Bayesian approach to investigate a two-state mixed model of COPD exacerbations

Chronic obstructive pulmonary disease (COPD) is a chronic obstructive disease of the airways. An exacerbation of COPD is defined as shortness of breath, cough, and sputum production. New therapies for COPD exacerbations are examined in clinical trials frequently based on the number of exacerbations that implies long-term study due to the high variability in occurrence and duration of the events. In this work, we expanded the two-state model developed by Cook et al. where the patient transits from an asymptomatic (state 1) to a symptomatic state (state 2) and vice versa, through investigating different semi-Markov models in a Bayesian context using data from actual clinical trials. Of the four models tested, the log-logistic model was shown to adequately characterize the duration and number of COPD exacerbations. The patient disease stage was found a significant covariate with an effect of accelerating the transition from asymptomatic to symptomatic state. In addition, the best dropout model (log-logistic) was incorporated in the final two-state model to describe the dropout mechanism. Simulation based diagnostics such as posterior predictive check (PPC) and visual predictive check (VPC) were used to assess the behaviour of the model. The final model was applied in three clinical trial data to investigate its ability to detect the drug effect: the drug effect was captured in all three datasets and in both directions (from state 1 to state 2 and vice versa). A practical design investigation was also carried out and showed the limits of reducing the number of subjects and study length on the drug effect identification. Finally, clinical trial simulation confirmed that the model can potentially be used to predict medium term (6–12 months) clinical trial outcome using the first 3 months data, but at the expense of showing a non-significant drug effect. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s10928-019-09643-6) contains supplementary material, which is available to authorized users.