2009
DOI: 10.1177/0272989x09336141
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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

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 mo… Show more

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Cited by 8 publications
(4 citation statements)
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“…We did not cover methods to adjust transition probabilities coming from different sources and different time horizons to 1 common cycle length. For example, the application of the expected maximum (EM) algorithm 25 has been suggested by Craig and Sendi 24 and Borg et al 26 Nevertheless, this mathematical background requires further research.…”
Section: Discussionmentioning
confidence: 99%
“…We did not cover methods to adjust transition probabilities coming from different sources and different time horizons to 1 common cycle length. For example, the application of the expected maximum (EM) algorithm 25 has been suggested by Craig and Sendi 24 and Borg et al 26 Nevertheless, this mathematical background requires further research.…”
Section: Discussionmentioning
confidence: 99%
“…Another problem is the presence in the data set of a large amount of the partially observed data. 14,21,22 This means that an individual can transit to some state not directly but after walking across a number of states. This problem can be solved by using the forward Kolmogorov equations as discussed in Welton and Ades.…”
Section: Discussionmentioning
confidence: 99%
“…The course of UC and CD is variable among patients, but an overall pattern has been modeled mathematically for CD. 3 It is estimated that some 50% of patients will have active disease at any point in time. 4 All these diseases are incurable; they last a lifetime, can have considerable morbidity, and often require “heavy” medication and surgery.…”
Section: Introductionmentioning
confidence: 99%