Three state markov model: Comparing three parameterizations of the transition intensity rate. Application to rheumatoid arthritis data Academic Article


  • Revista Colombiana de Estadistica


  • We consider a three state model with an absorbing state assuming an underlying Markov process to explain the dependence among observations within subjects. We compare, using a simulation study, three different parameterizations of the transition intensity rate: the first one is based on the Andersen-Gill's multiplicative hazard model (Andersen et al. 1993), the second one is based on the logistic model, and the third one depends on the complementary log-log model. The method to estimate the effect of the parameters is based on the likelihood function which can be optimized using the exact solutions of a Kolmogorov forward differential equations system in conjunction with the Newton-Raphson algorithm (Abramowitz & Stegun 1972). We use the relative bias to select the best estimation estrategy. The methodology is ilustrated using longitudinal data about rheumatoid arthritis (RA) from the Corporación para Investigaciones Biológicas, CIB.

publication date

  • 2007/12/1


  • Absorbing
  • Differential equation
  • Estimate
  • Exact Solution
  • Hazard Models
  • Likelihood Function
  • Logistic Model
  • Longitudinal Data
  • Markov Model
  • Markov Process
  • Methodology
  • Model
  • Multiplicative Model
  • Newton-Raphson Algorithm
  • Observation
  • Parameterization
  • Rheumatoid Arthritis
  • Simulation Study

International Standard Serial Number (ISSN)

  • 0120-1751

number of pages

  • 17

start page

  • 213

end page

  • 229