Jeffrey West, Eunjung Kim, Rob Noble, Yannick Viossat, David Basanta, Alexander Anderson: Treatment resistance in cancer therapy remains an overarching challenge across all types of cancer and all modes of treatment including targeted therapy, chemotherapy, and immunotherapy. Despite the ubiquity of the evolution of resistance, the ‘more is better’ paradigm still prevails as standard of care. Over the past decade, a small group of oncologists in collaboration with evolutionary biologists and experimental biologists have proposed an ‘adaptive therapy’ approach to cancer treatment (Gatenby et al., 2009b; Zhang et al., 2017; Zhang et al., 2022). Adaptive therapy maintains high levels of tumor burden in order to capitalize on competition between treatment-sensitive and treatment-resistant clones, and the potential cost of resistance.

In contrast to the periodic administration of dosing under intermittent therapy (e.g., in prostate [Hussain et al., 2013; Crook et al., 2012] or melanoma [Algazi et al., 2020] cancers), adaptive therapy is characterized by dynamic treatment protocols which update (or ‘adapt’) in anticipation to evolving tumor dynamics. These protocols are patient-specific, leading to variable dose modulation or dose timing between patients. While the term adaptive therapy is broad and encompasses many possible dynamic treatment protocols, the term is often used with specific reference to a recent pilot clinical trial in prostate cancer. This first adaptive trial enrolled a small cohort of metastatic castrate-resistant prostate cancer patients, contingent upon a minimum of 50% drop in the level of prostate-specific antigen biomarker (PSA; a proxy for tumor burden) under abiraterone administration. Abiraterone is then withdrawn until PSA returns to pre-treatment levels and then restarted. This 50% rule leads to treatment holidays that are patient-specific (treatment protocol varies considerably between patients). Holidays are often shorter in later treatment cycles when PSA dynamics speed up (Zhang et al., 2017). Initial results of the trial indicate a prolonged progression-free survival and lower cumulative dose when compared to a contemporaneous cohort of patients receiving the standard of care (Zhang et al., 2021). A schematic of adaptive therapy is shown in Figure 1 (purple), which prolongs relapse when compared to a high-dose schedule (blue). While initial results appear promising, this trial was performed on a small cohort of men and did not include a randomized control arm (Mistry, 2021; Zhang et al., 2021). A similar and larger, randomized trial in metastatic castrate-resistant prostate cancer is planned (ANZadapt; NCT05393791).

Figure 1

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The first trial has created interest in designing new adaptive treatment protocols in prostate cancer as well as other cancers. Adaptive treatment protocols are often binned into two dose-scheduling approaches: dose modulation and dose skipping. Both are designed to prolong sensitivity to therapy and both have been tested experimentally (Gatenby et al., 2009b; Enriquez-Navas et al., 2016), while only dose skipping has been translated to the clinic (Zhang et al., 2017). Throughout the text, we refer to the following treatment scheduling protocols:

1. Maximum tolerable dose (MTD): periodic administration of a high dose, limited by toxic side effects.

2. Intermittent therapy: periodic administration of a high dose with fixed, periodic treatment holidays.

3. Adaptive therapy (dose skipping): adaptive dosing where a high dose is administered until a desired tumor response (e.g., 50% size reduction), followed by a treatment holiday until a desired upper threshold (e.g., 100%) and repeated.

4. Adaptive therapy (dose modulation): adaptive dosing where dose is modulated (increased or decreased) at regular intervals depending on tumor response.

In Figure 1, we introduce 11 open questions regarding future directions of mathematical modeling in adaptive cancer therapy. These were the result of a 4-d workshop on Cancer Adaptive Therapy Models (CATMo; https://catmo2020.org/) in December 2020. The conference brought together a multidisciplinary group of mathematicians, clinical oncologists, and experimental biologists to discuss successes, challenges and opportunities in adaptive therapy. We have categorized these questions into three sections: (1) integrating the appropriate components into mathematical models, (2) the design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.

Integrating the appropriate components into mathematical models

What components are necessary for a mathematical model of adaptive therapy?

Fred Adler: It is thought that the success of adaptive therapy in delaying the emergence of resistance depends on three characteristics of the cancer: (a) resistance is costly, (b) resistant cells can be suppressed by competition with sensitive cells, and (c) therapy reduces the population of sensitive cells. Simple models based on these assumptions show that adaptive therapy can indeed delay the emergence of resistance. These simple models raise two further questions: (1) What are the appropriate objectives for evaluating the success of therapy? (2) Do the main results hold up in models that include additional components of real tumors?

Our ultimate objective is to maximize survivorship or quality-of-life adjusted survivorship of the patient. This depends on the cancer burden, the treatment burden, and the effectiveness of treatment in suppressing the cancer in the long run (Bayer et al., 2022). In most cases, we do not have sufficient information to quantify each of these costs and benefits over the long run, but we can consider them in concert to evaluate overall success.

Models of adaptive therapy typically include distinct sensitive and resistant cancer cell populations, although some recent models follow a continuum of cell types (Pressley et al., 2021). Model extensions include (a) healthy cells: these cells are always present within a tumor and they will interact with cancer cells (West et al., 2018). (b) Immune cells: these cells can help control cancer but can themselves be affected by treatments (Piretto et al., 2018; Schättler et al., 2016; Park et al., 2019). (c) Resources: hormones (Kareva and Brown, 2021) introduce delays and can alter evolutionary trajectories, and have been modeled as consumer-resource dynamics (Zazoua and Wang, 2019) and more mechanistic models with androgen dynamics (Jain et al., 2011). (d) Allee effect: cell populations that grow more slowly (per capita) at low populations (Konstorum et al., 2016) effectively introduce an element of cooperation. (e) Phenotypic plasticity: rapid changes in cell phenotypes can generate resistance far more quickly than mutation or population dynamics (Salgia and Kulkarni, 2018). See the table below for a list of common modeling approaches used in adaptive therapy.

A key result from our work on the basic model is a tradeoff curve between time for resistant cells to emerge and the mean cancer burden (Buhler et al., 2021). This tradeoff holds for both adaptive (dose skipping) and intermittent therapies, and is robust across all model extensions except for the Allee effect and cell plasticity. With an Allee effect, results are quite different. Recent experimental evidence suggests the presence of an Allee effect in vitro (Johnson et al., 2019), but the extent of this effect is unknown in vivo. Aggressive therapy can drive cells below the threshold and prevent both resistant cells and total cells from reaching their upper thresholds. Adaptive therapy, by backing off early to avoid favoring resistance, can behave quite poorly, leading to escape times nearly as short as those with no therapy and with a high total cell burden.

With the exception of the success of high-dose therapy with a strong Allee effect, no universal therapy can achieve all three objectives of lowering average dose, delaying time to emergence of resistant cells, and reducing total tumor burden. All strategies show a tradeoff between delaying emergence of resistant cells and a high cancer burden. Choosing the appropriate treatment requires assessing the individual patients and specific cancers, and include factors often not included in models, such as therapy toxicity (Ballesta and Clairambault, 2014). Phenotypic plasticity, where resistance is induced by therapy rather than arising from mutations or preexisting variants (Salgia and Kulkarni, 2018), makes resistance much more difficult to suppress (Feizabadi, 2017). Reversible behaviors can create complex responses to therapeutic timing (Hirata et al., 2010).

Effective adaptive therapies require fitting data on individual patients, and data may lack the resolution to distinguish among alternative models. In the case of PSA in prostate cancer, a simple model (Hirata et al., 2010), a more complex model with basic androgen dynamics (Portz et al., 2012), and a detailed model of androgen dynamics (Jain et al., 2011) all fit data on a set of patients reasonably well, although with some exceptions (Hatano et al., 2015). If models can be fit to the dynamics, adaptive therapies may be more robust to patient variability than prescribed timing of intermittent therapy. Although data may lack the resolution to identify specific mechanisms of interaction, such as the strength of competition between different cancer cell phenotypes, simple models may have the greatest potential to capture dynamics and guide therapy. The ideal combination will be patient-specific models combined with in vivo data, perhaps with immunocompetent mouse models, mouse PDX models (Siolas and Hannon, 2013), or in vitro data on patient derived cells that can reveal mechanisms of interaction in different treatment environments.

Paper	Model type	Key result
Martin et al., 1992b	Gompertzian, Lotka-Volterra	Theoretical models of extension of survival time using dose reduction strategies
Martin et al., 1992a	Gompertzian, Lotka-Volterra	Optimal control methods used to simulate tumors with drug-resistant and drug-sensitive cells in competition
Monro and Gaffney, 2009	Gompertzian	Sensitive-resistant competition can extend survival times, but failed cure can reduce survival
Gatenby et al., 2009b	Mathematical catastrophe theory	The term ‘adaptive therapy’ coined: mathematical and experimental exploration of adaptive therapy
Bacevic et al., 2017	Hybrid cellular automaton	Validation of cost of resistance in CDK inhibitors and role of spatial competition on fitness
Gallaher et al., 2018,	Off-lattice agent-based	Validation of cost of resistance in doxorubicin, and exploration of alternative adaptive protocols
Silva et al., 2012	Frequency-dependent competition	Low doses of auxiliary treatment to accentuate cost of chemo-resistance and improve adaptive therapy
Zhang et al., 2017	Lotka-Volterra	Publication of adaptive prostate trial data and associated Lotka-Volterra competition mathematical model
Smalley et al., 2019	Lotka-Volterra with phenotypic switching	In vivo adaptive dosing of BRAF inhibitors, compared to continuous or fixed intermittent therapy
Kim et al., 2021	Lotka-Volterra with phenotypic switching	Patient-specific prediction of adaptive melanoma therapy
Brady-Nicholls et al., 2021	Density-dependent competition	Patient-specific predictions of adaptive prostate therapy
Strobl et al., 2020	Lotka-Volterra with turnover	Mathematical investigation of cost, turnover, and competition in adaptive therapy
West et al., 2020	Lotka-Volterra	Mathematical investigation of multi-drug adaptive therapy protocols
Viossat and Noble, 2021	Frequency, density-dependent competition	Extensive mathematical analysis of conditions where tumor containment is superior

How competitive are treatment-resistant phenotypes?

Rob Noble: Adaptive therapy aims to exploit competition between treatment-sensitive and resistant cells. Key questions remain largely unanswered. First, what is the nature of this competition? Mathematical modelers typically assume that the fitness of resistant cells is a simple function of their relative abundance and/or the total tumor size (reviewed in Viossat and Noble, 2021). But frequency- or density-dependent mathematical functions only approximate average population dynamics. Actual clonal growth rates depend on the spatial arrangement of cells, their interaction ranges, and local levels of shared resources, all of which vary both within and between tumors (Noble et al., 2022; West et al., 2021; Fu et al., 2022). For example, if a tumor grows mainly at its boundary then spatial constraints alone could suffice to contain rare resistant clones, but only if they are located away from the boundary (Gallaher et al., 2018; Bacevic et al., 2017). A corollary is that the effectiveness of adaptive therapy may vary between cancer types due to different tumor architectures (Noble et al., 2022). Although spatially structured computational and experimental models can account for some important factors – such as competition for space and oxygen – the ability to predict clinical outcomes hinges on these models accurately matching the parameters of human intra-tumor cell–cell interactions, which remain largely uncharacterized. Further experimental studies and clinical image analyses are needed to quantify these parameters.

Second, are resistant cells less competitive? The seminal 2009 paper by Gatenby et al., 2009b postulated that cells insensitive to therapy incur a fitness cost in the absence of treatment, which adaptive therapy can exploit. A reduction in cell proliferation rate or carrying capacity (defined as the maximal cell density or the maximal cell number in the whole tumor) might result from cells diverting resources away from proliferation and towards breaking down or pumping out toxins. On the other hand, it is uncertain what fitness effects, if any, should result from mutations that modify specific drug targets. Experimental evidence is mixed. A study of tumor containment using a cyclin-dependent kinase inhibitor found a cost of resistance both in vitro and in mice (Bacevic et al., 2017). Conversely, cancer cells resistant to the tyrosine kinase inhibitor alectinib have been observed outcompeting ancestral cells in co-culture (Kaznatcheev et al., 2019). Competition assays should in any case be interpreted with caution because there are many potential mechanisms of resistance to a given treatment and the relative fitness of each phenotype will vary with its microenvironment. Theoretical analyses show that costs of resistance are not necessary to make adaptive therapy superior to higher dose treatment (Strobl et al., 2020; Viossat and Noble, 2021). Nevertheless, such costs – which could be exacerbated by auxiliary treatments (Silva and Gatenby, 2010; Silva et al., 2012) – are typically predicted to amplify clinical gains (Viossat and Noble, 2021).

Lastly, is competition the only important ecological interaction? Studies in vitro and in mice have detected positive ecological interactions (mutualism and commensalism; reviewed in Tabassum and Polyak, 2015) and asymmetric interactions (parasitism) between cancer clones (Miller et al., 1988; Noble et al., 2021). These observations suggest that our theoretical models of clonal dynamics during cancer treatment may be overly simplistic, and they underscore the need for more and better data. Emerging spatial genomic, transcriptomic, and proteomic technologies (Seferbekova et al., 2022) hold particular promise for inferring subclonal interactions within human tumors. Below, several sections discuss challenges and opportunities integrating mathematical models with wet lab data (How can we leverage mathematical modeling to support testing of adaptive therapy in the wet lab?) and clinical data (Is real-time patient prediction feasible?).

What is the role of plasticity and drug-induced mutations in adaptive therapy?

Eunjung Kim: The effectiveness of treatment holidays drastically changes when considering phenotype switching between drug-sensitive and -resistant phenotypes (Pillai et al., 2022). Plasticity is often modeled as the expression of resistant cellular traits that vary from completely sensitive to fully resistant (Clairambault and Pouchol, 2019; Clairambault, 2019), in multidimensional fashion to consider multi-drug resistance (Cho and Levy, 2018a; Cho and Levy, 2018b). Treatment breaks can halt the expansion of the resistant cell population facilitated by drug-induced mutations or phenotype switching from sensitive to resistant states during therapy. Since phenotype switching to resistant states is often reversible (reviewed in Boumahdi and de Sauvage, 2020), treatment holidays have the potential to re-sensitize the resistant cell population to future drug rechallenges. A recent experimental study demonstrated that gene expression in melanoma cells reversed during treatment holidays, causing the cells to re-sensitize to a BRAF inhibitor rechallenge (Kavran et al., 2022).

The switching rate from resistant to sensitive states can impact the benefit of adaptive therapy. One recent study introduced a mathematical model of plasticity-mediated drug resistance of melanoma treated with BRAF/MEK inhibitors (Hodgkinson et al., 2022). Here, the mathematical modeling predicts small differences resistance emergence between continuous and adaptive therapy, but the latter leads to increased spatial heterogeneity. Another recent study integrated mathematical models with clinical data of a cohort of patients with melanoma treated with continuous therapy of BRAF/MEK inhibitors (Kim et al., 2021). The resulting calibrated mathematical models then simulated alternative treatment protocols. Modeling predicted that adaptive therapy (dose skipping) outperforms standard of care at different degrees among the patients (Kim et al., 2021). Among mathematical model parameters that govern treatment response dynamics, both the switching rate from resistant to sensitive states and the growth rate of sensitive cells determine the benefits of adaptive therapy. In another mathematical modeling study, a fixed schedule intermittent therapy was predicted to outperform the standard of care when treatment could induce resistant mutations in the cells (Greene et al., 2019). These properties of tumor plasticity or drug-induced mutation are variable between cancer types and possibly vary between cancer cells. For example, in melanoma, it was shown that phenotypic plasticity is more evident in one cell line than another (Smalley et al., 2019). There may be even more variability across patients in terms of how resistance emerges and is maintained. Thus, identifying the presence of phenotypic plasticity in a specific tumor could be an important factor in deciding if and how adaptive therapy should be applied.

What is the role of homeostasis and normal tissue in adaptive therapy?

David Basanta: A feature of current models of adaptive therapy lies in their simplicity in terms of algorithms and assumptions. One key simplification is that tumor heterogeneity can be reduced to the types of cancer cells such as sensitive cells (that pay a significant fitness cost during treatment) and treatment-resistant cells (that may incur a cost of resistance relative to sensitive cells). In reality, the fitness of a cancer cell is not simply a cell-intrinsic property but includes its ability to take advantage of its dynamic tumor environment that includes not just other cancer cells but normal cells, vasculature, immune cells, and extracellular matrices (see Figure 2).

Figure 2

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Far from living in isolation, cancer cells colonize tissues with an existing ecosystem made up of healthy, stromal cells that communicate with each other via molecular factors in order to maintain homeostasis. The tissue has a distinct physical and spatial architecture (Basanta and Anderson, 2013). In the bone, for instance, homeostasis results from the interactions between several cell types such as osteoblasts, osteoclasts, osteocytes, monocytes, macrophages, and mesenchymal stem cells (MSC) (Bussard et al., 2008). While metastasis is a highly inefficient process, successful colonization of the bone by metastasizing prostate cancer cells leads to a process called the vicious cycle (Esposito et al., 2018; Cook et al., 2014). Successful prostate cancer cells in the bone take advantage of the interactions and signaling that goes on between the normal cells as they maintain homeostatic tissue microenvironments (Basanta and Anderson, 2013). Factors released by normal cells such as transforming growth factor $\beta$ are utilized by nearby prostate cancer cells. Such factors accelerate the proliferation and survival of the cancer cells.

Proximity to stromal cells provides other benefits to cancer cells undergoing treatment. For instance, bone metastatic prostate cancer cells near MSCs are pre-selected to possess some level of chemoresistance (McGuire et al., 2021). Such cells are primed for resistance even prior to treatment exposure. Also in the bone, myeloma cells (bone cancer) near MSCs or in the presence of growth factors secreted during bone remodeling can survive standard of care treatments based on proteosome inhibitors like bortezomib (Xu et al., 2012). This environmentally mediated drug resistance (EMDR) explains why anticancer treatments prove less effective than otherwise expected. In the context of adaptive therapy, EMDR may provide the cancer cells with a therapy refuge regardless of whether they are resistant or sensitive to treatment.

For cancers where EMDR plays a large role, it may be advisable to be more aggressive in applying therapy and reducing the tumor burden. This is because treatment sensitive cells will remain viable even after large reductions in tumor burden. These sensitive cells surviving in or near a stromal refuge can then provide a source of competition for resistant cancer cells during drug holidays. Furthermore, one can include adjuvant treatments, targeting stromal cells, to modulate the role of EMDR. The goal of EMDR modulating drugs would not be to maximize tumor kill. Rather, such modulation would aim to improve the efficacy of adaptive therapy approaches to better control tumor burden and maintain quality of life over long periods of time.

Future adaptive therapy models should allow for EMDR. Such models could more faithfully incorporate the tumor microenvironment and the role of normal cells. Such models could then evaluate how best to manage or exploit EMDR when designing adaptive therapy protocols (M A et al., 2022). Even more might be gained by developing models that also recapitulate tissue homeostasis prior to carcinogenesis. As discussed elsewhere (Basanta and Anderson, 2017), cancers initiate in normal tissue environments and progressively overcome and exploit the rules of homeostasis. Adaptive therapy aims to control the tumor by introducing a different type of homeostasis. Hence, in improving the original adaptive therapy algorithm, we should consider the homeostasis that was disrupted by the tumor as well as the homeostasis that might be engineered by therapy.

Challenges and opportunities in clinical translation

Is real-time patient prediction feasible?

Renee Brady-Nicholls: Predicting precisely when a patient will progress during adaptive therapy offers the opportunity to appropriately modulate treatment, thereby extending patient response and survival. This requires sufficient monitoring of an individual patient’s disease using appropriate clinical markers. Choosing an appropriate biomarker depends on the extent of the disease (e.g., localized versus metastatic, or hormone sensitive versus castration resistant prostate cancer), as well as how frequently said biomarker can be collected to adequately follow the disease trajectory.

Prior to making model predictions, the chosen model should be calibrated and validated to demonstrate that it can accurately describe patient-specific biomarker dynamics (Brady and Enderling, 2019). This requires analyzing the model to determine the sensitivity and identifiability of model parameters, relative to the data. Given a chosen model and available data, model parameters may be difficult to accurately estimate. This might be due to the model complexity or structure, as well as the given data. Evaluating the sensitivity of the model outputs, in this case the change in a modeled biomarker over time, with respect to small perturbations in the model parameters identifies sensitive and insensitive parameters (Banks and Tran, 2009). Sensitive parameters should be evaluated for correlations with other parameters as correlated parameters should not be estimated concurrently. If two parameters can be uniquely identified, then they are said to be identifiable (Olufsen and Ottesen, 2013) and parameter optimization techniques can be used to determine their optimal values relative to the given data. Appropriate model development, calibration, and validation are essential when developing predictive models. If the model cannot accurately describe the data, then it should not be used to make predictions of subsequent patient responses.

Figure 3 illustrates a case study of the feasibility of real-time patient prediction. Here, the longitudinal biomarker known as prostate-specific antigen (PSA) is used to fit a mathematical model and provide a patient-specific prediction in response to adaptive therapy in metastatic castration-resistant prostate cancer (Brady-Nicholls et al., 2021). Despite much controversy surrounding the clinical use of the absolute value of PSA in both the detection and monitoring of prostate cancer (Kim and Andriole, 2015), it has been shown to be an effective and inexpensive way to follow a patient’s response trajectory over time. Many mathematical models based on a variety of plausible mechanisms have been developed to describe PSA dynamics in response to treatment (Zhang et al., 2017; Baez and Kuang, 2016; Hirata et al., 2010; Morken et al., 2014; Portz et al., 2012).

Figure 3

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The mathematical model (Figure 3A) uses stem and non-stem cell dynamics to describe patient-specific PSA dynamics in response to treatment. The model has five parameters ($p_s$, $\lambda$, $\alpha$, $\rho$, $\phi$). Sensitivity analysis found that $\lambda$ was insensitive, while identifiability analysis showed that $p_s$, $\alpha$, $\rho$, and $\phi$ were uncorrelated and identifiable. A leave-one-out analysis was used to calibrate and validate the model to longitudinal PSA data from 16 patients. That is, nested optimization was used to estimate patient-specific parameters for $p_s$ and $\alpha$, and uniform parameters for $\phi$ and $\rho$ to accurately describe individual patient data for the 15 patients in the training cohort. The uniform $\phi$ and $\rho$ values were then fixed and optimization was used to find the $p_s$ and $\alpha$ values for the left-out patient (Figure 3B). Once calibrated and validated to the patient data, the model was used to make patient-specific response predictions. Parameter analysis identified the stem cell self-renewal rate $p_s$ as the primary driver of differences in treatment response dynamics between responsive and resistant patients. This parameter was used to make subsequent response predictions. That is, the distribution of changes in $p_s$ from treatment cycle $i$ to $i+1$ was used to predict an individual patient’s response in cycle $i+1$ (Figure 3C). The model was able to predict patient response with 81% accuracy (Brady-Nicholls et al., 2021) (defined as the sum of correct responsive and resistant predictions divided by the total number of predictions). A similar modeling approach was used in biochemically recurrent prostate cancer patients receiving intermittent androgen deprivation therapy to predict response dynamics with 89% accuracy (Brady-Nicholls et al., 2020). Clinically, an accurate predictive model can be used an additional tool that oncologists can use when making treatment decisions for individual patients. An accuracy above 50% (coin-toss) can provide clinicians with more confidence when making such critical decisions.

We can learn several lessons from these studies when applying real-time prediction of adaptive therapy in new diseases. Model predictions are dependent on the quality and time-resolution of patient-specific biomarkers. Alternative biomarkers such as circulating tumor DNA (ctDNA) (Hennigan et al., 2019; Ku et al., 2019; Lau et al., 2020), circulating tumor cells (CTCs) (Ried et al., 2020; Salami et al., 2019), and relatively new biomarkers such as urine Lemos et al., 2019; Tosoian et al., 2021 have been shown to be prognostic in prostate cancer and other diseases. Like PSA, these markers can be collected relatively frequently and via minimally invasive methods. They can be used to develop appropriate models that can be used to predict response to adaptive therapy.

Do adverse effects of maintaining high tumor burden negate potential benefit?

Joel Brown: The prostate adaptive trial (NCT024515621) is instructive here. The original model imagined two categories of sensitive cells that both require testosterone (Zhang et al., 2017). One producing its own, and the other requiring exogenous testosterone. Resistant cells are independent of testosterone and hence unaffected by androgen-focused therapy. In this model, the cost of resistance was assumed to occur primarily through carrying capacity (the maximal cell density) with some contribution of competition coefficients.

The adaptive therapy patients performed better than the contemporaneous controls (median of 33.5 and 14.3 mo radiographic progression free survival, respectively) (Zhang et al., 2021). To be considered for the trial, an initial response to therapy of at least a 50% decline in PSA and putative tumor burden was required. This meant they were responders and hence enjoyed a better prognosis than nonresponders, and nonresponders were not eligible for this trial (Mistry, 2021). The contemporaneous control group was selected from patients receiving continuous therapy and who, like the trial patients, were responders. No nonresponders were included in the control cohort. By way of caveat, this is an important consideration for any trial of adaptive therapy that lacks double-blind, randomized control arms. Most strikingly, some of the adaptive therapy patients performed better than expected from the initial model. At time of writing, four men remain on adaptive therapy after 4–6 y.

Evolutionary theory tells us that adaptive therapy, or more specifically competitive release therapy, works best if the sensitive cells are allowed to grow to the point where both frequency- and density-dependent feedbacks are strong. The frequency-dependent effects offer hope that the sensitive cells are competitively superior to the resistant ones. This cost of resistance can manifest as a reduction in maximum growth rates, reduction in carrying capacity, and the competitive effect of each cell type on the other (Zhang et al., 2022; Strobl et al., 2020; Pressley et al., 2021). A retrospective analysis of the near-finished trial (Zhang et al., 2022), permits parameter estimations, some patient specific, others estimated as patient-wide parameters. The efficacy of adaptive therapy seems best explained by highly asymmetric competition. It was estimated that the sensitive cells (a streamlined model combining the two sensitive cell types into one) have a competitive effect (per cell) on resistant cells that is six times higher than the reverse effect of resistant cells on sensitive ones. As others have noted in their models, such a high asymmetry favoring sensitive cells relative to resistant cells can result in indefinite control and disease containment (Viossat and Noble, 2021).

The prostate adaptive trial does provide some evidence that prolonged sensitivity may outweigh adverse effects of maintaining high tumor burden, but the promise of being able to perpetually control each patient’s disease did not happen. Why not? First, the periodic measurements of PSA on which to base decisions to stop or start therapy meant that patients often dropped more, and sometimes way more than the desired goal of 50%, and vice versa for when therapy was actually restarted. Virtually all models indicate a poorer performance of adaptive therapy with imprecise switch points that overshoot the targeted switch values. The second reason is decisive and it concerns enlisting the needed density-dependence. If the tumor burden and cancer cell populations sizes are well below carrying capacity, then both cell types may enjoy positive fitness in the absence of therapy (Zhang et al., 2017; Strobl et al., 2020; Hansen and Read, 2020a). As the tumor cell populations grow, per capita growth rates decline for both cell types, but with asymmetric competition, the resistant cells will experience negative fitness even as the sensitive cells continue to grow. This is a sweet spot. In this region of high tumor burden, the sensitive cells not only retard but reverse the growth rate of the resistant cells. Our retrospective analysis supports the conclusion of a number of mathematical and theoretical investigations. Namely, adaptive therapy seems to work best if (1) the threshold for ceasing therapy is quite high (80% rather than 50%, for instance), and (2) the overall tumor burden is maintained as high as possible without endangering the patient (Kim et al., 2021; Hansen and Read, 2020b; Viossat and Noble, 2021).

Retrospective analysis of mathematical modeling fit to adaptive patient data (Zhang et al., 2022) suggests that a physician ought to hold off resuming therapy until as late as possible in terms of the recovery of the tumor during a period of no therapy. With retrospective analysis of each patient, we find that failure of indefinite control happened because tumor burdens during periods of no therapy were being kept too low to permit sufficient density dependence to facilitate negative growth rates of the resistant cells. For these patients, therapy was resumed too soon! Yet, there are likely dangers associated with containment strategies aiming for overall high, and persistent tumor burdens. These fall into four important categories: (1) patients becoming symptomatic, (2) the ability of the biomarker to be sufficiently accurate and measurable frequently, (3) subsequent cancer evolution during the period of adaptive therapy, and (4) risk of new metastases.

An adaptive therapy clinical trial on metastatic thyroid cancer (NCT03630120) illustrates two of these concerns. The trial was suspended. The suspension was not mandated by the required stopping criteria, but because of two unanticipated issues. In one of the patients receiving adaptive therapy, there was an initially good response, therapy was stopped, and the tumor burden allowed to recover. However, the patient began to feel pain and other ill effects of the tumor burden before it had recovered to pretreatment level. The patient had become symptomatic at which point either treatment must be resumed or a different course of therapy considered. In another patient, after the resumption of therapy the tumor continued to grow, at least based on the biomarker, with no indication of a future decline (Christine Chung and Joel S. Brown, unpublished data). The small number of patients in both the randomized control arm (continuous therapy) and the adaptive therapy arm precluded meaningful interpretation of the potential efficacy of adaptive therapy. But it pointed to issues of patients becoming symptomatic, of the reliability of the biomarker as an accurate indicator of tumor burden, and of rapid changes in tumor burden and disease disposition that occurred at a faster time-scale than the ability to adjust therapies.

While not yet documented in any clinical trial of adaptive therapy, there remains the concern that high tumor burden, subjected to on and off therapy cycles may incubate additional mutations and adaptations by the cancer cells. For instance, with time, the resistant cancer cells may evolve traits that minimize or even reverse the cost of resistance. A large residual tumor population is more likely than a very small tumor burden to give rise to such mutations that propel the cancer cells to greater levels of malignancy. As of yet, models of adaptive therapy have not considered the risk of additional progressive evolution beyond that expected regarding drug sensitivity.

Current trials and most models of adaptive therapy consider the patient’s total tumor burden even when it is known that the cancer is spread across several or many metastatic sites. As the overall tumor burden shrinks, different lesions may not necessarily respond similarly or proportionately. Furthermore, the fraction of resistant and sensitive cells may differ among lesions, particularly if they are in different tissues. Over the course of adaptive therapy, the tumor burden may become more dispersed among lesions, more concentrated in a lower number of tumors, or, of most concern, metastasize to new sites. In the case of melanoma, whether under standard of care continuous therapy or as an adaptive therapy trial (NCT03543969), there is a risk of the disease metastasizing to the brain even as therapy efficacy may be good elsewhere in the patient’s body. A recent spatial model of the prostate clinical trial imagined dynamics both within and between metastatic sites in response to the on and off cycles of therapy. The model predicts that the adaptive therapy regimen will vary if the disease is represented by many small versus a few large tumors (Gallaher et al., 2022).

As more clinical trials of adaptive therapy emerge from integrating mathematical models with clinical opportunity and need, it will be essential to consider the tradeoffs associated with maintaining relatively large tumor burdens. A large tumor burden may increase the efficiency of an adaptive therapy regimen while increasing the risks of additional progressive evolution, other ill effects of tumor burden, and the appearance of new lesions within the same or different tissues. Balancing these costs and benefits will likely be disease and drug specific, and will require a continued lockstep between mathematical models and empirical studies, data, and observations of patients.

Can a mathematical model drive treatment decision-making?

Mark Robertson-Tessi and Sandy Anderson: Many models of adaptive therapy are currently hypothesis-generating models with less focus on predictive insight (Enderling and Wolkenhauer, 2020). One of the main goals of personalized therapy is the ability to predict likely tumor dynamics arising from all available treatment options, and then select the most promising. Therefore, there is a great need for clinically suitable predictive mathematical models that track patient-specific tumor dynamics. There are, however, numerous challenges that need to be surmounted for this approach to be broadly successful and able to be scaled to large numbers of patients.

To begin with, clinical data are often sparse and often collected at times of little value to a mathematical model. For example, imaging scans are often collected some time prior to therapy, and then, depending on the cancer, the first follow-up scan occurs after 6–12 wk. Yet, in many models of different diseases, the relevant action that would inform therapeutic decisions via modeling occurs during the immediate aftermath of therapy. Furthermore, the models benefit greatly from multiple data points, so it may take several follow-up scans to narrow the parameterization of a model to determine treatment efficacy and tumor dynamics, by which time the tumor may have progressed and thus no prediction is needed. In a sense, current imaging schedules are designed to detect progression reasonably soon after it occurs, often using the standard RECIST criteria or similar, while balancing the costs of repeated imaging. To move into predictive mathematical modeling, we must rethink how we collect patient data, in that we do not want to simply detect progression, but rather quantify and understand the tumor dynamics prior to progression such that one can inform treatment decisions to avoid it.

A second consideration is the uncertainty of the entire system, from patient to model. Even an optimally designed data collection protocol that would optimize model predictability will still leave significant uncertainties in such predictions. The idea that we will have the data and modeling to precisely predict the future course of a patient’s disease is not realistic, or even possible. Therefore, all predictions must include statistically rigorous uncertainty analyses. The concept of the ‘Phase i’ trial (Kim et al., 2016; Scott, 2012) has been developed as a framework to quantify and apply such uncertainties. The basic principle is to develop cohorts of virtual patients derived from a calibrated mathematical model and apply ‘clinical trials’ to such cohorts with varying regimens of treatment. Much like changes to the standard of care that arise from cohort-to-cohort comparisons, the same approach is used in the virtual cohorts to decide on the treatment that is most likely to succeed. In general, the complete virtual cohort is formed by examining historical data on the disease, both at the individual patient level and via cohort outcomes from clinical trials. Once this global cohort is established from the model, an individual patient can be compared to each virtual patient and matched to those that exhibit similar dynamics as the real patient. This patient-specific virtual subcohort is then subjected to the available therapy options, and their outcomes as a cohort are compared. The results provide decision-support for the treating physician. Using mechanistic models – as opposed to statistical models alone – has the advantage that as more patient data are collected on follow-up visits, the calibration and refinement of the patient’s subcohort can be improved by removing virtual patients that responded differently.

Adaptive therapy strategies are one part of a broader approach to introduce evolutionary principles into dose scheduling to mitigate the evolution of resistance (Gatenby and Brown, 2020b; Noorbakhsh et al., 2020; Belkhir et al., 2021; Stanková et al., 2019). Ongoing or planned evolution-based treatment trials include a trial in rhabdomyosarcoma, which includes both extinction therapy and adaptive therapy arms (NCT04388839) (Reed et al., 2020), adaptive androgen deprivation for castration-sensitive prostate cancer (NCT03511196), adaptive abiraterone or enzalutamide in castration-resistant prostate cancer (ANZadapt; NCT05393791), adaptive administration of BRAF-MEK inhibitors for advanced BRAF mutant melanoma (NCT03543969), adaptive carboplatin in ovarian cancer (ACTOv trial; NCT05080556), adaptive therapy of Vismodegib in advanced basal cell carcinoma (NCT05651828), and a feasibility study (Robertson-Tessi et al., 2023) for implementing evolution-based strategies with the aid of mathematical modeling decision-support (the ‘evolutionary tumor board’ at the Moffitt Cancer Center; NCT04343365). Given the complexity of cancer as an evolutionary disease, many of these trials have been planned with insights gained from mathematical models.

Concluding remarks

The questions outlined in the sections above can be categorized into the following: integrating the appropriate components into mathematical models (Integrating the appropriate components into mathematical models), the design and validation of dosing protocols (Design and validation of dosing protocols), and challenges and opportunities in clinical translation (Design and validation of dosing protocols). It is our opinion that work addressing these questions should occur concurrently, within an interdisciplinary framework of science.

Figure 4 shows a selection of influential papers and key clinical trials leading to advancements in the field of adaptive or evolution-based treatment. This figure illustrates that experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. Perhaps the most important challenge concerns the communication between different disciplines: the practice of oncology, the theories of ecology and evolution, and the application of mathematical models to data were not historically in sync in terms of possibilities for both practice and outcome. An integrated team science approach focused on gaining a deeper understanding of each disease and the implications of each decision during treatment is key for the future success of an evolution-based cancer management.

Figure 4

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Author details

1. Jeffrey West

   Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, United States

   Contribution

   Conceptualization, Visualization, Writing – original draft, Writing – review and editing

   For correspondence

   jeffrey.west@moffitt.org

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9579-4664

2. Fred Adler

   1. Department of Mathematics, University of Utah, Salt Lake City, United States
   2. School of Biological Sciences, University of Utah, Salt Lake City, United States

   Contribution

   Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

3. Jill Gallaher

   Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, United States

   Contribution

   Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9831-6676

4. Maximilian Strobl

   Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, United States

   Contribution

   Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4484-8823

5. Renee Brady-Nicholls

   Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, United States

   Contribution

   Visualization, Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

6. Joel Brown

   Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, United States

   Contribution

   Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

7. Mark Roberson-Tessi

   Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, United States

   Contribution

   Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

8. Eunjung Kim

   Natural Product Informatics Research Center, Korea Institute of Science and Technology, Gangneung, Republic of Korea

   Contribution

   Conceptualization, Writing – original draft, Writing – review and editing

   For correspondence

   eunjung.kim@kist.re.kr

   Competing interests

   No competing interests declared

9. Robert Noble

   Department of Mathematics, University of London, London, United Kingdom

   Contribution

   Conceptualization, Writing – original draft, Writing – review and editing

   For correspondence

   robert.noble@city.ac.uk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8057-4252

10. Yannick Viossat

    Ceremade, Université Paris-Dauphine, Université Paris Sciences et Lettres, Paris, France

    Contribution

    Conceptualization, Writing – original draft, Writing – review and editing

    For correspondence

    viossat@ceremade.dauphine.fr

    Competing interests

    No competing interests declared

11. David Basanta

    Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, United States

    Contribution

    Conceptualization, Writing – original draft, Writing – review and editing

    For correspondence

    david@cancerevo.org

    Competing interests

    No competing interests declared

12. Alexander RA Anderson

    Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, United States

    Contribution

    Conceptualization, Funding acquisition, Writing – original draft, Writing – review and editing

    For correspondence

    alexander.anderson@moffitt.org

    Competing interests

    No competing interests declared

    "This ORCID iD identifies the author of this article:" 0000-0002-2536-4383

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