Personalizing oncology treatmentsby predicting drug efficacy,side-effects, and improvedtherapy: mathematics, statistics,and their integrationZvia Agur,1,2∗ Moran Elishmereni1,2 and Yuri Kheifetz1,2
How to cite this article:WIREs Syst Biol Med 2014, 6:239–253. doi: 10.1002/wsbm.1263
INTRODUCTION
Conventionally, cancer patients have been treatedfollowing the ‘one-size-fits-all’ paradigm, by drug
protocols that showed acceptable results in many
∗Correspondence to: [email protected] for Medical BioMathematics, Hate’ena, Bene Ataroth,Israel2Optimata Ltd., Zichron Ya’akov, Tel Aviv, IsraelConflict of interest: The authors have declared no conflicts ofinterest for this article.
patients with a similar diagnosis. However, progressin human genetics has made it increasingly clearthat cancers of primary sites vary genetically andhence, respond differently to drugs. The conceptemerging today is to overcome this problem bypersonalizing drug treatment according to the specificmolecular characteristics of the patient’s tumor.Indeed, advances in pharmacogenomics have ledboth to the design of personalized drugs that targetparticular molecular sites, and to the acceleratedsearch for biomarkers that can predict how the patient
will respond to a drug (predictive biomarkers).1–3
At present, the repertoire of biomarkers approvedfor clinical use in oncology is rather limited.4 Itincludes key regulators, such as the epidermal growthfactor receptor (EGFR) for patients with non-smallcell lung cancer, the estrogen receptor (ER) protein,the Human Epidermal Growth Factor Receptor(HER2) amplification biomarker, the breast cancersusceptibility type 1 and 2 (BRCA-1, 2) for patientsof breast cancer (BC) and a few newer ones. Such asmall repertoire is insufficient, especially in view ofthe emerging complexity entailed in the use of someof these biomarkers.5
The concept of ‘personalized medicine’ repre-sents an important step forward in the evolution ofmedical science, toward greater mechanistic under-standing of health, disease, and treatment. But severalimpediments still prevent its bold acceptance. Theseinclude the insufficient validation of the suggestedpredictive biomarkers, the current drug developmentmethodology which is unsuitable for personalizedmedicine, the cost of new technologies and the doc-tors’ reluctance about their acceptance.6 These caveatsare further elaborated below.
Biomarker ValidationThe clinical benefit of predictive biomarkers is stillobscured by many difficulties, and many potentialbiomarkers that have been identified a priori,subsequently proved to be of poor clinical benefit.7
The generally poor achievements of molecularbiomarkers are not surprising given the emergingrecognition that single mutations do not encompassthe whole array of genetic alterations that characterizea progressing tumor, and that cancer will increasinglybe seen as a disease defined by its genetic fingerprint.8,9
Moreover, a disturbing confusion exists betweensurrogate biomarkers, which can represent treatmentendpoints for drug regulatory approval, and predictivebiomarkers which can stratify patients according totheir expected response to specific treatments. Thelatter biomarkers, essential for personalized medicine,do not require as stringent validation as the former.Yet, drug and diagnostic developers imagine thatthe overwhelming validation barriers to the use ofsurrogate end points also apply to regulatory issuesthat are pertinent to predictive biomarkers.6
How should predictive biomarkers be validated?Over the last few years, considerable attention ofstatisticians has been given to this subject, and manytrial designs have been analyzed with respect totheir efficiency and reliability in validating predictivebiomarkers under different clinical settings.10,11
One useful classification distinguishes betweenanalytical validation, clinical validation, and clinicalutility validation. Analytical validation of predictivebiomarkers checks that, based on the biomarker inquestion, one can be more accurate in predicting thepatient’s response than by a gold standard predictor.Clinical validation checks that the biomarker quantitycorrelates with a clinical end point or characteristic.Clinical utility validation requires that the use of thebiomarker results in improved response in patients.12
None of these different approaches are, however,standardized and applied in reality. Below we showhow the use of biomarkers and their validation canbe improved by their integration into computationalpersonalization support tools.
Clinical TrialsThe overall success rate of most clinical trials ischallenged by the large variability among patients,requiring large study populations to reach statisticalconfidence.13 In contrast, patient stratification oftenreduces the number of patients that can be recruitedto personalized-therapy trials; traditional statisticalmethods for clinical trials do not apply in suchcases. Another limitation of current trial designs isthat they apply the given drug to the patient inan unchanging regimen. This forces the cliniciansto use these regimens, in spite of problems thatmay oblige flexible personal regimens, such as theslowly emerging drug resistance. It appears, then,that a different paradigm is needed in personalizeddrug development.6 The recently suggested concept ofpersonalized clinical trials (p-trials) introduces the ideaof flexible personalized treatment schedules, basedon personalized mathematical models.14 The latterdynamic personalization method will be describedbelow.
Doctors’ ComplianceOne of the main caveats in embedding personalizedmedicine in the clinical practice is the conservatismof physicians and the healthcare system, in general.Physicians are biased toward interventions thatpermeate the healthcare system and are reluctant toadopt new technologies, even when they lead to betteroutcomes.6,15 In addition, personalized medicinedepends on a substantial reliance on electronicmedical records and decision support systems, butthe healthcare industry is still not comfortable withinformation technology.16 A vicious circle exists here,in which acceptance by the clinical community is aprimary prerequisite for the demonstration of successof personalized medicine technologies. At the same
WIREs Systems Biology and Medicine Models for personalizing oncology treatments
time, success of these technologies is a primaryprerequisite for acceptance by the clinical community.
A new comprehensive framework for reducingthe barriers to successful personalized medicine isneeded, and can be provided by a combined statisticaland mathematical modeling approach. Using such anapproach, drug–patient interactions can be capturedon many levels of biological organization, so thatforces as diverse as molecular effects on a patient’sdisease and population variability of molecularbiomarkers can be put together and implementedin a decision support algorithm. The algorithmshould be able to quantify the comprehensive effectof plural clinical and molecular measurements onthe patient’s parameters of the drug-driven diseaseprogression model, thus improving predictabilityof biomarkers and forecasting improved personaltreatment regimens. As a result, personalized medicinewill eventually be better integrated within clinicaltrials and the cost-effectiveness of clinical treatmentwill increase. Below we review several test cases,demonstrating the use of statistical and mathematicalmodels in personalized medicine, as well as putforward a more advanced methodology, integratingstatistical and mathematical models for improvedpersonalization.
USE OF MATHEMATICAL MODELS INPERSONALIZING ONCOLOGYTREATMENTS
The disillusionment with predictive biomarkers canbe explained by the complexity of drug–patientinteractions. Highly nonlinear relationships existbetween a molecular biomarker and its realizationin the patient’s reaction to treatment. For example,the effect of HER2 on the patient’s responseto trastuzumab is often obscured by genetic andepigenetic changes that limit the binding of drug toHER2.3,17 The inability to see the direct reflectionof the marker in the patient’s response calls foran intermediate system which can simulate diseasecomplexity, factoring in the patient’s molecular profileand the desired clinical treatment. Mathematicalmodeling can be used for constructing such anintermediate system, because of its power to describe,quantify and predict multifaceted behavior in asuccinct formal language, enabling to scrutinize thesystem’s behavior under various initial conditions.18
Many mathematical models investigating vari-ous dynamic aspects of known mechanisms in cancergrowth and therapy have been put forward overthe last 40 years,19–21 and mechanism-based models
have analyzed common methodologies of chemother-apy and suggested new approaches.22–24 Typically,however, parameterization of these models is coarse,and often done in a theoretical manner or relianton laboratory data or literature-derived data. There-fore, they fall short of capturing any specific clinicalscenario, and while contributing to development ofbio-modeling methodologies and to understanding ofgeneral treatment concepts, these models are still notused for prescribing specific treatment schedules at theclinical level.
A physician dealing with an individual patientmay be interested in precise short-term goals,such as, are three treatment cycles sufficient forstabilizing tumor progression in patient X, or shoulda more aggressive regimen be administered? Willthe scheduled drug dose be tolerable in patient X?etc. Such patient-oriented short-term questions canpossibly be tackled by a dynamic tumor model,a capacity which is beyond the scope of currentstatistical methodologies. Below it is shown how suchtreatment decisions can be supported by dynamicallypersonalized mathematical models, making the needto use mass historic data redundant.
Therapy-Induced NeutropeniaChemotherapy-induced neutropenia (CIN), a disorderin granulocyte development, is the major toxicity ofchemotherapy. It is associated with substantial mor-bidity, mortality, and excessive hospital admissions.25
The appearance of grade III/IV CIN frequently leads todelayed chemotherapy administration, or dose reduc-tion, both associated with poor clinical outcomes.26,27
These complications motivated the development ofmodels for predicting CIN and for analyzing gran-ulopoiesis, as affected by granulocyte colony stim-ulating factor (G-CSF) support.28–31 One of thesemodels focused on predicting the individual time toneutrophil nadir in patients treated by chemotherapy,a clinically valuable factor in the physician’s decisionmaking process.32,33 The personalization accuracy ofthis model was validated by retrospective clinical data,as described below.
The model describes granulopoiesis frommyeloid progenitors through the different bonemarrow compartments, to blood neutrophils. It alsofeatures explicit cell-cycle in mitotic compartmentsand the effects of G-CSF, the feedback moleculegoverning bone marrow maintenance of a quasisteadyneutrophil levels in blood. The secretion, diffusion,clearance, and interactions of G-CSF with different cellcompartments in the normal neutrophil developmentwere described as well. The parameters of the
granulopoiesis model were estimated based onextensive literature data and neutrophil profiles incancer patients subject to chemotherapy.30,34
The granulopoiesis model was integrated with adocetaxel pharmacokinetic (PK)/pharmacodynamics(PD) model, in order to predict blood toxicity inindividual docetaxel-treated patients.30,34 A three-compartment population PK model with linearelimination was assumed,35 and PK model parameterswere estimated using data from patients treatedby docetaxel (100 mg/m2, 1-h i.v infusion33); theresulting PK model was then validated by independentdata.36 Docetaxel’s effect on granulopoiesis wasmodeled as a direct killing of neutrophil proliferatingprogenitors, the most likely targets of docetaxel ingranulopoiesis.32
Model personalization was done in two stages:(1) adapt the granulopoiesis model to represent thepatient population, and (2) test the population modelfor its accuracy in predicting neutropenia profiles inindividual patients, taken from a new dataset. To thisend, blood counts were collected from 38 docetaxel-treated metastatic BC patients (from Nottingham CityHospital, UK, and Soroka Hospital, Israel). Patientswere randomly divided into a training set (n = 12),and a validation set (n = 26; 16 receiving a tri-weeklydocetaxel regimen and 10 receiving a weekly regimen).Docetaxel schedules and neutrophil baselines (median5080 neutrophils/μL; range 1800–15,500) were usedas model input. Some population model parameterswere re-estimated by fitting to training data, resultingin a single parameter set common for all patients,excluding individual initial baseline neutrophil countsand individual treatment regimen.30,34 Then, thebaseline neutrophil counts and the treatment regimenof each patient in the validation set were input intothe population model for predicting the patients’CIN. Model predictions were compared to clinicalneutrophil profiles in the validation set patients.The model showed high predictive accuracy of thetiming of the personal nadir, i.e. timing of lowestobserved neutrophil count at each cycle (r = 0.99,95% confidence interval (CI): 0.98–1; Figure 1), anda good prediction of the neutropenia grade for eachpatient from the validation set, positive and negativepredictive values of grade 3–4 neutropenia being86% and 83%, respectively (κ = 0.69, P < 0.001).30,34
Thus, even with this small dataset, the model gaveaccurate personal predictions of neutrophil nadir, ahighly significant factor for chemotherapy design inthe clinic.
It should be noted that the prediction accuracyrequired for evaluating the timing of nadir was muchlower than would be required for predicting, for
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FIGURE 1 | Model-predicted neutrophil counts over time comparedto the observed neutrophil counts of metastatic BC patients, treatedwith different docetaxel schedules. Model predictions of the nadir daysat each cycle vs. the observed nadir days (circles; N = 66; calculatedcorrelation coefficient is r = 0.99). The dashed line represents theidentity line.
example, the actual neutrophil value at nadir in eachpatient. Thus, the small patient cohort sufficed forthis purpose. Moreover, the requirement for a largedataset was made redundant here by use of data fromadditional sources. The neutropenia model, beingdesigned also on the basis of extensive literature,was not dependent on the clinical dataset only.Rather, most of the model parameters-mostly systemparameters-were already estimated at the populationlevel based on data from literature, and only a fewPK/PD parameters required re-estimation based on theclinical dataset of the 12 patients in the training set.Additionally, the variability aspect of this model wasrelatively simple, in that the only individually variablefactor was the initial neutrophil count, whereas therest of the processes were described on the populationlevel. Despite this low variability, the model succeededin predicting the requested time to nadir individually.In summary, the prediction goal of the model andits variability level are key factors in determining thesize of the clinical dataset required for its validation,and small datasets can be complemented by additionaldata from the literature.
Efficacy Response in MesenchymalChondrosarcomaIn this subsection we briefly describe a workthat combines mathematical models and xenograftexperiments for personalizing treatment protocols.The rationale underlying this work was to generatexenografts from the patient’s resected metastases,
WIREs Systems Biology and Medicine Models for personalizing oncology treatments
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FIGURE 2 | Vascular tumor growth dynamics. A schematic description of the multiscale mathematical model for vascular tumor growth. Tissues(medium gray), cells (dark gray), and molecules (light gray) interact as marked by the arrows. Vascular endothelial growth factor (VEGF) andplatlet-derived growth factor (PDGF) are secreted by the tumor cells. VEGF binds to endothelial cells and PDGF to pericytes, to generate new andmature blood vessels, respectively; the ratio of Angiopoietin1 (Ang1) and Angiopoietin2 (Ang2), secreted both by the tumor and by endothelial cells,affects the stability of the mature vessels.
in order to validate the model’s ability to predictshrinkage of the patient’s tumor under a varietyof treatment protocols. This intermediate validationinstrument was necessary, since there was no otherway to develop a personalized mathematical model,test its ability to predict an improved treatmenton the same patient, and still use the model forimproving treatment of this patient. Once the modelis validated by these xenograft experiments, it is up-scaled to humans and employed for suggesting animproved treatment schedule for the patient. The lattercomputational step was necessary as the xenograftexperiments on their own cannot practically test alarge number of potential treatment schedules, as thevalidated mathematical model can do.
Initially, a mechanistic model for vascular tumorgrowth in mesenchymal chondrosarcoma (MCS) wasdeveloped.37 This model was based on a pre-existing vascular tumor model, which accounts forthe molecular, cellular, and organ level interactions intumor growth, angiogenesis, and vessel maturation.Four proteins that mediate blood vessel formationand maturation were modeled: vascular endothelialgrowth factor (VEGF), platelet-derived growth factor(PDGF), angiopoietin-1 (Ang-1), and angiopoietin-2 (Ang-2). Coupled with estimation of modelparameters from the literature and laboratory results,the former model suitably predicted tumor andvasculature dynamics in human ovary carcinomaspheroids xenografted in mice37–39 (Figure 2).
This model was adapted to describe treatmentpersonalization for the MCS patient, as describedbelow.
A 45-year old male was in excellent health untila growing mediastinal mass was found. The primarytumor was resected and defined as MCS, but multiplenew bilateral pulmonary nodules were discoveredimmediately after the operation. Following a longperiod under chemotherapy, the disease was still pro-gressing and the patient suffered severe pancytopenia.An advisory panel was thus formed for identifying animproved drug treatment for this patient.
Tumor fragments, obtained from the MCSpatient were subcutaneously implanted in nudemale mice (xenografts). Once tumors grew to50–150 mm3 in size, animals were pair-matchedby tumor size into treatment and control groups,and treatment animals were administered drugs bydifferent monotherapy or combination regimens.In parallel, the initial vascular tumor model wasadjusted to describe the MCS xenograft dynamics.This was done by fitting to tumor growth dynamicsin the untreated mice. Using the xenograft-adjustedmodel, growth of the MCS xenografts and theirresponse to various drug therapies was simulated,in conjunction with the PK/PD models of therelevant drugs, and with the applied dosing regimens.Where available, patient-specific chemosensitivityinformation was used to construct PK/PD models.Otherwise, publicly available data were used. This
FIGURE 3 | Mathematical model predictions of tumor growthinhibition (TGI), calculated as TGI (%) = 100 · (1 − (T − T0)/(C − C0)),where T0, C0 are initial tumor sizes of the treated and the control tumorxenografts, respectively; T and C are sizes of treated or control tumorxenografts, respectively. The drug protocols that were simulated areshown at the bottom of each histogram bar: B/Doc denotesbevacizumab, 10 mg/kg, IV, Q3Dx10 +docetaxel, 25 mg/kg, IV, Q7Dx3;B/Doc/G denotes bevacizumab, 6.7 mg/kg, IV, day 1,8 + docetaxel,25 mg/kg, IV, Q7Dx3 + gemcitabine, 160 mg/kg, IV infusion, 24 hr(single dose); S denotes sunitinib, 40 mg/kg, PO b.i.d x28; B/D denotesbevacizumab, 5 mg/kg, IP, Q4Dx6 + docetaxel, 3 mg/kg, IV, QDx8;B/Sor denotes bevacizumab, 5 mg/kg, IP, Q4Dx6 + Sorafenib, 85 mg/kg,PO, QDx10; other bars denote predicted TGI by drugs and drugprotocols as above.
model was used to evaluate tumor growth inhibition(TGI) in the xenografted MCS patient tumors, bysimulating different monotherapies and combinationsof two or three cytotoxic and anti-angiogenic drugs.Model predictions suggested efficacy (TGI) differencesbetween the different drug protocols, applied to theMCS patient’s xenografts (Figure 3). The combinationof bevacizumab and docetaxel was predicted to bemost efficacious in inhibiting the growth of tumorsoriginating at the MCS lung metastasis. Modelpredictions were compared to the experimentallyobserved values with 87.1% prediction accuracy.40
The personalized MCS xenograft model servedas basis for the human model. Gene expressionanalyses of key proteins in the patient’s metastases andin the xenografted tumor (denoted as Met/F1 ratio)were used to up-scale relevant xenograft parameters.For example, gene expression analysis shows that theMet/F1 ratio of Ang-2 is 0.7; values of correspondingparameters in the xenograft model were multipliedby this coefficient to yield a new value in the humanmodel. Published data on the involved drugs wereused to model their PK in the MCS patient. The PD
functions used in the human modeling were those ofthe murine models.
Owing to the above mentioned xenograftpredictions and in vitro results, the mathematicalMCS patient model was used to study the patient’sresponse to many different docetaxel/bevacizumabcombination regimens. Simulations show that inthis patient, bevacizumab in combination with once-weekly docetaxel was most efficacious in suppressingtumor growth (Figure 4), consistent with theabove CIN model that suggested minimized risk ofdocetaxel-driven neutropenic toxicity when the drugis applied once weekly, rather than at other dosingschedules (see above).34 Subsequently, the MCSpatient himself received bevacizumab in combinationwith once weekly docetaxel, showing dramaticdisease stabilization and a substantial recovery ofhemoglobin, white blood cells, and platelets.40
This work shows the benefit of the mathematicalmodel in a prospective trial, albeit in one patient.Hopefully, following more extensive clinical trials,models such as the one described will replaceintermediate experimental tests. However, we donot exclude the possibility that in some treatmentpersonalization cases, the combined in vitro xenograftand in silico modeling approach will still be necessaryto identify personal PD effects. Since this combinedmethodology is costly, time consuming, and difficultto practice routinely in clinics, more practicalmethodologies for model personalization should besought. Some of the alternatives are described below.
Hormone Therapy in Prostate CancerAnother example of a clinically-oriented efficacymodel was shown in the prostate cancer (PCa)case. A mechanistic mathematical model of theform of a piecewise-linear dynamical ordinary dif-ferential equation (ODE) system,41,42 was devel-oped in order to identify the optimal conditionsfor replacing continuous hormone (androgen sup-pression) therapy in PCa patients—the conventionaltreatment mode—with intermittent hormone ther-apy, which has been hypothesized as more advanta-geous. Signaling pathways evolving with epigeneticand mutational changes in PCa cells can resultin reversible or irreversible androgen independence.Therefore, the mechanistic model describes threepopulations of tumor cells which are sensitive orreversibly/irreversibly insensitive to hormone abla-tion therapy: (1) androgen-dependent (AD) cells;(2) androgen-independent (AI) cells resulting fromreversible changes; (3) AI cells arising from irre-versible changes of genetic mutations. Under hor-mone treatment conditions, cells of state (1) may
WIREs Systems Biology and Medicine Models for personalizing oncology treatments
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FIGURE 4 | Model predicted effects of different bevacizumab and docetaxel combination regimens on tumor growth in the MCS patient.
change to those of state (2) or (3), and cells ofstate (2) may change to those of state (3). Underno treatment, cells of state (2) may return to ones ofstate (1).
The model was tested in 177 PCa patients fromthree medical centers. Clinical measurements of thePCa tumor biomarker prostate specific antigen (PSA),taken during the first 2.5 treatment cycles, were usedfor personalizing the model, and model predictions forPSA counts in subsequent treatment cycles were made.Visual comparison to the observed results appearedin line with the PSA dynamics observed clinically(Figure 5). The model also showed that PSA dynamicscan be sufficiently described by a linear equationfor each of on/off-treatment periods. The evaluationwas done by comparing the prediction errors ofthe radial basis function, a generic nonlinear model,with those of linear model. Model analysis revealedthat patients can be classified into three treatmentgroups, in which (1) relapse can be prevented byintermittent therapy, if appropriately scheduled, (2)relapse can only be delayed by intermittent therapy,and (3) continuous therapy is preferred to intermittenttherapy. Correlations between the classification bymedical doctors’ judgments and the classification bythe mathematical model proved significant. It stillremains to be seen whether this simple model canadequately describe more radical PCa therapies, wheredisease dynamics may be completely different.
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FIGURE 5 | Clinical and predicted PSA dynamics. Panels (a), (b),and (c) are the respective examples of type (1), type (2), and type (3)patients from the American cohort of 79 patients. In each panel, actualPSA values (red circles) are shown across intermittent therapy fits (bluesolid lines) and continuous therapy fits (green dashed line). In anotherexample (d) data from the first two and half treatment cycles was usedto predict the following cycles.
USE OF STATISTICAL MODELS INPREDICTING SURVIVAL OFONCOLOGY PATIENTS
Clinicians have long been interested in estimatingsurvival, for example in order to identify cancerpatients that are likely to live at least three months,who would then derive some benefit from surgery.43
Statistical tools that predict survival have been basedon population studies and on personal attributes, suchas tumor size, performance status, pathological stage,etc.43,44
A systematic review of biostatistical survivalmodels in renal cell carcinoma suggested that thevariability in their predictive power is a function ofthe role of tumor histotype in the statistical analyses,of the consistency of prognostic impact of certainvariables in different histotypes, of the level of modelvalidation, etc. Possibly, the predictive success ofstatistical models may be improved if patients arecategorized according to tumor histotype, or otherdisease characteristics.45 Yet this would require alarge and rich initial patient group as a basis for modeldevelopment, thus rendering the task more difficult.
Skeletal Metastatic DiseasesPersonalized survival estimates are important forclinical decision-making at different stages of diseaseprogression, for example, in skeletal metastaticdisease, as they can help identify which patient willbenefit from surgery and which surgical proceduremay be most appropriate. Based on data collectedfrom the Scandinavian Skeletal Metastasis Registryfor model training, two Bayesian classifiers, denotedBayesian-Estimated Tools for Survival (BETS) models,have been developed for estimating the likelihoodthat a patient will survive more than 3 or 12 months(BETS3 and BETS12, respectively43); two separatemodels had to be developed as Bayesian classifiersare suited to provide probabilities of one particularoutcome only. Both models were internally validatedusing 10-fold cross-validation methods. Subsequently,the two models were successfully validated by anindependent dataset comprising 815 records thatvaried from the training set in the distributions ofthe demographic and clinical Parameters.43
The successful validation of the BETS models,via independent data, demonstrates that statisticaltools can predict survival quite accurately and, there-fore, can assist decision-making at important medi-cal crossroads. The Bayesian Classifier methodologycan account for data uncertainty. In addition, BETSgenerate a joint distribution function describing theprobabilistic relationships between various prognosticfactors and display it graphically.43 These two aspectsof BETS are certainly an advantage when doctors’compliance is at stake.
But the BETS method also has disadvantages. Itis highly specific to estimations in patients with specificmedical conditions (e.g., locations of metastases),undergoing specific interventions (e.g., surgery), under
specific treatment philosophies. In addition, it canestimate the probability of a defined outcome (e.g.,3 month survival), but not a dynamic personalbehavior profile (e.g., tumor growth over time), whichis often critical to predict in the clinical setting.
Overall, the available statistical algorithms forprognosis (e.g., nomograms for metastatic BC andprostate cancer patients) are centered on statisticalanalysis of past clinical trials. Rather than modelingdynamical processes, these tools analyze retrospectivepatient data where one or more specific end-points have been monitored. Therefore, they arelimited to prediction of a patient’s state at onlya few predetermined time-points (typically, survivalprobability at 1–2 years and median survival months),and only for the same treatment protocols which werehistorically applied, excluding the ability to predictthe outcomes of any treatment modification. As such,these algorithms cannot satisfy all the specific needsof the physician, which in many cases fall outside thehistorically defined aims.
INTEGRATION OF MECHANISTICMATHEMATICAL MODELS WITHINDATA-DRIVEN STATISTICS
The application of PK models in drug developmenthas always been difficult,46 but over the last years auseful extension of these models has led to a signifi-cant step forward in the ability to predict populationand personal PK. When data from many patients areavailable, population PK models together with inter-patient PK variability can be used for distinguishingbiomarkers of the patient’s PK, so that subpopulationsof patients that would respond differently to drugcan be singled out.47–51 This methodology belongsto a group of population-based statistical and math-ematical models-nonlinear mixed effects (NLMEM)models, which has been increasingly applied for drugdevelopment. Termed pharmacometrics, these appli-cations quantify beneficial effects and side effectsof drugs.52 Generally, oncological pharmacometricsinclude, in addition to the mathematical population-based PK/PD models, also simple disease models thatare limited to linear, exponential, or logistic descrip-tion of tumor cell growth. But, unlike the ‘bottom-up’development of mechanism-based models, the modelbuilding process in pharmacometrics is of the ‘top-down’ methodology, essentially evaluating a range ofplausible models for their accuracy in reproducingresults from large clinical trials.52–55
Pharmacometric models have significantlyimpacted drug approval, labeling and trial designdecisions.56,57 Consequently, the number of drug
WIREs Systems Biology and Medicine Models for personalizing oncology treatments
submissions to the Food and Drug Administration(FDA), which included pharmacometric analyses, hasincreased by sixfold over the years 2000–2008.58 Still,this type of modeling has remained descriptive over theyears, using simple mathematical portrayal of cancergrowth, and focusing on retrieval of the populationbehavior. But given the large interpatient variability,such models cannot precisely describe drug–patientinteractions on the individual level. In order to antici-pate the response of specific individual patients withina real-time clinical scenario, NLMEM models mustascend to the individual perspective. Two examples ofsuch modeling are given below.
Chemotherapy-Induced NeutropeniaWhen a chemotherapeutic drug has cytotoxic side-effects (e.g., CIN), its dose is reduced by fixeddecrements. Attempting to replace this crude methodby a better approach, a semimechanistic NLMEMmyelosuppression model was recently transformedinto a patient-specific dosing tool. The tool,implemented in MS Excel, is based on a Bayesianestimation procedure. The procedure uses PK orPD information processed from neutrophil countsof a previous treatment cycle in order to adjustthe subsequent cycle dose for obtaining a desirednadir. In simulations with a hypothetical etoposide-like drug,59 the prevailing stepwise procedure of doseadjustment was compared to the model-based doseadjustment, the latter being superior in targeting adesired nadir, in terms of number of patients on targetwith no increased severe toxicity. In contrast to thestandard method, model-based adjustment may allowto increase dose for patients with a subtoxic levels.60
Underlying the development of thisNLMEM/MS Excel tool is the view that CINis highly variable between patients and betweentreatment cycles in the same patients. In contrast, theabove described fully mathematical CIN model didnot assume a significant interpatient and intercyclevariability. Yet, it yielded accurate personal predic-tions of neutrophil counts over several treatmentcycles, using only baseline neutrophil counts. Aprospective clinical study for comparing the twoapproaches may be worthwhile. Note, however, thateach of these models aimed at achieving differentendpoints: the NLMEM model in the current examplewas developed for predicting the neutrophils counts atthe nadir, and for assisting the adequate adjustmentsof these minimal values through dose individual-ization. In contrast, the purely mathematical CINmodel mentioned above was clinically evaluated forits ability to predict the nadir itself and the neutrophilprofile of the individual patient.
Metastatic BCThe NLMEM modeling strategy has been recentlyapplied for personalizing chemotherapy in metastaticBC, the most common cancer among women. Taxanesare commonly used cytotoxic treatments in BC,61
specifically docetaxel, which yields a 47% objectiveresponse rate and an overall survival of 15 months.62
Since taxanes are expected to remain a principalchemotherapeutic agent for BC, the ability to quantifyand predict response in a patient-specific manneris expected to assist in the personalized approachto BC treatment. Recently, a clinically applicablestatistical/mathematical model for BC patients treatedwith docetaxel was developed, using an NLMEMapproach, in order to accommodate the distribution ofPK/PD and biological parameters, naturally observedamong patients, and to account for errors in datameasurement (Kheifetz et al., in preparation).
Data from 33 metastatic BC patients (altogether64 tumor lesions) under docetaxel treatment wereused for creating the disease/PD model describingthe dynamics of tumor volume, angiogenic capacity,and long-term effects of docetaxel. Merged with apopulation PK model for docetaxel (designed using astudy in 521 patients from 22 Phase II trials35), the fullNLMEM model was implemented and calibrated inMonolix. Twelve molecular biomarkers measured inthe patients (estrogen receptor and VEGF expression,proliferation and mitotic indices, etc.) were testedfor inclusion as covariates, potentially linking clinicalparameters to individual lesion outcomes via theirdirect effects on model parameters. The model success-fully fit the observed lesion dynamic data, with an R2
value of 0.98 for individual fits. Stringent model selec-tion criteria that are normally applied in NLMEMmethodology were all satisfied (nonsingular FisherMatrix value, low p-values for covariate coefficients,realistic interindividual variability of parameters, lowcondition number of correlation matrices of estima-tions of parameters, low Akaike information criterionvalue, small standard errors of parameter values,etc.). The sole biomarker found to be well correlatedwith lesion elimination was the mitotic index, highvalues of which indicated good response to docetaxel.
Results show that, using three lesion data points(one baseline and two in-treatment) measured inthe individual patient, the personalized NLMEMmodel (simulated via a Bayesian Predictor) reliablypredicts the subsequent dynamic response (changeof lesion size over time) in that patient, duringtwo months following the last measurement. Thiswork shows the ability of such models to predictpersonal patient responses to chemotherapy, basedon early data, and to help personalize treatment
regimens that will divert the tumor lesion towardselimination. Implementation of model predictionsin clinical decision-making can be done upon alarge scale model validation and adaptation to theclinical needs. This can be done by identifying thecritical decision-making junctions during treatment,in which one protocol out of several authorized oneshas to be elected. In BC, for example, this canbe implemented for patients with recurrent disease,where recurrence is systemic, or in patients havingstage IV disease with distant metastases when firstdiagnosed. If such patients are also estrogen-receptor-positive, the doctor needs to choose between differenthormone therapies, or between aromatase inhibitorsand antiestrogen drugs, etc. In such decision-makingjunctions, the mathematical model can serve forproviding the patient’s individual prognosis forprogression or survival and for predicting response tothe pertinent therapies. This method extends to othermalignancies, and attests to efficient integration ofmixed-effects, biomathematical/statistical, modelingin the personalized oncotherapy realm.
ADAPTING CLINICAL TRIALS TOPERSONALIZED TREATMENTPROTOCOLS BY USE OFCOMPUTATIONAL MODELS
One may argue that computational methods carrylittle value for clinical medicine, as it may beimpossible, from the regulatory point of view, tomake changes in an ongoing treatment plan on thebasis of model predictions. Yet in reality, a great dealof medical deliberation is involved in determiningthe therapy route the patient will go through. InPCa, for example, oncologists base their treatmentdecisions on the clinical stage of the disease and on theevaluation of the primary surrogate marker PSA. Thisis done even though the oncologists are aware thatPSA alone is not sufficient for navigating the patient’streatment, and it is widely believed that to gain themaximal therapeutic effect, treatment of PCa patientsmust be personalized.14,63 For example, hormonesensitive PCa patients with potentially good prognosisare generally over-treated by the standard, androgendeprivation therapy (ADT), suffering unnecessaryadverse event and, possibly, accelerated emergenceof hormone resistance. In contrast, poor-prognosishormone sensitive patients who progress rapidly, donot benefit from standard ADT; they ought to beinitially treated more aggressively, for example, withADT combined with the new second-line hormonetherapy. In addition, 35–55% of castrate resistant
PCa patients do not respond to Docetaxel, the first linechemotherapy, making treatment futile (Dr. ManishKohli, personal communication).
We note that, similarly to other cancers, PCaprogression is realized in a transition at different rates,from a local stage to an advanced stage disease, withresistance to different drugs emerging and establishingthemselves at different rates. Nevertheless, the currentparadigm in oncology is inflexible and does not followthe personal disease-drug dynamics: adaptation, whenmade, is made a posteriori, rather than in ‘real-time.’It is therefore important to show that the time-window at which the patient is most responsive toa particular treatment protocol can be dynamicallycalculated. This will enable to properly plan acost-efficient individual therapeutic strategy, whichwill extend the patient’s survival and enhance thequality of life. A computational model based on anadequate mathematical description of the patient’sdrug-affected disease dynamics may be of aid in thispolicymaking process.
But is it possible to validate the predictionaccuracy of personalized mathematical models andstill use them to navigate long-term treatments ofindividual patients? It has been shown theoreticallythat this can be achieved by a method which entailsdynamic modification of the personalized model andconsequently, of the personalized treatment. Thismethod was developed on the basis of the notionthat for fully accomplishing personalized medicine,not only drug entities but also drug regimensshould be dynamically personalized64 (see below).When this happens, current large-scale clinical trials,yielding approved ‘packages’ of both drug entityand accompanying fixed drug regimen, are no morevalid. A new clinical trial methodology, denotedp-trials, has been suggested, which accommodatesapproval of flexible personal drug regimens. In thesuggested p-trials, the range between the minimallyeffective dose and the maximally tolerated dosewill be determined in a Phase I clinical trial, as isconventionally done, whereas the flexible personaltreatment schedule for the individual patient (withinthe above determined range) will be governed usingpersonalized mathematical models.14
The above marks a change in the perceptionof the patient’s treatment at any given momentas predetermined. Upon recognition by the clinicalcommunity of the advantage in flexible personalizedregimens, the necessary change to be made in theclinical trial paradigm is relatively minor: the currentparadigm of clinical trials is predicated on thestatistical methodology of hypothesis testing, gearedto ensure that the end result of a clinical trial is
WIREs Systems Biology and Medicine Models for personalizing oncology treatments
Large clinical sets
Mod
elIn
put (
data
)O
utpu
t
Statistical/phenomenologicalmodel
Mathematical/mechanisticmodel
All relevant information
Literature-based knowledgelaboratory/preclinical info
small clinical sets
Efficient patient stratification;unable to predict dynamicsand regimen changes
A clear view into underlyingpathophysiology;general population guidelinesfor treatment;inability to account for patientvariability
Integration of drug-patientdynamic interactions andpopulation variability for moreeffective personalization of drugsand regimens
Statistical/mathematicalmixed-effects
model
FIGURE 6 | The suggested approach for creating personalized response predictors uses nonlinear mixed effects modeling to integrate clinicalinformation with mechanistic mathematical models of drug–patient dynamic interactions.
provided with the prescribed statistical power andstatistical significance. For example, in Phase III,the trial answers the question, ‘is there convincingevidence that treatment A (i.e., the package containingone or several molecules and doses and treatmentintervals and other elements) has a better therapeuticeffect than treatment package B?’ This paradigmprovides a method to determine the necessary numberof subjects in the clinical trial. A failure in a clinicaltrial indicates nothing more precise than the failureof the tested treatment as a whole package. Thesame paradigm and the same significance of theconclusions should hold for testing treatment A versustreatment B in p-trials. The only difference between theconventional methodology and p-trials is that in thelatter, the treatment regimen of the patient is flexible.The necessary number of subjects in a p-trial shouldbe determined statistically, as is done in conventionalclinical trials and in adaptive clinical trials.
The p-trials methodology is briefly exemplifiedbelow.
Immunotherapy in Prostate CancerThe goal of this work was to show that it is feasibleto create personalized patients models, validate them
in early Phase II trials and use them in real-timefor suggesting an improved treatment regimen, tobe applied to the patient during the same clinicaltrial phase. This feasibility test was made using datafrom a Phase II clinical trial in PCa immunotherapy,an area in which personalized therapy is desperatelyneeded.
Designing drug regimens in PCa, a slowlyprogressing malignancy, is not an easy task,since patients display highly variable PSA profiles.Immunotherapy design in PCa is even morecomplicated, as such treatments must adapt tothe continuously evolving immunoediting of thetumor, one of the key processes responsible forthe high interindividual variability among cancerpatients. A mechanistic mathematical model for PCaimmunotherapy, describing the dynamic interactionsof tumor cells, immune cells and the vaccine, wasdeveloped for predicting PSA progression in advancedPCa patients treated by whole-cell autologousimmunotherapy in a Phase II study. A method wasdesigned for both personalizing the model and forvalidating the accuracy of its personalized predictionsearly in-trial. To prove its feasibility, personal PSAcounts collected pretreatment and in the early stagesof treatment were used for calibrating the model
for each of the patients, and reliability of patient-specific PCa models was demonstrated. In 7 out of9 patients tested, the model-suggested personalizedvaccination regimens were predicted to stabilizePSA levels, if applied immediately after individualmodel validation.64,65 This could significantly improveefficacy of this particular cellular immunotherapy,which in the actual clinical study failed to show ameaningful response.66
The latter study was unique in demonstrating thefeasibility and clinical benefit in an individualized adhoc modeling strategy, namely, to create personalizedpatients models, validate them early on in the givenpatient, and use them in real-time for suggesting animproved treatment regimen to be applied to thatpatient during the same clinical trial phase. In thebroad context, this study highlights why individualtreatments (particularly in immunotherapy, but alsoin other oncotherapy modalities) should ideally beflexible within an approved range of doses, as thenew dynamic personalization and p-trial conceptssuggest.14,63
CONCLUSIONS
‘Personalized medicine is the future. The onlyremaining question is how soon it will come about.’6
By reviewing computational predictive tools that weredeveloped for personalizing oncology treatments,we hope to contribute to further acceptance ofthis approach and, by that, to speeding up theestablishment of personalized medicine as a mainstream clinical practice.
A new type of decision support tools forpersonalized medicine is put forward, by whichstatistical-oriented mixed-effects PK/PD modeling ismerged with mathematical mechanistic modeling ofcellular and molecular processes at the core of thedrug–patient interactions. This method increases theprobability of proper model selection, via objectivetesting of a variety of reasonable model alternatives,having maximal parsimony and predictive ability,and minimal bias to data. An important feature
of this method is its comprehensiveness, enablinglong-range versatile predictions, in contrast to existingdecision-support tools which usually estimate singlefeatures, such as survival at a given time point43
(Figure 6).The success in predicting efficacy response,
as exemplified in this review, calls for a carefulconsideration of the promise, the suggested conceptmay have, for the future of personalized medicine.For example, the mathematical/statistical predictordescribed in the metastatic BC example may reducethe need for laborious biomarker validation, since, bythis method, the correlation of measured biomarkersto the system’s parameters and endpoints is stringentlyevaluated in the patient population. Biomarkers notcorrelating with response may still be significantlylinked with a parameter of the disease process,affecting response indirectly via synergism with otherparameter-correlated biomarkers. Analysis of sucheffects is part of the suggested methodology, sothat biomarker validation is embedded within thevalidation of the model-based tool.
Using the personalized models in clinicaltrials may be an important leap forward in theacceptance of personalized medicine; the new dynamicpersonalization strategy is expected to increase thesignificance of agents that are highly effective in part ofthe patients, yet fail to demonstrate significant overallefficacy under the standard clinical trial paradigm.Moreover, similarly to the conventional practice indrug development, we suggest that the currentlyavailable modeling approaches will be implementedin the clinic only following an acceptable regulatoryprocess.
Upon successful prospective clinical validation,novel strategies highlighted in this review willhopefully take the theoretical modeling approachesbeing applied in today’s biomedical research anddrug development arenas one step further, effectivelyextending them to the actual clinical arena where apersonalized treatment schemes should be applied toall cancer patients.
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