A survey of open questions in adaptive therapy bridging mathematics and clinical translation Jeffrey West1 Fred Adler34 Jill Gallaher1 Maximilian Strobl1 Renee

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A survey of open questions in adaptive therapy:

bridging mathematics and clinical translation

Jeffrey West1,*, Fred Adler3,4, Jill Gallaher1, Maximilian Strobl1, Renee

Brady-Nicholls1, Joel S. Brown1, Mark Robertson-Tessi1, Eunjung Kim6,*, Robert

Noble5,*, Yannick Viossat2,*, David Basanta1,*, and Alexander R. A. Anderson1,*

1Department of Integrated Mathematical Oncology, H. Lee Mofﬁtt Cancer Center & Research Institute.

Tampa, FL 33612, USA

2Ceremade, Universit´

e Paris-Dauphine, Universit´

e Paris Sciences et Lettres, Paris, France

3Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA

4School of Biological Sciences, University of Utah, Salt Lake City, UT 84112, USA

5Department of Mathematics, City, University of London, London, UK

6Korea Institute of Science and Technology

*Co-corresponding authors:

jeffrey.west@mofﬁtt.org

viossat@ceremade.dauphine.fr

robert.noble@city.ac.uk

eunjung.kim@kist.re.kr

david@cancerevo.org

alexander.anderson@mofﬁtt.org

Abstract

Adaptive therapy is a dynamic cancer treatment protocol that updates (or “adapts”) treatment de-

cisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible

dynamic treatment protocols of patient-speciﬁc dose modulation or dose timing. Adaptive therapy

maintains high levels of tumor burden to beneﬁt from the competitive suppression of treatment-

sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach

to cancer treatment has been integrated into several ongoing or planned clinical trials, includ-

ing treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant

melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy

has progressed synergistically with mathematical and computational modeling. In this work, we

discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are

split into three sections: 1) the necessary components of mathematical models of adaptive therapy 2)

design and validation of dosing protocols, and 3) challenges and opportunities in clinical translation.

Introduction: a survey of open questions in adaptive therapy

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 [1,2,3]. 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.

arXiv:2210.12062v1 [q-bio.TO] 18 Oct 2022

Figure 1. Open questions in adaptive cancer therapy modeling: Schematic of tumor burden under

maximum tolerable dose (blue) and adaptive dosing (purple), with corresponding biopsies. Adaptive therapy

is designed to exploit competition between treatment-sensitive (green) and resistant (red) cells to prolong the

emergence of resistance. 11 questions representing future challenges in the ﬁeld of adaptive therapy are

shown, and answered within the text. Questions are color-coded by section: the necessary components of

mathematical models (blue), design and validation of dosing protocols (red), and challenges and

opportunities in clinical translation (yellow).

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 [2]. 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 [4]. 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 [5,4]. A similar and larger, randomized trial in metastatic castrate-resistant prostate

cancer is planned (ANZadapt; NCT05393791).

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 [1,6], while only dose skipping has been translated to the

clinic [2]. 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 eleven open questions regarding future directions of mathematical

modeling in adaptive cancer therapy. These were the result of a four-day workshop on Cancer

Adaptive Therapy Models (CATMo; https://catmo2020.org/) in December 2020. The conference

brought together a multi-disciplinary group of mathematicians, clinical oncologists, and experi-

mental biologists to discuss successes, challenges and opportunities in adaptive therapy. We have

categorized these questions into three sections: 1) the necessary components of mathematical

models, 2) the design and validation of dosing protocols, and 3) challenges and opportunities in

clinical translation.

1 The necessary components of mathematical models

1.1 What are the necessary conditions for adaptive therapy to delay resistance?

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 [7]. 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 popula-

tions, although some recent models follow a continuum of cell types [8]. Model extensions include

a) Healthy cells: these cells are always present within a tumor and they will interact with cancer

cells [9], b) Immune cells: these cells can help control cancer but can themselves be affected by

treatments [10,11,12], c) Resources: hormones [13] introduce delays and can alter evolutionary

trajectories, and have been modeled as consumer-resource dynamics [14] and more mechanistic

models with androgen dynamics [15]. d) Allee effect: cell populations that grow more slowly

(per capita) at low populations [16] 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 [17].

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 [18]. 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. 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 [19]. Phenotypic plasticity, where resistance is induced by therapy

rather than arising from mutations or pre-existing variants [17], makes resistance much more difﬁcult

to suppress [20]. Reversible behaviors can create complex responses to therapeutic timing [21].

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 [21], a more complex model with basic androgen dynamics [22], and a detailed model

of androgen dynamics [15] all ﬁt data on a set of patients reasonably well, although with some

exceptions [23]. 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 mouse PDX models [24], or in vitro data on patient derived cells that can

reveal mechanisms of interaction in different treatment environments.

1.2 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 modellers typically assume that the ﬁtness of resistant cells is a simple function

of their relative abundance and/or the total tumor size (reviewed in [25]). 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 [26,27,28]. 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 [29,30]. A

corollary is that the effectiveness of adaptive therapy may vary between cancer types due to different

tumor architectures [26]. 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 uncharacterised. 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. [1]

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 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 [30]. Conversely, cancer cells resistant to the tyrosine kinase inhibitor alectinib have

been observed outcompeting ancestral cells in co-culture [31]. 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 [32,25]. Nevertheless, such costs – which could be exacerbated

by auxiliary treatments [33,34] – are typically predicted to amplify clinical gains [25].

Lastly, is competition the only important ecological interaction? Studies in vitro and in mice

have detected positive ecological interactions (mutualism and commensalism; reviewed in [35]) and

asymmetric interactions (parasitism) between cancer clones [36,37]. 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.

1.3 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. Plasticity is often modeled

as the expression of resistant cellular traits which vary from completely sensitive to fully resistant [38,

39], in multi-dimensional fashion to consider multi-drug resistance [40,41]. 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 [42]), 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 tp

re-sensitize to a BRAF inhibitor rechallenge [43].

The switching rate from resistant to sensitive states can impact the beneﬁt of adaptive therapy.

Tumor dynamics described by both competition and phenotypic plasticity predict that adaptive ther-

apy (dose skipping) outperforms standard of care at different degrees among patients with advanced

metastatic melanoma [44,45]. Among parameters that govern treatment response dynamics, both

the switching rate from resistant to sensitive states and the growth rate of sensitive cells determines

the beneﬁts of adaptive therapy. In another study, a ﬁxed schedule intermittent therapy was predicted

to outperform the standard of care when treatment could induce resistant mutations in the cells [46].

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 [47]. There may be even more variability

across patients in terms of how resistance emerges and is maintained. Thus, identifying the presence

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Asurveyofopenquestionsinadaptivetherapy:bridgingmathematicsandclinicaltranslationJeffreyWest1,*,FredAdler3,4,JillGallaher1,MaximilianStrobl1,ReneeBrady-Nicholls1,JoelS.Brown1,MarkRobertson-Tessi1,EunjungKim6,*,RobertNoble5,*,YannickViossat2,*,DavidBasanta1,*,andAlexanderR.A.Anderson1,*1DepartmentofI...

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A survey of open questions in adaptive therapy bridging mathematics and clinical translation Jeffrey West1 Fred Adler34 Jill Gallaher1 Maximilian Strobl1 Renee

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