**Virtual Patient Populations: Comparison of Approaches in Application to QSP Model Of Erythropoiesis**

Galina Kolesova (1), Oleg Demin (1), Alexander Stepanov (1)

(1) InSysBio, Moscow, Russia

**Introduction: **In a standard situation, the QSP model describes some “reference patient”, i.e. the model parameters are fixed values, allowing only mean values to be described. But 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 reproduction of the variability in response to a drug technique in the QSP model virtual patient population is usually generated.

**Objectives:** In the study we apply and compare results of four different approaches to generate virtual patient populations basing on experimentally measured mean data and standard deviation (sd).

**Methods:** To implement our approaches, we used QSP model of erythropoiesis [1].** **Model was constructed to comprehensively describe cell dynamics from hematopoietic stem cell to circulating red cells. The model describes cell self-renewal, differentiation, proliferation, migration from bone marrow into circulation and cell death. Binding of growth factors such as stem cell factor (SCF) and erythropoietin (EPO) to cell-surface receptors regulates cell dynamics modulated by interleukin-3 (IL-3). The model was calibrated across published in vitro/in vivo data.

Data describing time series of plasma reticulocyte count in response to single dose erythropoietin administered to 5 healthy subjects is used to generate the population of virtual patients (VP). Experimental data are given in the form of mean and sd. Reticulocyte count was measured at 16 time points.

The following four approaches to generate virtual patient populations (VPpop) were applied: (1) Monte-Carlo Markov Chain, (2) Model fitting to Monte-Carlo sample, (3) Population of clones, (4) Stochastically bounded selection. 39 parameters of the erythropoiesis model were chosen to be responsible for variability in observed clinical data. Initial VPpop was generated based on a priori distribution of the selected parameters. Number of VPs equal to that specified in clinical data and allowing to satisfactory describe both mean and SD of reticulocyte values measured clinically were chosen from initial VPpop on the basis of each of the approaches. The comparison of approaches was done for the relatively small population size (5 VPs) and relatively big one (207 VPs).

**Results:** All approaches were applied to create a population of virtual patients of size 5 (which corresponds to clinical trials) and size 207. In each approach we obtained some predicted distributions describing experimental data. Having these distributions, we compare their performance to decide which one is the most suitable. In the case of 5 patients Approach 1 gives poorly describes mean and sd measured experimentally. Better results were obtained in the Approach 2, which provides relatively accurate mean value estimates, however sd values turned out to be too small. The last flaw is resolved in the results of application of the Approach 4. In this case even for extremely small sample size relatively good estimates of both mean and sd values were obtained. Turning to the case of 207 patients, visual assessment of the results shows that all approaches appear to have relatively good accuracy of mean estimates at every moment of time. However, relatively precise estimates of sd are obtained only in the Approach 4. We also generate the Q-Q plots to compare the predicted in each approach distributions with the experimental ones. Doing this, we show that the Approach 4 provides the largest number of relatively accurate time points. In addition, since the experimental data are given in the form of series of mean and sd, we use one sample t-test to assess the statistical significance. Approach 1 provides statistically significant results at three time points, Approach 2 - in two time points, Approach 4 - in four time points.

**Conclusions:** The approaches proposed are capable for reproducing the endpoint distribution characteristics. According to the results of comparisons, Approach 4 is the most preferable and universal. Moreover, this approach appears to have the smallest computational complexity and, therefore, it can be applied even to the high dimensional models with large number of variable parameters.

**References:**

[1] ACoP11, "Stimulation of erythropoiesis with ESA or blood donation: QSP model", A. Stepanov, G. Lebedeva