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

  • Anna Largajolli
  • Misba Beerahee
  • Shuying YangEmail author
Original Paper


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.


Bayesian Two-state model Negative Binomial Exacerbations COPD 



The authors would like to thank the project team members who participated in conducting the studies and retrieving the data for this work.

Author contribution

AL, SY and MB made substantial contributions to the analysis and data interpretation and review of this manuscript. All the authors contributed to drafting the manuscript and revising it and all authors gave final approval of the version to be published, and all authors agreed to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.


This analysis was funded by GSK (data derived from GSK studies HZC102871/NCT01009463, HZC102970/NCT01017952, SFCB3024/and MKI113006/NCT01218126). Employees of the sponsor were involved in study concept, data collection, data analysis/review, and manuscript writing/review. Anna Largajolli was a post-doc researcher funded by GSK at the time of conducting this work.

Compliance with ethical standards

Conflict of interest

AL was a post-doc researcher of GlaxoSmithKline at the time of conducting this work. She now works at Certara Strategic Consulting. SY and MB are employees and shareholders of GlaxoSmithKline.

Supplementary material

10928_2019_9643_MOESM1_ESM.pdf (5.3 mb)
Supplementary material 1 (PDF 5376 kb)


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Anna Largajolli
    • 1
    • 2
  • Misba Beerahee
    • 1
  • Shuying Yang
    • 1
    • 3
    Email author
  1. 1.GlaxoSmithKline, Research and DevelopmentUxbridgeUK
  2. 2.Certara Strategic ConsultingMilanoItaly
  3. 3.Clinical Pharmacology Modelling and SimulationQuantitative Sciences, GlaxoSmithKlineMiddlesexUK

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