Population pharmacokinetic model selection assisted by machine learning

Abstract

A fit-for-purpose structural and statistical model is the first major requirement in population pharmacometric model development. In this manuscript we discuss how this complex and computationally intensive task could benefit from supervised machine learning algorithms. We compared the classical pharmacometric approach with two machine learning methods, genetic algorithm and neural networks, in different scenarios based on simulated pharmacokinetic data. Genetic algorithm performance was assessed using a fitness function based on log-likelihood, whilst neural networks were trained using mean square error or binary cross-entropy loss. Machine learning provided a selection based only on statistical rules and achieved accurate selection. The minimization process of genetic algorithm was successful at allowing the algorithm to select plausible models. Neural network classification tasks achieved the most accurate results. Neural network regression tasks were less precise than neural network classification and genetic algorithm methods. The computational gain obtained by using machine learning was substantial, especially in the case of neural networks. We demonstrated that machine learning methods can greatly increase the efficiency of pharmacokinetic population model selection in case of large datasets or complex models requiring long run-times. Our results suggest that machine learning approaches can achieve a first fast selection of models which can be followed by more conventional pharmacometric approaches.

Keywords: Deep learning; Genetic algorithm; Model-informed drug discovery and development; Neural network; Pharmacometrics; Population PK/PD.

Fig. 1

General workflow—the first step was the data and model library generation, followed by the investigation of the three approaches selected (PMX, GA, and NN). GA genetic algorithm, NN neural network, PMX pharmacometric

Fig. 2

Hybrid GA—the hybrid component makes the GA convergence faster by performing an exhaustive search around the best models. GA genetic algorithm. N is a parameter (integer) set by the user for the GA

Fig. 3

Example of training output parameters for the two NN tasks. CL clearance, Fr bioavailability, Ka 1 order absorption, Km and Vm Michaelis–Menten elimination, Ktr transitory compartment, Mtt transitory compartment, NN neural network, Q2 and Q3 inter-compartmental clearance, TK0 0 order absorption, T_lag lag time, V volume for central compartment, V2 volume for second compartment, V3 volume for third compartment. Note For the regression task, individual pharmacokinetic parameters constitute the output to be predicted (top table). Data for the classification task can be derived from this by combining parameters into model components binarily labeled according to their presence or absence (bottom table)

Fig. 4

NN train and test MSE obtained for regression, A during the learning phase for the global NN, and B if 14 independent NN were trained for each of the parameters. On panel A, train and test MSE obtained during the learning phase for the global NN are shown in dashed and solid lines, respectively, for the full NN (red) and for the NN without prediction of Km and V3 (blue). On panel B, train and test MSE obtained during the learning phase are shown in dashed and solid lines, respectively, for 14 independent NN trained for each of the parameters. CL clearance, Fr bioavailability, Ka 1 order absorption, Km Michaelis–Menten elimination, Ktr transitory compartment, Mtt transitory compartment, MSE mean squared error, NN neural network, Q2 and Q3 inter-compartmental clearance, TK0 0 order absorption, T_lag lag time, V volume for central compartment, V2 volume for second compartment, V3 volume for third compartment, Vm Michaelis–Menten elimination. Note Various NNs for regression were trained (Color figure online)

Fig. 5

Evolution of the percentage of the label correctly predicted in the NN classification task. NN, neural network. Note: NN classification results are shown for scenario 1 (random split) where the test set was randomly selected (red curves), and for scenario 2 (non-random) where all observations of two models not included in the training set were selected to compose the test set (Color figure online)