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A Maximum Likelihood Estimator of a Markov Model for Disease Activity in Crohn’s Disease and Ulcerative Colitis for Annually Aggregated Partial Observations

Author

Listed:
  • Sixten Borg

    (IHE, The Swedish Institute for Health Economics, Lund, Sweden, info@ihe.se)

  • Ulf Persson

    (IHE, The Swedish Institute for Health Economics, Lund, Sweden)

  • Tine Jess

    (Institute of Preventive Medicine, Copenhagen University Hospital, Copenhagen, Denmark)

  • Ole Østergaard Thomsen

    (Danish Crohn's Colitis Database, Department of Medical Gastroenterology, Herlev University Hospital, Copenhagen, Denmark)

  • Tryggve Ljung

    (Karolinska University Hospital, Stockholm, Sweden)

  • Lene Riis

    (Danish Crohn's Colitis Database, Department of Medical Gastroenterology, Herlev University Hospital, Copenhagen, Denmark)

  • Pia Munkholm

    (Danish Crohn's Colitis Database, Department of Medical Gastroenterology, Herlev University Hospital, Copenhagen, Denmark)

Abstract

Crohn’s disease (CD) and ulcerative colitis (UC) are chronic inflammatory bowel diseases that have a remitting, relapsing nature. During relapse, they are treated with drugs and surgery. The present study was based on individual data from patients diagnosed with CD or UC at Herlev University Hospital, Copenhagen, Denmark, during 1991 to 1993. The data were aggregated over calendar years; for each year, the number of relapses and the number of surgical operations were recorded. Our aim was to estimate Markov models for disease activity in CD and UC, in terms of relapse and remission, with a cycle length of 1 month. The purpose of these models was to enable evaluation of interventions that would shorten relapses or postpone future relapses. An exact maximum likelihood estimator was developed that disaggregates the yearly observations into monthly transition probabilities between remission and relapse. These probabilities were allowed to be dependent on the time since start of relapse and on the time since start of remission, respectively. The estimator, initially slow, was successfully optimized to shorten the execution time. The estimated disease activity model for CD fits well to observed data and has good face validity. The disease activity model is less suitable for UC due to its transient nature through the presence of curative surgery.

Suggested Citation

  • Sixten Borg & Ulf Persson & Tine Jess & Ole Østergaard Thomsen & Tryggve Ljung & Lene Riis & Pia Munkholm, 2010. "A Maximum Likelihood Estimator of a Markov Model for Disease Activity in Crohn’s Disease and Ulcerative Colitis for Annually Aggregated Partial Observations," Medical Decision Making, , vol. 30(1), pages 132-142, January.
    • Handle: RePEc:sae:medema:v:30:y:2010:i:1:p:132-142
    DOI: 10.1177/0272989X09336141
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    References listed on IDEAS

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    1. Nicky J. Welton & A. E. Ades, 2005. "Estimation of Markov Chain Transition Probabilities and Rates from Fully and Partially Observed Data: Uncertainty Propagation, Evidence Synthesis, and Model Calibration," Medical Decision Making, , vol. 25(6), pages 633-645, November.
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    2. 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.

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