Dynamics and implications of models for intermittent androgen suppression therapy

Phan, Tin; He, Changhan; Martínez, Alejandro; Kuang, Yang

doi:10.3934/mbe.2019010

Cited by 12 publications

(31 citation statements)

References 24 publications

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“…This was missed by the original effort, most likely because their attention was focused on intermittent therapy. Phan et al [48] show that the main reason for this biological limitation is due to the PKN model having a reversible transformation between the two subpopulations. On the other hand, by having only a transformation from AD to AI cells, which inversely depends on the serum androgen level, the BK model avoids this biological limitation and can produce relapse for CAS.…”

Section: Portz Et Al (2012)mentioning

confidence: 99%

“…Phan et al [48] also compared a two subpopulation version of the BK model and a three subpopulation version with a similar structure to the HBA model. They observed that the limitation of data types and data points hinders significant improvements in using a more complex model.…”

Section: Phan Et Al (2019)mentioning

confidence: 99%

“…In the case of difficulty in estimating certain parameters from laboratory data, researchers also rely on experts' opinions or fix the parameters in an ad hoc way [20,43]. Alternatively, the model can also be derived from physical laws (e.g., conservation laws), which introduce competition rates without adding additional explicit parameters for competition between cells [47,48,50]. For readers interested in how some parameters are estimated in existing models, we refer to studies [16,51], where binding rates are estimated from multi-level processes.…”

Section: Parameter Rangesmentioning

confidence: 99%

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Review: Mathematical Modeling of Prostate Cancer and Clinical Application

et al. 2020

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We review and synthesize key findings and limitations of mathematical models for prostate cancer, both from theoretical work and data-validated approaches, especially concerning clinical applications. Our focus is on models of prostate cancer dynamics under treatment, particularly with a view toward optimizing hormone-based treatment schedules and estimating the onset of treatment resistance under various assumptions. Population models suggest that intermittent or adaptive therapy is more beneficial to delay cancer relapse as compared to the standard continuous therapy if treatment resistance comes at a competitive cost for cancer cells. Another consensus among existing work is that the standard biomarker for cancer growth, prostate-specific antigen, may not always correlate well with cancer progression. Instead, its doubling rate appears to be a better indicator of tumor growth. Much of the existing work utilizes simple ordinary differential equations due to difficulty in collecting spatial data and due to the early success of using prostate-specific antigen in mathematical modeling. However, a shift toward more complex and realistic models is taking place, which leaves many of the theoretical and mathematical questions unexplored. Furthermore, as adaptive therapy displays better potential than existing treatment protocols, an increasing number of studies incorporate this treatment into modeling efforts. Although existing modeling work has explored and yielded useful insights on the treatment of prostate cancer, the road to clinical application is still elusive. Among the pertinent issues needed to be addressed to bridge the gap from modeling work to clinical application are (1) real-time data validation and model identification, (2) sensitivity analysis and uncertainty quantification for model prediction, and (3) optimal treatment/schedule while considering drug properties, interactions, and toxicity. To address these issues, we suggest in-depth studies on various aspects of the parameters in dynamical models such as the evolution of parameters over time. We hope this review will assist future attempts at studying prostate cancer.Prostate cancer (PCa) is the leading cause of cancer in US men (behind non-melanoma skin cancers), as well as the second leading cause of cancer-related mortality in men. The American Cancer Society estimates that in 2020, 191,930 Americans will be diagnosed with prostate cancer, with approximately 21.5% of all new cancer cases in men. The average five-year survival rate for all cases of prostate cancer is about 99%, which is a 31% point higher than in the 1970s [1]. However, once cancer metastasizes, the five-year survival rate drops to 30%, an increase of 10 percentage-point compared to the 1970s [2]. While the incidence of prostate cancer in the US is decreasing (see Figure 1), one possible cause is doctors' discouragement of early PCa diagnosis due to the fear of overtreating cancer. Globally, the incidence of prostate cancer is increasing, especially among developing nations [3].

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Section: Portz Et Al (2012)mentioning

confidence: 99%

Section: Phan Et Al (2019)mentioning

confidence: 99%

Section: Parameter Rangesmentioning

confidence: 99%

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Review: Mathematical Modeling of Prostate Cancer and Clinical Application

et al. 2020

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“…In this paper, we focus on a previous approach by Baez and Kuang, which was the first successful attempt at using both PSA and androgen data for fitting and forecasting [8]. A recent work by Phan et al [18] shows that, with the available types of data (e.g., PSA and androgen data), the model in Baez and Kuang (BK model) has the optimal population structure to describe and to forecast the dynamics of prostate cancer under IAS. On the other hand, the model fails to completely capture the growth phase of the PSA level when the patient is taken off treatment.…”

Section: Introductionmentioning

confidence: 99%

“…The data is taken from a clinical study from the Vancouver Prostate Center [19]. Similar to [18], we select 26 patients with sufficient data for fitting and forecasting comparisons, over 2.5 cycles of treatment.…”

Section: Introductionmentioning

confidence: 99%

The Impact of Intermittent Androgen Suppression Therapy in Prostate Cancer Modeling

et al. 2018

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Previous studies on prostate cancer modeling under hormonal therapy successfully fit clinical serum androgen data, under the assumption that the levels of intracellular and serum androgen are similar. However, such an assumption may not hold throughout the course of treatment. In this paper, we propose a model that directly accounts for serum androgen and its interaction with intracellular androgen. We establish biological links between the model and clinical data, and discuss in detail parameter ranges and the initialization of model variables. We further investigate parameter sensitivity over time, which gauges the maximum effect of varying each parameter and allows us to fix some parameters, to increase the robustness of the parameter fitting process. By relying on the characteristics of intermittent androgen suppression therapy (IAS), we employ a two-part weighted error function for fitting. We also carry out mathematical analyses to study the dynamic aspects of the system with different androgen thresholds. We find that the proposed model shows superior forecasting ability, compared to its predecessor. Furthermore, we demonstrate the impact of androgen on the dynamics of the androgen-dependent and -independent cancer cells, which suggests the discrete description of androgen dependency may not give a realistic characterization of the cancer population. We show that IAS has certain characteristics that need to be considered for parameter estimation. Our results demonstrate that the model and the fitting scheme are viable for similar applications of prostate cancer modeling under hormonal therapy.

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Intermittent Hormone Therapy Models Analysis and Bayesian Model Comparison for Prostate Cancer

et al. 2021

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The prostate is an exocrine gland of the male reproductive system dependent on androgens (testosterone and dihydrotestosterone) for development and maintenance. First-line therapy for prostate cancer includes androgen deprivation therapy (ADT), depriving both the normal and malignant prostate cells of androgens required for proliferation and survival. A significant problem with continuous ADT at the maximum tolerable dose is the insurgence of cancer cell resistance. In recent years, intermittent ADT has been proposed as an alternative to continuous ADT, limiting toxicities and delaying time-to-progression. Several mathematical models with different biological resistance mechanisms have been considered to simulate intermittent ADT response dynamics. We present a comparison between 13 of these intermittent dynamical models and assess their ability to describe prostate-specific antigen (PSA) dynamics. The models are calibrated to longitudinal PSA data from the Canadian Prospective Phase II Trial of intermittent ADT for locally advanced prostate cancer. We perform Bayesian inference and model analysis over the models’ space of parameters on- and off-treatment to determine each model’s strength and weakness in describing the patient-specific PSA dynamics. Additionally, we carry out a classical Bayesian model comparison on the models’ evidence to determine the models with the highest likelihood to simulate the clinically observed dynamics. Our analysis identifies several models with critical abilities to disentangle between relapsing and not relapsing patients, together with parameter intervals where the critical points’ basin of attraction might be exploited for clinical purposes. Finally, within the Bayesian model comparison framework, we identify the most compelling models in the description of the clinical data.

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Dynamics and implications of models for intermittent androgen suppression therapy

Cited by 12 publications

References 24 publications

Review: Mathematical Modeling of Prostate Cancer and Clinical Application

Review: Mathematical Modeling of Prostate Cancer and Clinical Application

The Impact of Intermittent Androgen Suppression Therapy in Prostate Cancer Modeling

Intermittent Hormone Therapy Models Analysis and Bayesian Model Comparison for Prostate Cancer

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