## Abstract

Antimitograms are prototype *in vitro* tests for evaluating chemotherapeutic efficacy using patient-derived primary cancer cells. These tests might help optimize treatment from a pharmacodynamic standpoint by guiding treatment selection. However, they are technically challenging and require refinements and trials to demonstrate benefit to be widely used. In this study, we performed simulations aimed at exploring how to validate antimitograms and how to complement them by pharmacokinetic optimization. A generic model of advanced cancer, including pharmacokinetic–pharmacodynamic monitoring, was used to link dosing schedules with progression-free survival (PFS), as built from previously validated modules. This model was used to explore different possible situations in terms of pharmacokinetic variability, pharmacodynamic variability, and antimitogram performance. The model recapitulated tumor dynamics and standalone therapeutic drug monitoring efficacy consistent with published clinical results. Simulations showed that combining pharmacokinetic and pharmacodynamic optimization should increase PFS in a synergistic fashion. Simulated data were then used to compute required clinical trial sizes, which were 30% to 90% smaller when pharmacokinetic optimization was added to pharmacodynamic optimization. This improvement was observed even when pharmacokinetic optimization alone exhibited only modest benefit. Overall, our work illustrates the synergy derived from combining antimitograms with therapeutic drug monitoring, permitting a disproportionate reduction of the trial size required to prove a benefit on PFS. Accordingly, we suggest that strategies with benefits too small for standalone clinical trials could be validated in combination in a similar manner.

**Significance:** This work offers a method to reduce the number of patients needed for a clinical trial to prove the hypothesized benefit of a drug to progression-free survival, possibly easing opportunities to evaluate combinations. *Cancer Res; 78(7); 1873–82. ©2018 AACR*.

#### Major Findings

Pharmacokinetic-pharmacodynamic disease model-based clinical trial simulations showed that antimitogram-based treatment selection and therapeutic drug monitoring, used separately, result in small improvements of progression-free survival (PFS). But their combination is synergistic and results in a disproportionate reduction of the trial size required to prove a benefit on PFS. Trials evaluating antimitograms should leverage therapeutic drug monitoring. Other strategies, with benefits too small for standalone clinical trials, could be validated in combination in a similar fashion.

## Introduction

Pharmacokinetic optimization (PKO) with therapeutic drug monitoring is somewhat effective in oncology, although it remains underused (1). Challenges to more widespread use include heterogeneity in practices and technical challenges, which are exacerbated by the difficulty in conducting clinical trials on an unpatentable procedure that provides only modest improvement. In practice, most cancer therapies hit the market with a fixed dosage to simplify their use and accelerate adoption, but this leaves PKO's potential for increased efficacy unrealized.

Pharmacodynamic optimization (PDO) involves individualized selection of chemotherapy, based on patient-specific characteristics. This optimization is considered an example of precision medicine. To date, most assays improve stratifications of the patient population. Those assays are frequently based on tumor mutations (2), but that approach requires clinical trials that evaluate every molecule in each subpopulation.

Advances in biotechnology, such as 3D cell culture (3), have provided a different approach: selecting a treatment based on *in vitro* assays of the specific individual tumor. Typically, these approaches require measuring the *C _{50}* (the drug concentration at which the cancer cell death rate is half maximum). These so-called antimitograms assays are roughly similar to antibiograms used by infectious disease specialists to assess

*in vitro*efficacy of a drug on the particular strains that infect individual patients. They represent an additional predictive tool for oncologists, but their widespread use will require clinical trials to demonstrate clinical benefit. This benefit will initially be relatively modest (3); thus, trials will require large numbers of patients. Theoretically, antimitograms and therapeutic drug monitoring are complementary: The first assay identifies the drug that elicits the most sensitive tumor response; the second ensures that drug exposure is sufficiently high. We hypothesized that these two strategies, which might show inconsistent efficacy when taken separately, could complement each other when combined; thus, synergistic efficacy might be demonstrable in smaller and shorter clinical trials, making the addition of therapeutic drug monitoring to antimitogram-based strategies an attractive proposition both for patients and for antimitogram developers.

#### Quick Guide to Equations and Assumptions

The model combined previously validated modules for efficacy (4) and toxicity (5) and a simple, one-compartment pharmacokinetic module. Patients could be treated with one of three theoretical drugs X, Y, or Z.

##### Individual variability of parameters

Individual variability was implemented as a deviation from a median population value, as per the log-normal model:

where *i* is the individual, *A* is a generic notation for the parameter, *A(i)* is the individual value, *θ _{A}* is the population median, and

*η*is the individual variability term drawn from a normal distribution with mean 0 and SD

_{A}^{(i)}*σ*.

_{A}*σ*was different for each parameter

_{A}*A*and is approximately equal to the coefficient of variation when

*σ*is small. For parameters with no variability,

_{A}*σ*= 0; otherwise,

_{A}*σ*ranged from 0.1 to 1, depending on the parameter.

_{A}##### Tumor growth and drug efficacy

An established colorectal cancer model (4) was used to simulate a single tumor mass per patient (no metastases). The live tumor compartment volume (*L*) grew and shrank as per the following equations:

Growth was first-order with doubling time *T _{growth}*. The killing rate corresponds to a Hill model, with maximum

*M*, midpoint

*C*(specific to X), and Hill coefficient

_{1/2,X}*h*.

*C*increased as the tumor became resistant, with a doubling time

_{1/2,X}*T*. For simplicity, only one drug, X, is represented. An apoptotic/necrotic compartment was also modeled (see Supplementary Fig. S1).

_{res,X}##### Drug toxicity

The toxicity module, adapted from a published model (5), simulated neutrophil counts, which were considered a proxy for all adverse effects causing disruptions in homeostatic processes without short-term cumulative toxicity (6). The 4-compartment module was governed by the following equations:

*H* is the self-renewing compartment, *P _{1}* and

*P*are progenitor compartments,

_{2}*N*is the neutrophil count,

_{c}*N*is the equilibrium value for all compartments,

_{eq}*k*is the transition time constant between compartments,

_{h}*γ*is the strength of feedback (5),

*k*is the “slope” parameter (drug toxicity on

_{tox,X}*H*), and

*C*is the drug concentration. Parameterization was done to obtain distributions in line with published data (5, 7).

_{X}Medians for *k _{tox,X}, k_{tox,Y}*, and

*k*were determined by extensive trial and error using Monte Carlo simulations to observe severe toxicity in 20%, 25%, and 30% [95% confidence interval (CI) within 0.3% of those values] of patients with X, Y, and Z respectively. Severe toxicity was defined as

_{tox,Z}*N*< 0.5 G/L at any time during the first 4 cycles.

_{c}##### Treatments and pharmacokinetics

Drugs were infused into the bloodstream and eliminated directly every 21 days until progression. First-order elimination occurred without metabolization. The volume of distribution was considered known. Therefore, drug dosage was expressed as a target peak concentration, and area under curve (AUC) variability was equal to drug half-life variability. The three simulated drugs had the same efficacy, but different toxicities. Thus, standard dose was assumed to have been set based on efficacy, and “worse” drugs had higher toxicity. Similar therapeutic situations have been reported in the literature (8).

##### Interpatient variability scenarios and antimitogram model

With respect to interpatient variability, two quantities were interesting: *σ _{PK}*, the AUC's log-scale SD; and PD, the initial C

_{50}'s log-scale SD.

*σ*and

_{PK}*σ*could each take one of three values: 0.3, 0.5, or 0.7, which represent low, medium, and high pharmacokinetic and/or pharmacodynamic variability, and correspond to median-normalized interquartile ranges of 82% to 122%, 71% to 140%, and 62% to 160%, respectively.

_{PD}The antimitogram assay was a noisy measure of the initial *C _{50}* for each patient. For each simulated drug, an

*in vitro C*was drawn from the same distribution as the initial

_{50}*in vivo C*. Patients were subsequently treated with the drug predicted as most potent for them (lowest

_{50}*in vitro C*). Accuracy was modeled by

_{50}*ρ*, the correlation coefficient between the

*in vitro*C

_{50}and the

*in vivo*C

_{50}, which was the same for all simulated drugs (and might be estimated in practice by performing xenograft experiments).

*ρ*could equal 0.7, 0.9, or 1, which corresponded to 64%, 79%, and 100% of patients, respectively, being given the most potent drug for them (for these patients, the same drug had the lowest

*C*both

_{50}*in vivo*and

*in vitro*).

##### Detailed model specifications

See Supplementary Fig. S1, and Supplementary Appendix for sensitivity analyses.

To test this hypothesis, we built a full pharmacokinetic–pharmacodynamic model based on the efficacy and toxicity of three theoretical drugs. Clinical trial simulations (Fig. 1) were then performed. We implemented PKO, based on simple therapeutic drug monitoring; PDO, based on antimitogram data; and both PKO and PDO combined (PKPDO). The main outcomes were the progression-free survival (PFS) curves and the power diagrams, which showed the relationship between the number of subjects, type I/α (one-sided) risk and statistical power in pairwise head-to-head trials between the 4 different arms.

## Materials and Methods

### Virtual trial course and endpoints

The trial plan and the statistical analyses are summarized in a flow chart (Fig. 1). Simulated virtual patients were randomly allocated to receive the PDO or not. Then, independently, virtual patients were again randomly allocated to receive the PKO or not. This procedure resulted in four arms: no optimization (NO, standard therapy), PKO, PDO, and PKPDO (both types of optimization). Standard therapy applied the least toxic drug (20% toxicity, defined as a neutrophil count <0.5 G/L).

PDO applied the drug with the lowest *in vitro C _{50}* value (described above), regardless of toxicity, except in the unlikely case of equal

*C*values, where the least toxic drug was applied. The PKO intervention was applied after the first drug infusion. The intervention was implemented when no neutropenia occurred during the first cycle (nadir ANC >1.5 G/L), and when the drug half-life individual variability term was less than the 84

_{50}^{th}percentile of its distribution (corresponding to +1 SD). In those conditions, the PKO intervention increased the individual dose to obtain an AUC at the 84th percentile (+1 SD on a logarithmic scale). In other words, PKO aimed to achieve maximum efficacy. Subsequently, the dose was adjusted on the basis of toxicity. Two levels of toxicity were defined and impacted the therapeutic schedule: first, an absolute neutrophil count of 0.5 G/L or less at any point during any cycle led to a definitive 20% dose reduction (30% if during the first cycle); and second, a count of less than 1.5 G/L on the day of the infusion led to a temporary additional 20% dose reduction for the next dose only. This strategy aimed to mimic the empirical dose reductions commonly practiced by oncologists. For computational simplicity, we chose to implement a temporary one-time dose reduction for counts <1.5 G/L, rather than the more commonly practiced delay until the count reaches >1.5 G/L. This PKO led to reasonable model behavior (Supplementary Fig. S2). Finally, the PKPDO intervention combined the two optimizations without modification.

The main endpoint in the virtual trials was PFS. We adapted the RECIST criteria to volumetric threshold determination, because the model specified tumor volume rather than tumor dimensions. Therefore, the classical 20% increase in the longest dimension was interpreted as a 73% increase in volume, as proposed elsewhere (9, 10). Consequently, we set the progression date to the day the tumor reached 173% of its nadir size (determined with a time resolution of 21 days, before drug infusions). Values of PFS>1,050 days were rare and were not determined.

### Statistical analysis

We obtained 50,000 virtual patients for each simulated treatment arm and each parameter set. Kaplan–Meier curves (equivalent to cumulative mass functions, due to the lack of censoring) were drawn with these 50,000 values. Power calculations, our main focus, were performed with 100,000 bootstrapped Monte–Carlo trial simulations for each point; for each value of *N* (the number of subjects, an even integer), the model drew *N*/2 samples from each arm (out of 50,000 patients, with replacement), and a Mann–Whitney *U* test (one-tailed, assuming no missing data) was performed, 100,000 times. As a consequence, 100,000 *P* values were obtained, and these were used to compute statistical power values for the relevant one-sided α risks; for a certain N and α risk, the statistical power was reasonably approximated by the proportion of 100,000 *P* values that were under the α risk. The number of subjects for which the power calculation was made varied from 2,000 to 46, in 25% increments, and two classical values of α risk were considered: 1% and 5%. Interpolation was log-linear, rounded up to the nearest even integer.

To improve reproducibility, the same random generator seeds were used for all parameter sets. Because of the way the software used random numbers, this rule caused each virtual patient to always be in the exact same quantile of pharmacokinetic individual variability (which was scaled up or down depending on *σ _{PK}*), but not of pharmacodynamic variability or antimitogram accuracy. The first 10,000 patients were simulated in four-arm trials, with a random seed of 0. Once we established that random seeds were functioning properly, the next 40,000 patients were simulated separately for the PKO and NO arms (random seed 1) and for the PDO and PKPDO arms (random seed 2) This approach avoided repeating similar computations for the NO and PKO arms, when only

*ρ*changed (the NO and PKO arms did not use antimitograms; thus,

*ρ*was irrelevant).

Nonparametric 95% CIs for the PFS medians were computed with Jeffreys CIs applied to ranks, with linear interpolation; these CIs are shown (though very small) as horizontal lines on PFS curves. To estimate the absolute error for power calculations, the following approach was applied to the results from the parameter set for which the reduction in trial size brought by a PKPDO versus NO design, relative to a PDO versus NO design, was the smallest (*σ _{PK}* = 0.3,

*σ*= 0.7, and

_{PD}*ρ*= 1): the survival values results were resampled 200 times with replacement, then sampled again within each sample for each trial size as above, to finally compute 200 × 10,000

*P*values per trial size. The resulting

*P*values were used to compute SDs for each trial design (see Supplementary Fig. S3), and significance was evaluated by applying the Mann–Whitney

*U*test to 200

*P*values per trial size. We did not repeat this demanding computation for other parameter sets, because improvements in power were undoubtedly significant (

*P*< 10

^{−55}) for each point, even in this worst-case scenario, where the error was overestimated due to the use of only 10,000

*P*values per bootstrap.

### Hardware and software

All simulations were run on a 64-bit Windows Server cluster with 32 cores. We used Simulo v6.10 (SGS; ref. 11), which relied on the ordinary differential equation solver, “ode.” in R.

Data analysis was performed with R CRAN v3.2.4 and the parallel package for computing bootstrapped *P* values.

## Results

As expected, the magnitude of PKO benefit compared with no optimization (NO) varied with *σ _{PK}*, and the magnitude of PDO benefit compared with NO varied with

*σ*and

_{PD}*ρ*(variability of drugs' efficacy and ability to measure them accurately, respectively). Even when the values of

*σ*, and

_{PK}, σ_{PD}*ρ*were not favorable for using either PKO or PDO as standalone regimens, PKPDO always showed synergistic effects on PFS and even larger synergistic effects on the number of patients required to show benefit.

### Effect of pharmacokinetic optimization and/or pharmacodynamic optimization

We found that the PDO improved the median PFS by +10% to +37% (Fig. 2, A to E, dark blue lines). This modest to average improvement translated into the prediction that a head-to-head PDO versus NO trial would require 122 to >2,000 patients, depending on the statistical risk accepted (Fig. 2A to E). PKO yielded slightly worse results; it improved the median PFS by +5% to +25% and required 208 to >2,000 patients for the PKO versus NO trials (Fig. 2A to E, cyan lines). In contrast, the PKPDO improved the median PFS by +18% to +63%; thus, the clinical trials required only 50 to 714 patients, depending on variabilities and statistical risks selected. In particular, combining the two types of optimization resulted in a substantial improvement for the worst-case scenario (Fig. 2B), with *σ _{PK}* =

*σ*= 0.3 and

_{PD}*ρ*= 0.7, which indicated that both PKO and PDO had low efficacy. In this case, the improvement in median PFS went from +6% and +10% with PDO and PKO, respectively, to +18% with PKPDO. Accordingly, the trial size for typical values of statistical risk α = 0.05 and power = 0.9 was reduced from 1554 patients for PDO versus NO, to 568 patients for PKPDO versus NO. The smallest relative improvement achieved by combining the two types of optimization was found for the case where

*σ*= 0.3,

_{PK}*σ*= 0.7, and

_{PD}*ρ*= 1, which corresponded to low pharmacokinetic variability, high pharmacodynamic variability, and a high accuracy in detection (Fig. 2E). In that case, the median PFS increase was improved from +37% (PDO vs. NO) to +45% (PKPDO vs. NO), and the trial size (α = 0.05 and power = 0.9) was reduced from 168 (PDO vs. NO) to 118 patients (PKPDO vs. NO). Other parameterizations and sensitivity analyses yielded comparable results (see Supplementary Figs. S4, S5, and S6 for the full set of graphs, and S7 and S8 for sensitivity analyses).

### Effect of antimitogram performance

We tested the effect of antimitogram accuracy by running simulations with different values of *ρ*, when *σ _{PK}* and

*σ*were maintained at 0.5 (Fig. 3A–C). The antimitogram accuracy was increased by increasing

_{PD}*ρ*from 0.7 to 0.9 to 1. We observed incremental, modest improvements in the median PFS; in particular, in the PKPDO arm, the median PFS increased by +32%, +40%, and +43%, respectively, and trial sizes were reduced to 194, 136, and 118 for the PKPDO versus NO design (α = 0.05 and power = 0.9). These results showed that, although perfecting the antimitogram accuracy will probably provide diminishing returns, no threshold effect should be expected.

### Toxicity

Toxicity was higher for schemes that used PKO and/or PDO. The percentage of patients that presented aplasia at least once was 6 to 24 points higher in the PKPDO arm compared to the NO arm (Fig. 4, A), with a commensurate increase in patients with multiple grade 3 toxicities (Fig. 4B). Despite this increase in toxicity, which led to dose reductions, antimitogram use always improved PFS (Figs. 2 and 3; Supplementary Figs. S4, S5, and S6). Two unrelated toxicity models (12, 13) were tested in sensitivity analyses and had similar results (Supplementary Fig. S8).

## Discussion

This study addressed the translational issue of antimitogram clinical validation. We approached this issue by performing complete pharmacokinetic–pharmacodynamic simulations of an oncology clinical trial. Our findings highlight good design principles for such trials.

### Pharmacokinetic optimization in oncology trials

PKO was found to improve PFS and reduce clinical trial size, even in situations where pharmacokinetic variability was low. Furthermore, even when the PKO effect was too small to detect in practice, it significantly reduced the number of required subjects in a PKPDO versus NO trial, due to the non-linearity between efficacy and the number of required subjects. Therefore, teams and organizations developing antimitogram assays for patient care can benefit by employing PKO in addition to their antimitogram technology in a trial. Adding PKO will provide benefit both for the patients and for the trial sponsors, because trials will be shorter and smaller. From a cost perspective, given that clinical trials cost up to $40,000 per patient (14), a simple addition of therapeutic drug monitoring, as implemented in our virtual trials, could be expected to be well worth the small additional effort required, due to the substantial reduction in the number of patients required. This may be a first-mover advantage, because the PKPDO versus PKO design would be the only ethical design, once PKO has shown benefit; however, the PKPDO versus PKO design required a sample size similar to that required in a PDO versus NO design (in Figs. 2 and 3, black and blue lines remain very close).

The PKO strategy in our theoretical simulations was relatively simple. It resulted in an acceptable level of toxicity, which could be adequately managed in practice with symptomatic treatments, such as G-CSF for neutropenia. Other PKO strategies could be useful in clinical practice, such as pharmacogenetics (15, 16), adjustments for drug–drug interactions (17, 18), or more complex covariate-based posology- or rhythm-adaptation algorithms (19), depending on the pharmacological and clinical situation.

The effect we observed with standalone therapeutic drug monitoring may be surprising, given its low adoption, but our results are consistent with observational studies that link pharmacokinetic variability and outcomes in clinical oncology (20). The results were consistent in several sensitivity analyses (Supplementary Figs. S7 and S8). Clinical trials that specifically and prospectively evaluate standalone PKO strategies have been uncommon, but they have showed improvements (21–23) of the same order of magnitude as those obtained with new therapies (24–26).

### Pharmacodynamic optimization in oncology trials

Controlling pharmacokinetic and pharmacodynamic variability is not in the hands of the biotechnologists that develop antimitograms. However, antimitogram technology can be improved and refined to increase accuracy. We used simulations to determine the expected impact of antimitogram performance on patient outcomes. We found that antimitogram accuracy should be relatively good (*ρ* = 0.7 in our simulations) for significant improvements that make clinical trials feasible. In addition, we found that efficacy would benefit by improving the accuracy of the antimitogram results up to a perfect measure of the *in vivo* initial *C _{50}*, without any threshold effect. Therefore, it would be advantageous to continue improving antimitogram technology until near-perfect accuracy is achieved.

One could argue that antimitograms may not require clinical trials at all when they are used to choose between several approved therapies. We find it unlikely that this argument would hold up in practice, given the parsimonious and evidence-based nature of modern clinical medicine. In addition, although antimitograms could be used in a few expert centers, they are expensive, due to the requirement for complex cell culture, and it would be difficult to justify the cost of large scale use to insurers, public and private, without evidence from trials that showed a clear benefit.

In combination with PKO, other useful PDO strategies may also be used, such as adaptation to protein, epigenetic, or genetic markers recognized for their treatment-specific prognostic value (27–30), or biological early efficacy markers (31, 32). One such example of PDO, the use of targeted therapy tailored to genetic aberrations, has been tested in a negative trial (33), which could have had different results under the PKPDO paradigm, because most of its drugs have clinically relevant exposure–response relationships (34–44).

### Perspectives

Drug combination studies in oncology are increasingly becoming the rule rather than the exception. For modeling studies, drug combinations are still challenging (45), and we were not able to find validated generic models of synergic efficacy/toxicity at this time. Such combination efficacy/toxicity models should become available in the future, and should be incorporated to integrated simulations like the one presented here.

We tested our model with a wide range of sensitivity analyses, which all gave similar results. This robustness suggests that beyond the particular case of PKO and PDO in oncology, in general, combinations of moderately useful therapeutic strategies may offer synergistic clinical benefit, and thus could make trials more feasible for sponsors, and in turn bring additional benefit to patients. This is particularly relevant for non-patentable interventions or therapeutic algorithms, which are much more difficult to develop clinically (46).

Our simulations were relatively generic; they presented a theoretical, typically advanced cancer situation with several treatment options. This combination of validated models could compute how the magnitude of different outcomes changed, depending on antimitogram performance and pharmacologic variabilities. Future studies in this field could investigate different models and parameter sets, and this type of integrated platform could be adapted to specific cases.

## Disclosure of Potential Conflicts of Interest

No potential conflicts of interest were disclosed.

## Authors' Contributions

**Conception and design:** S. Haviari, B. You, M. Tod

**Development of methodology:** S. Haviari, B. You, M. Tod

**Analysis and interpretation of data (e.g., statistical analysis, biostatistics, computational analysis):** S. Haviari, B. You

**Writing, review, and/or revision of the manuscript:** S. Haviari, B. You, M. Tod

**Study supervision:** M. Tod

## Acknowledgments

We thank SGS Exprimo, and in particular, Quentin Leirens and Ruben Faelens, for their active collaboration in the clinical trial simulations, the Simulo license, and the service around it. We also thank Olivier Colomban for setting up and maintaining the server. This study was funded by the payroll of the parent institutions, without any specific research grant. We thank Hospices Civils de Lyon and Université Claude Bernard Lyon 1 for the academic freedom they granted us, and Université Claude Bernard Lyon 1 for hosting the computation server.

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked *advertisement* in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

## Footnotes

**Note:**Supplementary data for this article are available at Cancer Research Online (http://cancerres.aacrjournals.org/).

- Received June 16, 2017.
- Revision received October 30, 2017.
- Accepted January 5, 2018.
- Published first January 9, 2018.

- ©2018 American Association for Cancer Research.