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Identification of a Multistate Continuous-Time Nonhomogeneous Markov Chain Model for Patients with Decreased Renal Function

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  • Alexander Begun
  • Andrea Icks
  • Regina Waldeyer
  • Sandra Landwehr
  • Michael Koch
  • Guido Giani

Abstract

Objectives . Markov chain models are frequently used to study the clinical course of chronic diseases. The aim of this article is to adopt statistical methods to describe the time dynamics of chronically ill patients when 2 kinds of data sets—fully and partially observable data are available. Model . We propose a 6-state continuous-time Markov chain model for the progression of chronic kidney disease (CKD), where little is known about the transitions between the disease stages. States 1 to 3 of the model correspond to stages III to V of chronic kidney disease in the Kidney Disease Outcomes Quality Initiative (KDOQI) CKD classification. States 4 and 5 relate to dialysis and transplantation (renal replacement therapy), respectively. Death is the (absorbing) state 6. Methods and Data . The model can be investigated and identified using Kolmogorov’s forward equations and the methods of survival analysis. Age dependency, covariates in the form of the Cox regression, and unobservable risks of transition (frailties) can be included in the model. We applied our model to a data set consisting of all 2097 patients from all renal centers in a region in North Rhine-Westphalia (Germany) in 2005–2010. Results . We compared transitions and relative risks to the few data published and found them to be reasonable. For example, patients with diabetes had a significantly higher risk for disease progression compared with patients without diabetes. Conclusions . In summary, modeling may help to quantify disease progression and its predictors when only partially observable prospective data are available.

Suggested Citation

  • Alexander Begun & Andrea Icks & Regina Waldeyer & Sandra Landwehr & Michael Koch & Guido Giani, 2013. "Identification of a Multistate Continuous-Time Nonhomogeneous Markov Chain Model for Patients with Decreased Renal Function," Medical Decision Making, , vol. 33(2), pages 298-306, February.
    • Handle: RePEc:sae:medema:v:33:y:2013:i:2:p:298-306
    DOI: 10.1177/0272989X12466731
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    1. Franck Maunoury & Aurore Clément & Chizoba Nwankwo & Laurie Levy-Bachelot & Armand Abergel & Vincent Di Martino & Eric Thervet & Isabelle Durand-Zaleski, 2018. "Cost-effectiveness analysis of elbasvir-grazoprevir regimen for treating hepatitis C virus genotype 1 infection in stage 4-5 chronic kidney disease patients in France," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-20, March.
    2. Fernando Alarid-Escudero & Eline Krijkamp & Eva A. Enns & Alan Yang & M. G. Myriam Hunink & Petros Pechlivanoglou & Hawre Jalal, 2023. "An Introductory Tutorial on Cohort State-Transition Models in R Using a Cost-Effectiveness Analysis Example," Medical Decision Making, , vol. 43(1), pages 3-20, January.

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