Extension of Continuous-Time PK/PD Markov Models to Published Count Data
Doerthe Steller(1), Sven Mensing(1)
(1)Abbott, Ludwighafen, Germany
Objectives: Availability of rich clinical data forms the basis of reliable PK/PD modeling. Incorporation of literature data is an important goal whenever individual study data is sparse or erratic. Joint (Meta) analysis of data from multiple sources provides reliable models capable for further simulations and decisions over subsequent study designs and trial success.
Markov models have been successfully applied in several categorical PK/PD modeling tasks for individual data. Aim of this work was hence to extend the Markov approach to aggregated data settings.
Methods: Markov modeling techniques had to be developed and refined for summarized rather than individual categorical data. This was exemplified by published Infliximab data from the studies ACT1 and ACT2 for the treatment of Ulcerative Colitis (UC) [1, 2]. Literature data was processed for Markov model needs, i.e. subjects in the states of ‘remission', ‘no ‘remission' and ‘dropout' were summarized at the time points given. A structural PK/PD model was established with continuous transitions between those discrete model states and incorporation of a stimulating drug effect.
Markov models were implemented in NONMEM 7.1.2 via the Kolmogorov backward equations [3]. Since published count data instead of individual data formed the base of analysis, a binomial likelihood was to be minimized for the parameter estimation process. Model quality was assessed by simulations with Trial Simulator software (Version 2.2.1, Pharsight Corporation, Mountain View, CA).
Results: The continuous-time Markov approach was successfully transferred and adapted from the individual to the aggregated categorical data setting. A three-state Markov model on the basis of published mean data only was built which adequately described disease progression as shown by VPCs. This comprehensive model could then be used for simulations of different scenarios and comparison to other treatments of UC (competitive profiling).
Conclusions: We have developed Markov modeling and simulation techniques for individual, aggregated or combined categorical data and encourage its use and further exploration.
References:
[1] Rutgeerts P, Sandborn WJ, et al. Infliximab for Induction and Maintenance Therapy for Ulcerative Colitis. N Engl J Med (2005);353:2462-2476.
[2] Fasanmade A et al. Population Pharmacokinetic Analysis of Infliximab in Patients with Ulcerative Colitis. Eur J Clin Pharmacol (2009);65:1211-1228.
[3] Welton NJ, Ades AE. Estimation of Markov Chain Transition Probabilities and Rates from Fully and Partially Observed Data: Uncertainty propagation, Evidence Synthesis, and Model Calibration, Med Decis Making (2005);25:633-645
