Modelling a spontaneously reported side-effect by use of a Markov mixed-effects model

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Objectives: To present a method for analyzing side effect data where change in severity of the side effect 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 pharmacokinetics was described with a two-compartment model and the side effect data were analyzed using a transition model with Markov elements. The observed numbers of transitions between scores were from 0 to 1: 24, from 0 to 2: 11, from 1 to 2: 23, from 2 to 1: 1, from 2 to 0: 32 and from 1 to 0: 2. The side-effect model consisted of an effect-compartment model with a tolerance compartment. The proportional odds model as previously implemented for ordered categorical pharmacodynamic data [1, 2, 3] assumes that observations are independent under the model. For frequently measured categorical type data, there is a clear correlation between neighbouring observations that a standard proportional odds model could not predict. For such situations, transition models including Markov elements have been used [4, 5]. Such models, usually implemented with one model for each transition, were not considered appropriate, as the data set was not sufficiently informative-rich to allow appropriate estimation of all resulting parameters and the graded nature of the scores not naturally recognized. A different approach by using a transition model but also recognising the ordered nature of the data in the parameterisation of the model was therefore applied. This model estimates the probabilities of a having a certain side effect score conditioned on the preceding observation. The model is a hybrid between the proportional odds model and the transition model and it can therefore also be viewed as a proportional odds model where the probabilities are dependent on the preceding stage through a first-order Markov element. The predictive performance of the 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 to 1: 26, from 0 to 2: 11, from 1 to 2: 25, from 2 to 1: 1, from 2 to 0: 35 and from 1 to 0: 1.

Conclusions: This approach of incorporating Markov elements in an analysis of spontaneously reported categorical side-effect data could adequately predict the time course of the observed data and could be considered in analyses of categorical data where dependence between observations is an issue.

References:
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