Model based optimization of dose-finding studies for drug-combinations.
T. Papathanasiou 1,2, A. Strathe 2, R.V. Overgaard 2, T.M. Lund 1, A.C. Hooker 3
1 Department of Drug Design and Pharmacology, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark; 2 Novo Nordisk A/S, Quantitative Clinical Pharmacology, Søborg, Denmark; 3 Department of Pharmaceutical Biosciences, Uppsala University, Sweden
Objectives:
Combinations of pharmacological treatments are increasingly being investigated for potentially higher clinical benefit, especially when the combined drugs are expected to act via synergistic drug interactions [1,2]. The clinical development of combination treatments is particularly challenging, especially during the dose selection phase, where a vast range of possible combination doses exist [3]. Traditionally, dose-finding drug-combination studies are conducted based on factorial designs and variations thereof [3]. While simple in their conception and construction, the choice of the investigated dose levels is often empirical.
Model-Based Drug Development (MBDD) has been proposed by regulatory agencies, academia and pharmaceutical industry as an efficient approach to mitigate the risks of dose selection and improve confidence in decision-making [4, 5]. As part of MBDD, exposure-response (E-R) analyses that associate an exposure metric, such as average concentration in steady state, and a continuous response variable measured at a single time point, have become a critical component for supporting dose selection for phase III [6]. It has previously been shown that dose selection can be improved though the modeling of exposure-response (E-R) relationships of combinatory drug effects and that the study design is important in correctly characterizing these models used for dosing decisions [3].
In this work we investigate how dose selection can be optimized in drug-combination studies through the use of optimal design methodology in tandem with E-R analyses. The optimized designs are compared to a typical drug-combination dose-finding design (3x3 factorial) [3] in regard to overall parameter accuracy and precision, precision of pre-specified effect level predictions and their ability to correctly identify the minimum effective combination dose (MEDA,B) to be brought forward to a confirmatory clinical trial.
Methods:
Model based optimizations were performed using the R package PopED [7]. The true combination model was assumed to be an effect addition model with one interaction term [2,3], where the pharmacodynamic effect is driven by steady state concentrations of both drugs (Css). The E-R relationships of the individual mono-components were assumed to be described by Emax models with different maximal effects and their pharmacodynamic interaction was assumed to be synergistic [3].
Optimizations of the allocations of the investigated dose levels were performed using a local optimality criterion (D-optimality) to maximize the precision of all model parameters in a simulated exposure-response (E-R) surface [2,3]. ED-optimality with a uniform distribution around the effect parameters was also used to obtain a generalizable design for situations where uncertainty around the effect parameters is present.
Since the objective of dose-finding studies is to identify the best doses to be brought forward to confirmatory trials, good precision around a target effect level is highly desirable. In the case of single-drug therapies, where the treatment response is driven by the exposure of a single drug, trial optimization towards this goal can be achieved by either approaching the target exposure level as a model parameter with uncertainty that should be minimized or by constructing designs that minimize the asymptotic variance of the target concentration estimates [9]. For drug combinations, such approaches are complicated by the fact that the treatment effect is driven by the combination of two variables (i.e. exposures of Drug A and Drug B). The approach used here was to utilize an optimality criterion that aims to reduce the average prediction variance in a specific region of the three-dimensional E-R surface (V-Optimality) [10]. V-Optimal designs can be hard to construct and generally lead to poor parameter estimation [10], which is undesirable when performing a model-based analysis. To mitigate this, we considered a compound criterion incorporating D- and V- optimality characteristics (D/V-optimality), with equal contribution from both criteria.
Stochastic simulation and estimation (n=1000) was performed to determine the parameter precision resulting from the reference and optimized study designs. Overall parameter precision was defined as the average %RSE of all the parameters in the model for each competing design, which was compared to the same value calculated for the reference study design. All simulations and estimations were performed in NONMEM version 7.3 [11] using PsN [12].
Lastly, all designs were evaluated regarding their ability to correctly identify the correct minimum effective combination dose (MEDA,B), defined as the dose leading to a wanted pre-specified effect level that simultaneously minimizes the needed dose from both mono-components. The MEDA,B was calculated using the true and SSE derived model parameters and the probabilities of identifying the correct dose A alone (MEDA), correct dose B alone (MEDB) and the true combination dose (MEDA,B) were derived (where correct is assumed to be a dose that is within 20% of the true MEDA,B).
Results:
The D-efficiency of the D-optimal design as compared to the reference design was 141%. When the D/V-optimality criterion was used, the D-efficiency was slightly lower (107.5%). A slight loss in the D-efficiency of the globally optimal design was observed 98.7%.
The overall parameter precision was improved in the optimized designs. The average %RSE for the D-optimal design was 13.6%, followed by the D/V- and ED-optimal designs (16.1% and 17.9% respectively). The %RSE for the reference design was 17.3%.
Regarding correct MEDA,B identification, the highest probabilities were observed for the D/V-Optimal design (88.2%), followed by the D- and ED-optimal design (76.7% and 73.7% respectively). The lowest probability for identifying the correct MEDA,B was seen when the reference design was used (67.7%).
Conclusions:
Our study results indicate that using optimal design in tandem with E-R analyses can be an attractive method for dose allocation in drug-combination dose-finding studies. Optimized studies significantly improved the extracted amount of information, allowing for the same information from as little as 60% of the subjects as compared to a typical drug-combination design. Additionally, the flexibility in defining the optimality criteria can help improve the probability of identifying the optimal combination dose to be brought forward in late stage development.
References:
[1] Zimmermann GR, Lehár J, Keith CT. Multi-target therapeutics: when the whole is greater than the sum of the parts. Drug Discov Today. 2007;12(1-2):34-42.
[2] Greco WR, Bravo G, Parsons JC. The search for synergy: a critical review from a response surface perspective. Pharmacol Rev. 1995;47(2):331-85.
[3] Papathanasiou T, Strathe A, Hooker AC, Lund TM, Overgaard RV. Feasibility of Exposure-Response Analyses for Clinical Dose-Ranging Studies of Drug Combinations. AAPS J. 2018;20(3):64.
[4] Kimko H, Pinheiro J. Model-based clinical drug development in the past, present and future: a commentary. Br J Clin Pharmacol. 2015;79(1):108-16.
[5] Musuamba FT, Manolis E, Holford N, Cheung S, Friberg LE, Ogungbenro K, et al. Advanced Methods for Dose and Regimen Finding During Drug Development: Summary of the EMA/EFPIA Workshop on Dose Finding (London 4-5 December 2014). CPT Pharmacometrics Syst Pharmacol. 2017;6(7):418-29.
[6] Overgaard RV, Ingwersen SH, Tornøe CW. Establishing Good Practices for Exposure-Response Analysis of Clinical Endpoints in Drug Development. CPT Pharmacometrics Syst Pharmacol. 2015;4(10):565-75.
[7] Nyberg J, Ueckert S, Strömberg EA, Hennig S, Karlsson MO, Hooker AC. PopED: an extended, parallelized, nonlinear mixed effects models optimal design tool. Comput Methods Programs Biomed. 2012;108(2):789-805.
[8] Miller, F., Guilbaud, O., and Dette, H. Optimal designs for estimating the interesting part of a dose-effect curve. Journal of Biopharmaceutical Statistics, 17(6), 1097-115, 2007.
[9] Kågedal M, Karlsson MO, Hooker AC. Improved precision of exposure-response relationships by optimal dose-selection. Examples from studies of receptor occupancy using PET and dose finding for neuropathic pain treatment. J Pharmacokinet Pharmacodyn. 2015;42(3):211-24.
[10] Atkinson AD, AlexanderTobias, Randall. Optimum Experimental Designs, With SAS: Oxford University Press; 2007.
[11] Beal S, Sheiner L, Boeckmann A, Bauer R. NONMEM user’s guides. (1989–2009). Ellicott City: Icon Dev. Solut. 2009
[12] Keizer RJ, Karlsson MO, Hooker A. Modeling and Simulation Workbench for NONMEM: Tutorial on Pirana, PsN, and Xpose. CPT Pharmacometrics Syst Pharmacol. 2013;2:e50.
