title: Modelling a spontaneously reported side effect by use of a Markov mixed-effects model.
abstract: OBJECTIVE
  To present a method for analyzing side-effect data where change in severity is spontaneously reported during the experiment.
  
  
  METHODS
  A clinical study in 12 healthy volunteers aimed to investigate the concentration-response characteristics of a CNS-specific side-effect was conducted. After an open session where the subjects experienced the side-effect and where the individual pharmacokinetic parameters were evaluated they were randomized to a sequence of three different infusion rates of the drug in a double-blinded crossover way. The infusion rates were individualized to achieve the same target concentration in all subjects and different drug input rates were selected to mimic absorption profiles from different formulations. The occurrence of the specific side-effect and any subsequent change in severity was self-reported by the subjects. Severity was recorded as 0 = no side-effect, 1 = mild side-effect and 2 = moderate or severe side-effect.
  
  
  RESULTS
  The side-effect data were analyzed using a mixed-effects model for ordered categorical data with and without Markov elements. The former model estimated the probability of having a certain side-effect score conditioned on the preceding observation and drug exposure. The observed numbers of transitions between scores were from 0 -> 1: 24, from 0- > 2: 11, from 1 - >, 2: 23, from 2- > 1: 1, from 2- > 0: 32 and from 1 - >0: 2. The side-effect model consisted of an effect-compartment model with a tolerance compartment. The predictive performance of the Markov model was investigated by a posterior predictive check (PPC), where 100 datasets were simulated from the final model. Average number of the different transitions from the PPC was from 0 - > 1: 26, from 0 - > 2: 11, from 1 - > 2: 25, from 2 - >1: 1, from 2 - >0: 35 and from 1 - > 0: 1. A similar PPC for the model without Markov elements was at considerable disparity with the data.
  
  
  CONCLUSIONS
  This approach of incorporating Markov elements in an analysis of spontaneously reported categorical side-effect data could adequately predict the observed side-effect time course and could be considered in analyses of categorical data where dependence between observations is an issue.
authors.affiliation: Department of Clinical Pharmacology, AstraZeneca R&D, Södertälje, Sweden. per-henrik.zingmark@astrazeneca.com
authors.forename: Per-Henrik
authors.initials: PH
authors.lastname: Zingmark
authors.forename: Matts
authors.initials: M
authors.lastname: Kågedal
authors.forename: Mats O
authors.initials: MO
authors.lastname: Karlsson
mesh_terms: D000328:Adult; D000465:Algorithms; D002491:Central Nervous System Agents / Q000008:administration & dosage / Q000493:pharmacokinetics; D018592:Cross-Over Studies; D004311:Double-Blind Method; D064420:Drug-Related Side Effects and Adverse Reactions; D006801:Humans; D007262:Infusions, Intravenous; D008297:Male; D008390:Markov Chains; D015233:Models, Statistical; D010599:Pharmacokinetics; D012984:Software
chemical_list: D002491:Central Nervous System Agents