Bayesian Drug Disease Model with Stan - Using published longitudinal data summaries in population models
Sebastian Weber(1), Bob Carpenter(2), Daniel Lee(2), Frederic Y. Bois(3), Andrew Gelman(2), Amy Racine(1)
(1) Novartis, Basel (2) Columbia University, New York (3) Universite de Technologie de Compiegne
Objectives: Model based comparison of an in-house drug to a within class registered drug is critical during drug development. This is often challenged by the need for (i) a complex drug disease model to describe the drug effect over time and (ii) the lack of patient level data of other compounds in the landscape. As an example, a turn-over K-PD model for best corrected visual acuity (BCVA) in wet age-related macular degeneration (AMD) patients is considered. This modelling effort is not only to describe ranibizumab BCVA time profile, but also to evaluate the drug disease model of aflibercept for which only published summary data from the two phase III studies VIEW 1+2 [2] are available. In this presentation we show how a Bayesian framework can resolve challenges (i) and (ii).
Methods: To demonstrate the approach, results are shown based on a sparse in-house data set with about 1000 patients. The patient population are wet AMD who received either sham injection, 0.3 mg or 0.5 mg ranibizumab as an intra-vitreous injection, dosing frequencies were monthly for the first 3 months and continued with a monthly or every 3 months schedule over a year. BCVA was assessed monthly. Bayesian analysis was performed with an extended version of Stan 2.2.0 [3]. A variant of sample importance resampling (SIR) is used to update the model parameters with VIEW1+2 summary data.
Results: A turn-over model was used to describe the patient natural disease progression and the patients were started at baseline in a non-steady state. The drug effect was modelled as a stimulation of Kin. As the initial response to the drug was observed to be rapid, a time-varying Emax function was used. To achieve a stable model fit informative priors on the natural disease progression parameters (i.e. Kin and Kout) and weakly informative priors for drug related parameters, that is Emax and EC50, were used. The final model described the in house data well and resulted in good convergence properties. The SIR procedure allowed the inclusion of the longitudinal summary data and enabled the estimation of EMAX and EC50 for aflibercept.
Conclusions: The Bayesian approach with weakly/informative priors was essential to improve computing efficiency and enabled fast convergence. Key for this achievement was the extended version of Stan with an ODE solver. This Bayesian method coupled with SIR algorithm enabled us to overcome computational challenges and to include summary level longitudinal data in the model parameter estimation for aflibercept.
References:
[1] Ophthalmol Clin North Am. 2006 Sep;19(3):361-72
[2] Ophthalmol 2012 Dec 119(12):2537
[3] Stan Development Team. 2014. http://mc-stan.org.
