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Personalizing oncology treatments by predicting drug efficacy, side‐effects, and improved therapy: mathematics, statistics, and their integration

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Despite its great promise, personalized oncology still faces many hurdles, and it is increasingly clear that targeted drugs and molecular biomarkers alone yield only modest clinical benefit. One reason is the complex relationships between biomarkers and the patient's response to drugs, obscuring the true weight of the biomarkers in the overall patient's response. This complexity can be disentangled by computational models that integrate the effects of personal biomarkers into a simulator of drug–patient dynamic interactions, for predicting the clinical outcomes. Several computational tools have been developed for personalized oncology, notably evidence‐based tools for simulating pharmacokinetics, Bayesian‐estimated tools for predicting survival, etc. We describe representative statistical and mathematical tools, and discuss their merits, shortcomings and preliminary clinical validation attesting to their potential. Yet, the individualization power of mathematical models alone, or statistical models alone, is limited. More accurate and versatile personalization tools can be constructed by a new application of the statistical/mathematical nonlinear mixed effects modeling (NLMEM) approach, which until recently has been used only in drug development. Using these advanced tools, clinical data from patient populations can be integrated with mechanistic models of disease and physiology, for generating personal mathematical models. Upon a more substantial validation in the clinic, this approach will hopefully be applied in personalized clinical trials, P‐trials, hence aiding the establishment of personalized medicine within the main stream of clinical oncology. This article is categorized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Mechanistic Models Translational, Genomic, and Systems Medicine > Translational Medicine

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Model‐predicted neutrophil counts over time compared to the observed neutrophil counts of metastatic BC patients, treated with different docetaxel schedules. Model predictions of the nadir days at each cycle vs. the observed nadir days (circles; N = 66; calculated correlation coefficient is r = 0.99). The dashed line represents the identity line.
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The suggested approach for creating personalized response predictors uses nonlinear mixed effects modeling to integrate clinical information with mechanistic mathematical models of drug–patient dynamic interactions.
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Clinical and predicted PSA dynamics. Panels (a), (b), and (c) are the respective examples of type (1), type (2), and type (3) patients from the American cohort of 79 patients. In each panel, actual PSA values (red circles) are shown across intermittent therapy fits (blue solid lines) and continuous therapy fits (green dashed line). In another example (d) data from the first two and half treatment cycles was used to predict the following cycles.
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Model predicted effects of different bevacizumab and docetaxel combination regimens on tumor growth in the MCS patient.
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Mathematical model predictions of tumor growth inhibition (TGI), calculated as TGI (%) = 100 · (1 − (TT0)/(CC0)), where T0, C0 are initial tumor sizes of the treated and the control tumor xenografts, respectively; T and C are sizes of treated or control tumor xenografts, respectively. The drug protocols that were simulated are shown at the bottom of each histogram bar: B/Doc denotes bevacizumab, 10 mg/kg, IV, Q3Dx10 +docetaxel, 25 mg/kg, IV, Q7Dx3; B/Doc/G denotes bevacizumab, 6.7 mg/kg, IV, day 1,8 + docetaxel, 25 mg/kg, IV, Q7Dx3 + gemcitabine, 160 mg/kg, IV infusion, 24 hr (single dose); S denotes sunitinib, 40 mg/kg, PO b.i.d x28; B/D denotes bevacizumab, 5 mg/kg, IP, Q4Dx6 + docetaxel, 3 mg/kg, IV, QDx8; B/Sor denotes bevacizumab, 5 mg/kg, IP, Q4Dx6 + Sorafenib, 85 mg/kg, PO, QDx10; other bars denote predicted TGI by drugs and drug protocols as above.
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Vascular tumor growth dynamics. A schematic description of the multiscale mathematical model for vascular tumor growth. Tissues (medium gray), cells (dark gray), and molecules (light gray) interact as marked by the arrows. Vascular endothelial growth factor (VEGF) and platlet‐derived growth factor (PDGF) are secreted by the tumor cells. VEGF binds to endothelial cells and PDGF to pericytes, to generate new and mature blood vessels, respectively; the ratio of Angiopoietin1 (Ang1) and Angiopoietin2 (Ang2), secreted both by the tumor and by endothelial cells, affects the stability of the mature vessels.
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Models of Systems Properties and Processes > Mechanistic Models
Analytical and Computational Methods > Computational Methods
Translational, Genomic, and Systems Medicine > Translational Medicine

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