Non-homogeneous Markov models in the analysis of survival after breast cancer

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 considered: no relapse, relapse and death. As relapse times change over time, we have extended previous approaches for a time homogeneous model to a non-hom...

Full description

Saved in:
Bibliographic Details
Published in:Applied statistics 2001, Vol.50 (1), p.111-124
Main Authors: Pérez-Ocón, Rafael, Ruiz-Castro, Juan Eloy, Gámiz-Pérez, M. Luz
Format: Article
Language:English
Subjects:
Analysis. Health state
Applications
Biological and medical sciences
Breast cancer
Cancer
Chemotherapy
Covariates
Disease models
Diseases
Epidemiology
Estimation
Exact sciences and technology
General aspects
Hormone therapy
Life expectancy
Markov processes
Markovian processes
Mathematical foundations
Mathematical functions
Mathematical independent variables
Mathematics
Maximum likelihood estimate
Medical sciences
Non-homogeneous Markov process
Probability
Probability and statistics
Public health. Hygiene
Public health. Hygiene-occupational medicine
Radiotherapy
Relapse
Sciences and techniques of general use
Statistics
Survival data
Transition probabilities
Weibull distribution
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 considered: no relapse, relapse and death. As relapse times change over time, we have extended previous approaches for a time homogeneous model to a non-homogeneous 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 empirical survival functions.
ISSN:0035-9254
1467-9876
DOI:10.1111/1467-9876.00223