Single objective genetic algorithm based approach for optimal population pharmacokinetic/pharmacodynamics (PK/PD) model selection for tumor growth response
Nikhil Pillai1, Sihang Liu2*, Mohamed Ismail2, Beth Pflug3, Mark Sale4, Robert Bies1,2. *co-first author
1 Computational and Data Enabled Sciences, University at Buffalo, Buffalo, NY, USA; 2 Department of Pharmaceutical Sciences, School of Pharmacy and Pharmaceutical Sciences, University at Buffalo, Buffalo, NY, USA; 3 Roswell Park Comprehensive Cancer Center, Buffalo, NY, USA; 4 Nuventra Pharma Sciences, Durham, North Carolina, USA
Objectives:
Traditional approach to PK/PD model selection proceeds in a stepwise manner, first finding the best base structural model, and then searching for significant covariate relationships and statistical models. The stepwise approach ignores the interaction between structural, statistical and covariate effects; it involves a local search, is time consuming and is prone to errors as it involves manual editing of control streams. Thus, the model selected using the traditional stepwise approach may not be a globally optimal model. To overcome the issues faced by traditional approach one can use a global search algorithm. Genetic algorithm (GA) is one such method, which can help the modeler to find a global optimal model. The objective of this work is to develop a model, which best describes the dataset using single objective GA (SOGA) [1] and compare it to the model obtained using traditional approach.
Methods:
24 mice with established LNCaP xenograft tumors were randomized into four groups: control, vehicle treatment (5 intact mice); intact (not castrated) with diazepam treatment (5 mice), castrated mice with vehicle treatment (7 mice) and castrated mice receiving diazepam treatment (7 mice). Kinetics of tumor growth were modeled using nonlinear mixed effects modeling with NONMEM 7.4. First order conditional estimation with interaction was used for estimation purposes. While developing the model using traditional approach we used goodness of fit plots and objective function values for model selection and while developing the model using SOGA we used a fitness function to guide the model selection (eqn 1).
Fitness=-2LL+2*Npar+10*Pconvergence+10*Pcovariance 1
Where -2LL is the negative 2 log likelihood, Npar is the number of estimated parameters, Pconvergence is penalty for unsuccessful convergence and Pcovariance is a penalty for an unsuccessful covariance step.
While developing the model using traditional approaches the initial modelling focused on selecting a growth function capable of characterizing the tumor growth without intervention. Gompertz, Simeoni[2], Koch[3], logistic and exponential growth models were evaluated. Since there is a delay between drug treatment and tumor regression, a transit compartment model was used to describe the effect of drug on tumor. To analyze whether a particular intervention had a significant effect on the tumor growth, each intervention was tested using a stepwise addition and backward elimination strategy. In each growth model, combinations of four IIV model structures (none, additive, proportional, logarithmic) and three residual error structures (additive, proportional, additive+proportional) were tested.
Results:
The model selected using the traditional approach was the Simeoni model with an OFV value of 5135.724. This model had a proportional IIV on λ0, λ1, k1, k2 and a combined residual error model. The model selected using SOGA approach was the Koch model and had a fitness value of 4958, OFV value of 4922, had logarithmic IIV on λ0, λ1 and baseline tumor size. The treatment (intact) group had no IIV on k1, proportional IIV on k2. The model for castrated mice with vehicle treatment had logarithmic IIV on k1, normal IIV on k2. The model for castrated mice with drug treatment group had no IIV on k1, proportional IIV on k2 and a proportional residual error model was selected.
Conclusions:
SOGA was able to identify a model that had substantially lower OFV and fitness value compared to the model selected by traditional approach. SOGA automates the model development process and helps the researchers to focus on model evaluation, hypothesis testing and interpretation and application of resulting models rather than spending time on manual editing of control streams.
References:
[1]. Ismail M, Sale M, Bies R. An open source software solution for automating pharmacokinetic / pharmacodynamic model selection. Page Meeting, June 2018 https://www.page meeting.org/default.asp?abstract=8526, accessed 14 Feb, 2019
[2]. Simeoni M, Magni P, Cammia C, De Nicolao G, Croci V, Pesenti E, Germani M, Poggesi I,Rocchetti M (2004) Predictive pharmacokinetic–pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Res 64:1094–1101
[3]. Koch G1, Walz A, Lahu G, Schropp J. Modeling of tumor growth and anticancer effects of combination therapy. J Pharmacokinet Pharmacodyn. 2009 Apr;36(2):179-97.