  S W Lagakos,et al.  Analysis of doubly-censored survival data, with application to AIDS. , 1989, Biometrics.

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

[10]  D. Cox Regression Models and Life-Tables , 1972 .

[11]  P Pezzotti,et al.  Estimation of the acquired immunodeficiency syndrome incubation period in intravenous drug users: a comparison with male homosexuals. , 1992, American journal of epidemiology.

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

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

[14]  Odd Aalen,et al.  Nonparametric Estimation of Partial Transition Probabilities in Multiple Decrement Models , 1978 .