Analyzing the quality robustness of chemotherapy plans with respect to model uncertainties

Hoffmann, Anna; Scherrer, Alexander; Küfer, Karl‐Heinz

doi:10.1016/j.mbs.2014.11.003

Cited by 5 publications

(4 citation statements)

References 24 publications

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“…Due to the complexity of these models, however, it is difficult to trace the effect of the choice of growth model and determine how this choice might alter the model’s predictions. In fact, while model predictions are often assessed for sensitivity to errors in estimates of the parameters [ 48 , 49 ], the effect of model assumptions is often neglected. Our findings, however, indicate that these assumptions could have a profound effect on model predictions since our simple models show that different choices of growth model result in large variations in model predictions.…”

Section: Discussionmentioning

confidence: 99%

Differences in predictions of ODE models of tumor growth: a cautionary example

2016

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BackgroundWhile mathematical models are often used to predict progression of cancer and treatment outcomes, there is still uncertainty over how to best model tumor growth. Seven ordinary differential equation (ODE) models of tumor growth (exponential, Mendelsohn, logistic, linear, surface, Gompertz, and Bertalanffy) have been proposed, but there is no clear guidance on how to choose the most appropriate model for a particular cancer.MethodsWe examined all seven of the previously proposed ODE models in the presence and absence of chemotherapy. We derived equations for the maximum tumor size, doubling time, and the minimum amount of chemotherapy needed to suppress the tumor and used a sample data set to compare how these quantities differ based on choice of growth model.ResultsWe find that there is a 12-fold difference in predicting doubling times and a 6-fold difference in the predicted amount of chemotherapy needed for suppression depending on which growth model was used.ConclusionOur results highlight the need for careful consideration of model assumptions when developing mathematical models for use in cancer treatment planning.

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Section: Discussionmentioning

confidence: 99%

Differences in predictions of ODE models of tumor growth: a cautionary example

2016

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“…Further, from any such optimal control problem, one could perform a sensitivity or elasticity analysis (similar to the one performed herein; see SI Results) to quantify how parametric changes influence the quality of an optimal treatment protocol, as in ref. 48.…”

Section: Discussionmentioning

confidence: 99%

Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy

Barish

Ochs

Sontag

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Cancer is a highly heterogeneous disease, exhibiting spatial and temporal variations that pose challenges for designing robust therapies. Here, we propose the VEPART (Virtual Expansion of Populations for Analyzing Robustness of Therapies) technique as a platform that integrates experimental data, mathematical modeling, and statistical analyses for identifying robust optimal treatment protocols. VEPART begins with time course experimental data for a sample population, and a mathematical model fit to aggregate data from that sample population. Using nonparametric statistics, the sample population is amplified and used to create a large number of virtual populations. At the final step of VEPART, robustness is assessed by identifying and analyzing the optimal therapy (perhaps restricted to a set of clinically realizable protocols) across each virtual population. As proof of concept, we have applied the VEPART method to study the robustness of treatment response in a mouse model of melanoma subject to treatment with immunostimulatory oncolytic viruses and dendritic cell vaccines. Our analysis (i) showed that every scheduling variant of the experimentally used treatment protocol is fragile (nonrobust) and (ii) discovered an alternative region of dosing space (lower oncolytic virus dose, higher dendritic cell dose) for which a robust optimal protocol exists.robust therapies | cancer treatment | mathematical modeling | virotherapy | immunotherapy H eterogeneity is a defining feature of cancer (1, 2). Interpatient heterogeneity manifests clinically in variable disease progression and treatment response between patients with the same diagnosis, whereas intrapatient heterogeneity describes variations that exist between tumor cells in a single patient. Intrapatient heterogeneity can be broken down further into intratumor heterogeneity, intrametastatic heterogeneity, intermetastatic heterogeneity, and temporal heterogeneity (2, 3). Intratumor heterogeneity is evident through the presence of multiple genetic subclones within a primary tumor (2), which have even been shown to exist in spatially distinct regions of the primary tumor (4). Intrametastatic heterogeneity is similar to intratumor heterogeneity, but describes heterogeneity within a single metastatic lesion instead of within the primary tumor (2). Intermetastatic heterogeneity, on the other hand, describes variations in subclones between different metastases in the same patient (2). Finally, temporal heterogeneity is defined as changes that take place in the tumor over time, whether they are a result of genomic instability, natural selection, non-Darwinian evolution, or selective pressures imposed by treatment (4-6). Note that, in each case, heterogeneity need not be genetic but may also be epigenetic, phenotypic, or microenvironmental (2, 7, 8).For decades, cancer patients have been treated using standard of care, meaning they receive the best known treatment that has been deemed as efficacious and safe in epidemiological studies (9). However, in the face of such int...

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“…Even within the framework of a mathematical model, how exactly to quantify the effectiveness of the schedule and multidrug mixture when the schedule is adaptive (i.e., not fixed and repeatable) is not at all straightforward. We address this important issue of uncertainty quantification and robustness [22][23][24] of tumor response to adaptive therapy schedules and synergystic vs. antagonistic multidrug interactions [25,26] by using a stochastic finite-cell fitness-dependent Moran process evolutionary game theory tumor model with an adaptive schedule designed from the deterministic adjusted replicator dynamical system [27], which is the large cell limit (N → ∞) of the finite-cell stochastic process [28,29]. We describe the main features of our model as well as the connections between the finite cell stochastic model and infinite cell deterministic model in the next section.…”

Section: Introductionmentioning

confidence: 99%

Are Adaptive Chemotherapy Schedules Robust? A Three-Strategy Stochastic Evolutionary Game Theory Model

Dua

Newton

2021

Cancers

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We investigate the robustness of adaptive chemotherapy schedules over repeated cycles and a wide range of tumor sizes. Using a non-stationary stochastic three-component fitness-dependent Moran process model (to track frequencies), we quantify the variance of the response to treatment associated with multidrug adaptive schedules that are designed to mitigate chemotherapeutic resistance in an idealized (well-mixed) setting. The finite cell (N tumor cells) stochastic process consists of populations of chemosensitive cells, chemoresistant cells to drug 1, and chemoresistant cells to drug 2, and the drug interactions can be synergistic, additive, or antagonistic. Tumor growth rates in this model are proportional to the average fitness of the tumor as measured by the three populations of cancer cells compared to a background microenvironment average value. An adaptive chemoschedule is determined by using the N→∞ limit of the finite-cell process (i.e., the adjusted replicator equations) which is constructed by finding closed treatment response loops (which we call evolutionary cycles) in the three component phase-space. The schedules that give rise to these cycles are designed to manage chemoresistance by avoiding competitive release of the resistant cell populations. To address the question of how these cycles perform in practice over large patient populations with tumors across a range of sizes, we consider the variances associated with the approximate stochastic cycles for finite N, repeating the idealized adaptive schedule over multiple periods. For finite cell populations, the distributions remain approximately multi-Gaussian in the principal component coordinates through the first three cycles, with variances increasing exponentially with each cycle. As the number of cycles increases, the multi-Gaussian nature of the distribution breaks down due to the fact that one of the three sub-populations typically saturates the tumor (competitive release) resulting in treatment failure. This suggests that to design an effective and repeatable adaptive chemoschedule in practice will require a highly accurate tumor model and accurate measurements of the sub-population frequencies or the errors will quickly (exponentially) degrade its effectiveness, particularly when the drug interactions are synergistic. Possible ways to extend the efficacy of the stochastic cycles in light of the computational simulations are discussed.

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Analyzing the quality robustness of chemotherapy plans with respect to model uncertainties

Cited by 5 publications

References 24 publications

Differences in predictions of ODE models of tumor growth: a cautionary example

Differences in predictions of ODE models of tumor growth: a cautionary example

Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy

Are Adaptive Chemotherapy Schedules Robust? A Three-Strategy Stochastic Evolutionary Game Theory Model

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