Dose selection by covariate assessment on the optimal dose for efficacy – application of machine learning in the context of PKPD
Venelin Mitov(1), Anne Kuemmel(1), Nathalie Gobeau(2), Mohammed Cherkaoui(2), Thomas Bouillon(1)
(1) Intiquan GmbH, Basel CH, (2) Medicines for Malaria Venture, Geneva, CH
Objectives: Dose finding (covariate/group based regimens) requires knowledge of the relationship between the dose and the treatment goal as well as the “safe” exposure range. Traditionally, these decisions are made by population pharmacokinetic-pharmacodynamic (PKPD) modeling and simulation, performing the covariate search on the PKPD model parameters. The approach suffers from high dimensionality, is time consuming and intricate. Identified covariates may not impact dose selection for the intended treatment effect. We propose an alternative approach, shifting the search for covariates from parameters of the PKPD model to the optimal dose for efficacy within a “safe” search space, reducing the dimensionality of the problem.
Methods: The proposed approach consists of 3 main steps: Step A: Based on individual PKPD parameters, covariates, specific values of an efficacy and a safety criterion, a suitable algorithm is used to determine the optimal dose for each (virtual) patient. Step B: A machine learning or regression analysis is used to describe the relationship between the optimal individual dose and the patient characteristics to determine dosing rules adapted to patient groups within the target population. Step C: This regimen is then tested for target attainment and safety in a population setting.
The approach is illustrated with a virtual antimalarial drug. A PKPD model either based on data from a large clinical trial or using a PBPK + PD model is mandatory. Here, PK observations were generated from a PBPK model of the virtual drug. 3000 virtual individuals (Asians (Tanaka, 1996); 0-2ys, 2-18ys, 18-81ys, n=1000 each) were sampled (PK-sim ) and concentration time courses simulated. A compartmental popPK model was fitted to this data, simulated PD parameters, initial total parasite load and the individual covariates were added prior to further processing. Single Dose (SD), q24h*3 (MD3) and q24h*5 (MD5) regimens and 2 max. kill rates (0.25 1/h, 0.6 1/h) were investigated (6 scenarios).
Step A: The efficacy goal was defined as eradication of the initial individual parasite load, as predicted by the PKPD model, the max. individual doses constraining the search space were calculated corresponding to a “safe” AUCinf. Using a root finding algorithm in R, the lowest dose fulfilling the efficacy criterion was determined for each patient. Virtual patients for whom a safe and efficacious dose could not be found were flagged and their proportion reported. For the others, the doses identified were considered the optimal individual doses.
Step B: A covariate search on the optimal doses was performed with multivariate adaptive regression splines (MARS)  (R package “earth”). Covariates considered were weight, age, gender, and initial parasite load. The resulting doses were scaled up to achieve >=0.95 fraction cured in the population (median ED95/ED50 over population subgroups, factor 6.5).
Step C: The population PKPD model was simulated with discretized derived dosing rules (3 tablet sizes, 1-4 tablets per dosing event) to assess target attainment and safety of the covariate based “real world” dosing regimen.
Step A, For the low max. kill rate, the fraction of patients for whom a safe and efficacious dose was found was 0.08, 0.56 and 0.89, for the high max. kill rate 0.51, 0.87 and 0.96 (SD, MD3, MD5, respectively). The third scenario was carried forward into step B.
Step B, MARS determined age and weight as important covariates for the dose and discarded gender and initial parasite load, both correlated with weight. The complex dosing rule was discretized yielding 3 dose sizes to be administered in 1-4 tablets.
Step C: Corresponding target attainment is >0.95 in all subgroups, attainment of safety is 99.85% overall.
Conclusions: The proposed approach can be developed into a highly automated and efficient dose finding workflow. The single steps are rather simple and the dimensionality of covariate modeling is reduced to finding relevant predictors of achieving the treatment goal rather than establishing their effect on a multitude of model parameters. Safety is implied in dose selection by constraining the search space to doses not violating a safety criterium. “If you can model it, you can find a safe and effective dose.”
 Friedman J. Multivariate Adaptive Regression Splines. Annals of Statistics 1991 (19): 1-141