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Non‐homogeneous Markov models in the analysis of survival after breast cancer
Author(s) -
PérezOcón Rafael,
RuizCastro Juan Eloy,
GámizPérez M. Luz
Publication year - 2001
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/1467-9876.00223
Subject(s) - weibull distribution , homogeneous , piecewise , covariate , statistics , mathematics , survival analysis , survival function , breast cancer , proportional hazards model , markov process , markov chain , hazard ratio , medicine , cancer , combinatorics , mathematical analysis , confidence interval
A cohort of 300 women with breast cancer who were submitted for surgery is analysed by using a non‐homogeneous Markov process. Three states are onsidered: no relapse, relapse and death. As relapse times change over time, we have extended previous approaches for a time homogeneous model to a non omogeneous multistate process. The trends of the hazard rate functions of transitions between states increase and then decrease, showing that a changepoint can be considered. Piecewise Weibull distributions are introduced as transition intensity functions. Covariates corresponding to treatments are incorporated in the model multiplicatively via these functions. The likelihood function is built for a general model with k changepoints and applied to the data set, the parameters are estimated and life‐table and transition probabilities for treatments in different periods of time are given. The survival probability functions for different treatments are plotted and compared with the corresponding function for the homogeneous model. The survival functions for the various cohorts submitted for treatment are fitted to the mpirical survival functions.