Markov model transition probability matrix transformed cycle length

Somethimes the cycle length of a transition probability matrix needs to be changed. In my example I derived transition probabilities from a study with 3-year interval in measurements. I wanted to change the transition probabilities to 1-year cycle length. Various possibilities exist, which are explained here by Dr. Jagpreet Chhatwal et al.:

I do not explain the traditional approach:

As explained in the document the Eigendecomposition approach has some advantages. Below the R code to transform it:

Be aware that some disadvantages were mentioned in the document. Among them is the possibility of negative values which can not be used as transition probability. In the document by dr. Chhatwal et al. they provide several sollutions. One approach is “to add the negative values back to all entries of the same row, proportional to their absolute value”. An excel example can be downloaded transition probabilities.


(Systematic) reviews:

  • Gustavsson A, Green C, Jones RW, Förstl H, Simsek D, de Reydet de Vulpillieres F, Luthman S, Adlard N, Bhattacharyya S, Wimo A. Current issues and future research priorities for health economic modelling across the full continuum of Alzheimer’s disease. Alzheimers Dement. 2017 Mar;13(3):312-321. doi: 10.1016/j.jalz.2016.12.005. PubMed
  • Hernandez L, Ozen A, DosSantos R, Getsios D. Systematic Review of Model-Based Economic Evaluations of Treatments for Alzheimer’s Disease. Pharmacoeconomics. 2016 Jul;34(7):681-707. doi: 10.1007/s40273-016-0392-1. PubMed
  • Green C, Zhang S. Predicting the progression of Alzheimer’s disease dementia: A multidomain health policy model. Alzheimers Dement. 2016 Jul;12(7):776-85. doi: 10.1016/j.jalz.2016.01.011. PubMed
  • Handels RL, Wolfs CA, Aalten P, Joore MA, Verhey FR, Severens JL. Diagnosing Alzheimer’s disease: a systematic review of economic evaluations. Alzheimers Dement. 2014 Mar;10(2):225-37. PubMed
  • Hyde C, Peters J, Bond M, Rogers G, Hoyle M, Anderson R, Jeffreys M, Davis S, Thokala P, Moxham T. Evolution of the evidence on the effectiveness and cost-effectiveness of acetylcholinesterase inhibitors and memantine for Alzheimer’s disease: systematic review and economic model. Age Ageing. 2013 Jan;42(1):14-20. doi: 10.1093/ageing/afs165. PubMed
  • Bond M, Rogers G, Peters J, Anderson R, Hoyle M, Miners A, Moxham T, Davis S, Thokala P, Wailoo A, Jeffreys M, Hyde C. The effectiveness and cost-effectiveness of donepezil, galantamine, rivastigmine and memantine for the treatment of Alzheimer’s disease (review of Technology Appraisal No. 111): a systematic review and economic model. Health Technol Assess. 2012;16(21):1-470. doi: 10.3310/hta16210. PubMed
  • Green C, Shearer J, Ritchie CW, Zajicek JP. Model-based economic evaluation in Alzheimer’s disease: a review of the methods available to model Alzheimer’s disease progression. Value Health. 2011 Jul-Aug;14(5):621-30. PubMed
  • Cohen JT, Neumann PJ. Decision analytic models for Alzheimer’s disease: state of the art and future directions. Alzheimers Dement. 2008 May;4(3):212-22. PubMed
  • Green C. Modelling disease progression in Alzheimer’s disease: a review of modelling methods used for cost-effectiveness analysis. Pharmacoeconomics. 2007;25(9):735-50. PubMed

Studies not included in the above reviews (updated 2016)

  • Valcárcel-Nazco C, Perestelo-Pérez L, Molinuevo JL, Mar J, Castilla I, Serrano-Aguilar P. Cost-effectiveness of the use of biomarkers in cerebrospinal fluid for Alzheimer’s disease. J Alzheimers Dis. 2014;42(3):777-88. PubMed
  • Sköldunger A, Johnell K, Winblad B, Wimo A. Mortality and treatment costs have a great impact on the cost-effectiveness of disease modifying treatment in Alzheimer’s disease–a simulation study. Curr Alzheimer Res. 2013 Feb;10(2):207-16. PubMed
  • Biasutti M, Dufour N, Ferroud C, Dab W, Temime L. Cost-effectiveness of magnetic resonance imaging with a new contrast agent for the early diagnosis of Alzheimer’s disease. PLoS One. 2012;7(4):e35559. PubMed
  • Guo S, Getsios D, Hernandez L, Cho K, Lawler E, Altincatal A, Lanes S, Blankenburg M. Florbetaben PET in the Early Diagnosis of Alzheimer’s Disease: A Discrete Event Simulation to Explore Its Potential Value and Key Data Gaps. Int J Alzheimers Dis. 2012;2012:548157. PubMed
  • Handels RLH, Wimo A, Dodel R, Kramberger MG, Visser PJ, Molinuevo JL, Verhey FRJ, Winblad B. Cost-Utility of Using Alzheimer’s Disease Biomarkers in Cerebrospinal Fluid to Predict Progression from Mild Cognitive Impairment to Dementia. J Alzheimers Dis. 2017;60(4):1477-1487. doi: 10.3233/JAD-170324. PubMed
  • Green C, Zhang S. Predicting the progression of Alzheimer’s disease dementia: A multidomain health policy model. Alzheimers Dement. 2016 Jul;12(7):776-85. doi: 10.1016/j.jalz.2016.01.011. PubMed
  • Spackman DE, Kadiyala S, Neumann PJ, Veenstra DL, Sullivan SD. Measuring Alzheimer disease progression with transition probabilities: estimates from NACC-UDS. Curr Alzheimer Res. 2012 Nov;9(9):1050-8. PubMed

These lists have not been based on a systematic search.

Example decision models

NICE DSU patient level simulation

In the NICE DSU technical support document 15: Cost-effectiveness modelling using patient-level simulation, a decision model was described as a learning source including its source code in the languages R, Excel, TreeAge Pro, and SIMUL8. It was written by Davis S, Stevenson M, Tappenden P, Wailoo A in 2014.

Decision Modelling for Health Economic Evaluation

Briggs A, Sculpher M, Claxton K have described Markov modelling methods in health care in 2006. The book contains a Markov model and preparation analyses in Excel in its additional material.

Simulate individual patient survival

Here is a suggestion how to model individual patient survival. The code is written in R. You are welcome to share your comments or your suggested methodology.