Predicting time to castration resistance in hormone sensitive prostate cancer by a personalization algorithm based on a mechanistic model integrating patient data

From Fitting the Average to Fitting the Individual: A Cautionary Tale for Mathematical Modelers

An outstanding challenge in the clinical care of cancer is moving from a one-size-fits-all approach that relies on population-level statistics towards personalized therapeutic design. Mathematical modeling is a powerful tool in treatment personalization, as it allows for the incorporation of patient-specific data so that treatment can be tailor-designed to the individual. Herein, we work with a mathematical model of murine cancer immunotherapy that has been previously-validated against the average of an experimental dataset. We ask the question: what happens if we try to use this same model to perform personalized fits, and therefore make individualized treatment recommendations? Typically, this would be done by choosing a single fitting methodology, and a single cost function, identifying the individualized best-fit parameters, and extrapolating from there to make personalized treatment recommendations. Our analyses show the potentially problematic nature of this approach, as predicted personalized treatment response proved to be sensitive to the fitting methodology utilized. We also demonstrate how a small amount of the right additional experimental measurements could go a long way to improve consistency in personalized fits. Finally, we show how quantifying the robustness of the average response could also help improve confidence in personalized treatment recommendations.

Mathematical model of hormone sensitive prostate cancer treatment using leuprolide: A small step towards personalization

In this paper we present a new version of a mathematical model of Elishmereni et al. describing androgen deprivation therapy (ADT) for hormone sensitive prostate cancer patients (HSPC). We first focus on the detail description of the model, and then we present mathematical analysis of the proposed model, starting from the simplified model without resistance and ending on the full model with two resistance mechanisms present. We make a step towards personalization proposing an underlying tumor growth law base on a cohort of patients from Mayo hospital. We conclude that the model is able to reflect reality, that is in clinical scenarios the level of testosterone in HSPC patients inevitably rises leading to the failure of ADT.

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

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.

Nomogram Incorporating Contrast-Enhanced Ultrasonography Predicting Time to the Development of Castration-Resistant Prostate Cancer

Background

It is valuable to predict the time to the development of castration-resistant prostate cancer (CRPC) in patients with advanced prostate cancer (PCa). This study aimed to build and validate a nomogram incorporating the clinicopathologic characteristics and the parameters of contrast-enhanced ultrasonography (CEUS) to predict the time to CRPC after androgen deprivation therapy (ADT).

Methods

Patients with PCa were divided into the training (n = 183) and validation cohorts (n = 37) for nomogram construction and validation. The clinicopathologic characteristics and CEUS parameters were analyzed to determine the independent prognosis factors and serve as the basis of the nomogram to estimate the risk of 1-, 2-, and 3-year progress to CRPC.

Results

T stage, distant metastasis, Gleason score, area under the curve (AUC), prostate-specific antigen (PSA) nadir, and time to PSA nadir were the independent predictors of CRPC (all P < 0.05). Three nomograms were built to predict the time to CRPC. Owing to the inclusion of CEUS parameter, the discrimination of the established nomogram (C-index: 0.825 and 0.797 for training and validation datasets) was improved compared with the traditional prediction model (C-index: 0.825 and 0.797), and when it excluded posttreatment PSA, it still obtained an acceptable discrimination (C-index: 0.825 and 0.797).

Conclusions

The established nomogram including regular prognostic indicators and CEUS obtained an improved accuracy for the prediction of the time to CRPC. It was also applicable for early prediction of CRPC when it excluded posttreatment PSA, which might be helpful for individualized diagnosis and treatment.

Predicting patient-specific response to adaptive therapy in metastatic castration-resistant prostate cancer using prostate-specific antigen dynamics

Abiraterone acetate (AA) has been proven effective for metastatic castration-resistant prostate cancer (mCRPC), and it has been proposed that adaptive AA may reduce toxicity and prolong time to progression, when compared to continuous AA. We developed a simple quantitative model of prostate-specific antigen (PSA) dynamics to evaluate prostate cancer (PCa) stem cell enrichment as a plausible driver of AA treatment resistance. The model incorporated PCa stem cells, non-stem PCa cells and PSA dynamics during adaptive therapy. A leave-one-out analysis was used to calibrate and validate the model against longitudinal PSA data from 16 mCRPC patients receiving adaptive AA in a pilot clinical study. Early PSA treatment response dynamics were used to predict patient response to subsequent treatment. We extended the model to incorporate metastatic burden and also investigated the survival benefit of adding concurrent chemotherapy for patients predicted to become resistant. Model simulations demonstrated PCa stem cell self-renewal as a plausible driver of resistance to adaptive therapy. Evolutionary dynamics from individual treatment cycles combined with metastatic burden measurements predicted patient response with 81% accuracy (specificity=92%, sensitivity=50%). In those patients predicted to progress, simulations of the addition of concurrent chemotherapy suggest a benefit between 1% and 11% reduction in probability of progression when compared to adaptive AA alone. This study developed the first mCRPC patient-specific mathematical model to use early PSA treatment response dynamics to predict subsequent responses to adaptive AA, demonstrating the putative value of integrating mathematical modeling into clinical decision making.

Review: Mathematical Modeling of Prostate Cancer and Clinical Application

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-specific antigen dynamics predict individual responses to intermittent androgen deprivation

Intermittent androgen deprivation therapy (IADT) is an attractive treatment for biochemically recurrent prostate cancer (PCa), whereby cycling treatment on and off can reduce cumulative dose and limit toxicities. We simulate prostate-specific antigen (PSA) dynamics, with enrichment of PCa stem-like cell (PCaSC) during treatment as a plausible mechanism of resistance evolution. Simulated PCaSC proliferation patterns correlate with longitudinal serum PSA measurements in 70 PCa patients. Learning dynamics from each treatment cycle in a leave-one-out study, model simulations predict patient-specific evolution of resistance with an overall accuracy of 89% (sensitivity = 73%, specificity = 91%). Previous studies have shown a benefit of concurrent therapies with ADT in both low- and high-volume metastatic hormone-sensitive PCa. Model simulations based on response dynamics from the first IADT cycle identify patients who would benefit from concurrent docetaxel, demonstrating the feasibility and potential value of adaptive clinical trials guided by patient-specific mathematical models of intratumoral evolutionary dynamics.

MRI-Guided Ultrafocal Salvage High-Dose-Rate Brachytherapy for Localized Radiorecurrent Prostate Cancer: Updated Results of 50 Patients

PURPOSE

Most patients with local prostate cancer recurrence after radiation therapy undergo palliative androgen deprivation therapy because whole-gland salvage treatments have a high risk of severe toxicity. Focal treatment reduces this risk while offering a second opportunity for cure. We report updated outcomes of ultrafocal salvage high-dose-rate brachytherapy (HDR-BT).

METHODS AND MATERIALS

Prospectively collected data from the first 50 treated patients were analyzed. Disease status was assessed by 3T multiparametric magnetic resonance imaging (MRI), 18F-Choline or 68Ga-prostate-specific membrane antigen positron emission tomography/computed tomography, and systematic or tumor-targeted biopsies. Ultrafocal salvage HDR-BT (1 × 19 Gy) was performed by implanting the clinical target volume (CTV: gross tumor volume + 5 mm margin) under fused transrectal ultrasound/MRI guidance. Follow-up included toxicity grading (using Common Terminology Criteria for Adverse Events 4.0), quality of life assessment, and prostate-specific antigen (PSA) testing.

RESULTS

Median follow-up was 31 months. Median CTV D95% was 18.8 Gy. We observed 2% grade 3 genitourinary toxicity, no grade 3 gastrointestinal toxicity, and 22% newly developed grade 3 erectile dysfunction. Five of 13 patients (38%) with self-reported pretreatment potency (International Index of Erectile Function >17) remained potent. Clinically relevant quality of life deterioration was reported for only 6 of 31 items and was not statistically significant. Biochemical failure (nadir + 2) occurred in 26 patients. Among intraprostatic recurrences, 73% were in field. After 2.5 years, biochemical disease-free survival was 51% (95% confidence interval, 37%-69%), metastases-free survival was 75% (64%-89%), androgen deprivation therapy-free survival was 90% (82%-99%), and overall survival was 98% (94%-100%). Presalvage PSA, CTV size, and stage ≥T3 were significantly associated with biochemical failure. Higher-risk patients (stage ≥T3, PSA ≥10, or PSA double time ≤9 months) had 25% biochemical disease-free survival at 2.5 years versus 71% for lower-risk patients.

CONCLUSIONS

At this early stage, MRI-guided ultrafocal HDR-BT seems to be a safe salvage treatment option, with acceptable biochemical control in a well-selected group of patients and potential for effectively postponing androgen deprivation therapy.

Personal response to immune checkpoint inhibitors of patients with advanced melanoma explained by a computational model of cellular immunity, tumor growth, and drug

Immune checkpoint inhibitors, such as pembrolizumab, are transforming clinical oncology. Yet, insufficient overall response rate, and accelerated tumor growth rate in some patients, highlight the need for identifying potential responders. To construct a computational model, identifying response predictors, and enabling immunotherapy personalization. The combined dynamics of cellular immunity, pembrolizumab, and the melanoma cancer were modeled by a set of ordinary differential equations. The model relies on a scheme of T memory stem cells, progressively differentiating into effector CD8⁺ T cells, and additionally includes T cell exhaustion, reinvigoration and senescence. Clinical data of a pembrolizumab-treated patient with advanced melanoma (Patient O’) were used for model calibration and simulations. Virtual patient populations, varying in one parameter or more, were generated for retrieving clinical studies. Simulations captured the major features of Patient O’s disease, displaying a good fit to her clinical data. A temporary increase in tumor burden, as implied by the clinical data, was obtained only when assuming aberrant self-renewal rates. Variation in effector T cell cytotoxicity was sufficient for simulating dynamics that vary from rapid progression to complete cure, while variation in tumor immunogenicity has a delayed and limited effect on response. Simulations of a-specific clinical trial were in good agreement with the clinical results, demonstrating positive correlations between response to pembrolizumab and the ratio of reinvigoration to baseline tumor load. These results were obtained by assuming inter-patient variation in the toxicity of effector CD8+ T cells, and in their intrinsic division rate, as well as by assuming that the intrinsic division rate of cancer cells is correlated with the baseline tumor burden. In conclusion, hyperprogression can result from lower patient-specific effector cytotoxicity, a temporary increase in tumor load is unlikely to result from real tumor growth, and the ratio of reinvigoration to tumor load can predict personal response to pembrolizumab. Upon further validation, the model can serve for immunotherapy personalization.

Predicting response to pembrolizumab in metastatic melanoma by a new personalization algorithm

BACKGROUND

At present, immune checkpoint inhibitors, such as pembrolizumab, are widely used in the therapy of advanced non-resectable melanoma, as they induce more durable responses than other available treatments. However, the overall response rate does not exceed 50% and, considering the high costs and low life expectancy of nonresponding patients, there is a need to select potential responders before therapy. Our aim was to develop a new personalization algorithm which could be beneficial in the clinical setting for predicting time to disease progression under pembrolizumab treatment.

METHODS

We developed a simple mathematical model for the interactions of an advanced melanoma tumor with both the immune system and the immunotherapy drug, pembrolizumab. We implemented the model in an algorithm which, in conjunction with clinical pretreatment data, enables prediction of the personal patient response to the drug. To develop the algorithm, we retrospectively collected clinical data of 54 patients with advanced melanoma, who had been treated by pembrolizumab, and correlated personal pretreatment measurements to the mathematical model parameters. Using the algorithm together with the longitudinal tumor burden of each patient, we identified the personal mathematical models, and simulated them to predict the patient's time to progression. We validated the prediction capacity of the algorithm by the Leave-One-Out cross-validation methodology.

RESULTS

Among the analyzed clinical parameters, the baseline tumor load, the Breslow tumor thickness, and the status of nodular melanoma were significantly correlated with the activation rate of CD8+ T cells and the net tumor growth rate. Using the measurements of these correlates to personalize the mathematical model, we predicted the time to progression of individual patients (Cohen's κ = 0.489). Comparison of the predicted and the clinical time to progression in patients progressing during the follow-up period showed moderate accuracy (R² = 0.505).

CONCLUSIONS

Our results show for the first time that a relatively simple mathematical mechanistic model, implemented in a personalization algorithm, can be personalized by clinical data, evaluated before immunotherapy onset. The algorithm, currently yielding moderately accurate predictions of individual patients' response to pembrolizumab, can be improved by training on a larger number of patients. Algorithm validation by an independent clinical dataset will enable its use as a tool for treatment personalization.

The Impact of Intermittent Androgen Suppression Therapy in Prostate Cancer Modeling

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.

Intermediate PSA half-life after neoadjuvant hormone therapy predicts reduced risk of castration-resistant prostate cancer development after radical prostatectomy

Background

The magnitude and rapidity of the tumor response to androgen deprivation is known to predict the durability of the therapy. We have investigated the predictive value of categorizing patients by the half-life of PSA under neoadjuvant androgen deprivation therapy in patients with biochemical recurrence after radical prostatectomy.

Methods

Medical records of 317 patients who received neoadjuvant androgen deprivation therapy before radical prostatectomy and developed biochemical recurrence were analyzed. The patients were categorized into five groups according to PSA half-life. Risk of developing castration resistance was evaluated by Kaplan-Meier analysis and by Cox proportional risk regression analysis.

Results

The median follow-up duration was 50.1 months (IQR 31.8–68.7) and median PSA half-life was 22.1 days (IQR 12.7–38.4). Comparison of survival curves revealed that patients in the intermediate response group showed significantly lower 5-year castration-resistant prostate cancer rate (37.5%) compared to non-response and ultra-rapid response groups (63.6%, p = 0.007; 56.1%, p = 0.031; respectively). In the multivariate regression model, intermediate response compared to non-response was associated with significantly reduced risk of castration resistance development (hazard ratio 0.397, 95% confidence interval 0.191–0.823, p = 0.013) and overall mortality (hazard ratio 0.138, 95% confidence interval 0.033–0.584, p = 0.007). When subcategorized by Gleason score, Kaplan-Meier curve revealed that, in the high Gleason score stratum, 5-year castration-resistant prostate cancer rate for intermediate response group (44.0%) was exceptionally lower than that in non-response group (66.7%, p = 0.047), while castration resistance increased in other groups.

Conclusion

Short PSA half-life as well as no response after androgen deprivation is associated with increased risk of treatment failure compared to intermediate PSA half-life.

Electronic supplementary material

The online version of this article (10.1186/s12885-017-3775-6) contains supplementary material, which is available to authorized users.

Tools for Predicting Clinical and Patient-reported Outcomes in Prostate Cancer Patients Undergoing Androgen Deprivation Therapy: A Systematic Review of Prognostic Accuracy and Validity

Androgen deprivation therapy (ADT) can result in a range of adverse symptoms that reduce patients' quality of life. Careful patient counseling on the likely clinical outcomes and adverse effects is therefore vital. The present systematic review was undertaken to identify and characterize all the tools used for the prediction of clinical and patient-reported outcome measures (PROMs) in patients with prostate cancer undergoing ADT. PubMed and EMBASE were systematically searched from 2007 to 2016. Search terms related to the inclusion criteria were: prostate cancer, clinical outcomes, PROMs, ADT, and prognosis. Titles and abstracts were reviewed to find relevant studies, which were advanced to full-text review. The reference lists were screened for additional studies. The Centre for Evidence Based Medicine critical appraisal of prognostic studies tool was applied. The search strategy identified 8755 studies. Of the 8755 studies, 22 on clinical outcomes were identified. However, no studies of PROMs were found. Nine tools could be used to predict clinical outcomes in treatment-naive patients and 10 in patients with recurrence. The Japan Cancer of the Prostate Risk Assessment (J-CAPRA) nomogram was the best performing and validated tool for the prediction of clinical outcomes in treatment-naive patients, and the Chi and Shamash prognostic indexes have been validated for use in patients with castration-resistant disease in different clinical contexts. Using the J-CAPRA nomogram should help clinicians deliver accurate, evidence-based counseling to patients undergoing primary ADT. A strong need exists for primary studies that derive and validate tools for the prediction of PROMs in patients undergoing ADT under any circumstance because these are currently absent from the literature.

Employing dynamical computational models for personalizing cancer immunotherapy

INTRODUCTION

Recently, cancer immunotherapy has shown considerable success, but due to the complexity of the immune-cancer interactions, clinical outcomes vary largely between patients. A possible approach to overcome this difficulty may be to develop new methodologies for personal predictions of therapy outcomes, by the integration of patient data with dynamical mathematical models of the drug-affected pathophysiological processes.

AREAS COVERED

This review unfolds the story of mathematical modeling in cancer immunotherapy, and examines the feasibility of using these models for immunotherapy personalization. The reviewed studies suggest that response to immunotherapy can be improved by patient-specific regimens, which can be worked out by personalized mathematical models. The studies further indicate that personalized models can be constructed and validated relatively early in treatment.

EXPERT OPINION

The suggested methodology has the potential to raise the overall efficacy of the developed immunotherapy. If implemented already during drug development it may increase the prospects of the technology being approved for clinical use. However, schedule personalization, per se, does not comply with the current, 'one size fits all,' paradigm of clinical trials. It is worthwhile considering adjustment of the current paradigm to involve personally tailored immunotherapy regimens.

Survival predictors in patients with prostate adenocarcinoma with hormonal blockade

Ki-67 index and clinical-pathological factors such as the Gleason score and the presence of neuroendocrine differentiation have been used for predicting survival in patients with prostate cancer. We examined prostate tissue from 45 patients with advanced prostate cancer who were treated with maximal androgen blockade and analysed their cancer-specific survival (CSS). We assessed the Gleason index, performed an immunohistochemical analysis of Ki-67 (MIB-1) and determined the presence of neuroendocrine differentiation (chromogranin A). A survival study was conducted using Kaplan-Meier curves (log-rank test) and a Cox regression analysis. Twenty-four patients (53.3%) died from the disease, with a mean follow-up of 68.7±7.7 months (56.6% CSS at 5 years and 31.8% at 10 years). In the univariate analysis, survival was associated with an interquartile distribution of Ki-67 (0-5, 6-12%, 13-25%, >25%; log-rank, p=0.01), Gleason 5 (total index 9-10; log-rank, p=0.002) and the presence of metastases during the diagnosis (M1; log-rank, p=0.004) but not to cT category (T3-T4; log-rank, p=0.26) or neuroendocrine differentiation (immunohistochemically positive tumour cell nests; log-rank, p=0.46). The multivariate analysis revealed that a Ki-67 index ≤12% (HR, 0.22; p=0.0009) and the absence of metastases (M0) during diagnosis (HR, 0.17; p=0.0002) were protective factors in this population. In conclusion, Ki-67 proliferation index and the lack of metastases at diagnosis predict CSS in patients with advanced prostate cancer who undergo hormonal blockade. Neuroendocrine differentiation in tumour tissue had no prognostic value in this study.