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

Sixten Borg, Ulf Persson, Tine Jess, Ole Østergaard Thomsen, Tryggve Ljung, Lene Riis and Pia Munkholm
Additional contact information
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

Medical Decision Making, 2010, vol. 30, issue 1, 132-142

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.

Keywords: maximum likelihood estimator; aggregated and partial observations; Markov model; transition probability matrix; inflammatory bowel disease; disease activity. (Med Decis Making 2010; 30:132—142) (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:sae:medema:v:30:y:2010:i:1:p:132-142

DOI: 10.1177/0272989X09336141

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