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 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.

Alternative Conversion Methods for Transition Probabilities in State-Transition Models: Validity and Impact on Comparative Effectiveness and Cost-Effectiveness

“…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.…”

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

“…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.…”

A medicoeconomic review of early intervention with biologic agents in the treatment of inflammatory bowel diseases

“…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.…”