Galina Kolesova (1), Oleg Demin (1), Evgeny Metelkin (1), Dmitry Shchelokov (1,2)
(1) InSysBio, Moscow, Russia, (2) Lomonosov Moscow State University, Faculty of Biology, Moscow, Russia
Introduction: Conventional approach of QSP modelling includes the procedure of fitting of a model output to series of mean data values. As a result parameters of the model represent fixed numbers enabling to describe mean data. However, the results of clinical trials include description of variability in patient response to a drug which is typically expressed in terms of conventional statistics such as standard deviations from mean values. To allow a QSP model to reproduce the variability in response to a drug technique of generation of virtual patient population is usually applied. In framework of the technique some selected parameters of the QSP model are represented as random variable with some distribution. The empiric distribution is determined on the basis of mean data and statistics measured clinically via generation and selection of virtual patient populations described by a series of parameters randomly chosen from distribution of the selected parameters. Several techniques can be applied to generate virtual patient populations.
Objectives: In the study we propose and compare two different techniques to generate virtual patient populations basing on experimentally measured mean data and statistics. We apply these techniques to determine distribution of selected parameters of two different models: the one of Physiologically based pharmacokinetic model of anti-PD-1 therapeutic antibodies [1] and the model imitating skin inflammation. We use the distributions to reproduce variability of initial experimental data, i.e. to compare predictive power of these techniques.
Methods: We used following models:
- a minimal physiologically based pharmacokinetic (PBPK) model of drug disposition focusing on a group of immune checkpoint inhibitors blocking the PD-1 receptor;
- the model describing interaction between keratinocytes and T-cells.
Experimental data are given in the form of mean (m) and standard deviation (sd). The source of variability in QSP model is selected variabe parameters. Distributions of the selected variable parameters are chosen in such a way to provide coincidence between experimentally observed and simulated statistics (m and sd). The following techniques were applied to generate virtual patient populations:
Approach 1 (based on Bayesian approach [2])
- Assume that prior distributions of the parameters , to which the model is most sensitive, are described by particular distribution (e.g. truncated normal) with some parameters
- Means of parameters’ values are fixed (results of the fitting of the model)
- To obtain the desired distribution of the control function we use Monte-Carlo Markov Chain (MCMC)
Approach 2 (Monte-Carlo based approach)
- Generate a series of control function values from appropriate distribution characterized by m and sd.
- Fit the model parameters to every control function value.
- As a result of fitting one obtains a series of vectors of parameters’ values. This series represents sample from required parameters’ distribution.
To accelerate both procedures one can use some approximation of the model results with respect to chosen variable parameters. This approximation may be used instead of exact model output during MCMC algorithm or for parameters fitting.
Results: We provide the proof of concepts by the example of the model of skin inflammation. To test the approaches instead of real control function we used a function constructed as linear combination of the model variables. Both approaches were used to generate virtual patients populations. The approaches were compared in terms of distribution characteristics approximation quality and operation time needed.
- Approach 1
|
|
Data |
Results with model approximation |
Results with exact model |
|
m |
3.5 . 106 |
3.5 . 106 |
3.5 . 106 |
|
sd |
2.8 . 105 |
2.9 . 105 |
2.9 . 105 |
- Approach 2
Control function means:
|
Time, hour |
168 |
336 |
672 |
1008 |
1344 |
|
Data |
-12.01 |
-24.57 |
-37.95 |
-41.77 |
-42.87 |
|
Results with model approximation |
-13.11 |
-27.27 |
-36.90 |
-37.22 |
-37.06 |
|
Results with exact model |
-22.30 |
-33.49 |
-42.05 |
-43.45 |
-44.37 |
Control function standard deviations:
|
Time, hour |
168 |
336 |
672 |
1008 |
1344 |
|
Data |
24.49 |
32.66 |
38.78 |
40.82 |
40.82 |
|
Results with model approximation |
29.16 |
29.82 |
31.95 |
33.55 |
34.84 |
|
Results with exact model |
36.17 |
33.04 |
32.57 |
33.79 |
34.59 |
Conclusion: Both approaches proposed are capable for reproducing the control function distribution characteristics. The choice of a specific technique is determined by characteristics of the particular problem. Namely, in case of distribution with relatively small sd both methods work similarly. However, to reproduce distributions with relatively large sd second methodology is preferable.
References:
[1] Sengers BG, et al. Modeling bispecific monoclonal antibody interaction with two cell membrane targets indicates the importance of surface diffusion. MAbs. 2016 Jul;8(5):905-15.
[2] Gupta, Ankur; Rawlings, James B. (April 2014). “Comparison of Parameter Estimation Methods in Stochastic Chemical Kinetic Models: Examples in Systems Biology”. AIChE Journal. 60 (4): 1253–1268. doi:10.1002/aic.14409.
Reference: PAGE 28 (2019) Abstr 9008 [www.page-meeting.org/?abstract=9008]
Poster: Methodology - Covariate/Variability Models