Abstract
A nonhomogeneous Markov process is applied for analysing a cohort of women with breast cancer that were submitted to surgery. The follow-up was scheduled every month. 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 nonhomogeneous multistate process. The transition intensity functions among states are the hazard rate functions of different lognormal distributions; we therefore build the likelihood function for this model, estimate the parameters and compare the empirical and nonhomogeneous models in terms of the survival probability functions. The parameter estimation is done following the maximum likelihood method. The effect of treatments is incorporated as covariates by means of the lognormal hazard rate functions, following the proportional hazard model. Thus, we have a multistate model with multidimensional covariates. Survival functions for the different cohorts submitted to treatments are obtained and goodness-of-fit tests are performed.
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The first author gratefully acknowledges the financial support by DGES, Proyecto PB97-0827, Ministerio de Educación y Cultura, Spain.
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Pérez-Ocón, R., Ruiz-Castro, J.E. & Gámiz-Pérez, M.L. Markov models with lognormal transition rates in the analysis of survival times. Test 9, 353–370 (2000). https://doi.org/10.1007/BF02595740
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DOI: https://doi.org/10.1007/BF02595740
Key Words
- Covariates
- lognormal distribution
- maximum-likelihood estimate
- nonhomogeneous Markov process
- survival data