WO2021097653A1

WO2021097653A1 - Optimisation of combination drug therapies

Info

Publication number: WO2021097653A1
Application number: PCT/CN2019/119393
Authority: WO
Inventors: Dean Ho; Xianting DING; Yun Yen; Chih-Ming Ho; Hung-Shu Chang
Original assignee: National University Of Singapore; Shanghai Jiao Tong University; Taipei Medical University; The Regents Of The University Of California
Priority date: 2019-11-19
Filing date: 2019-11-19
Publication date: 2021-05-27

Abstract

A method of optimising a combination drug therapy comprises: receiving, by at least one processor, exposure data indicative of measurements of a sample of a subject to whom two or more drugs have been administered at an initial dosing regimen, the measurements being of exposure levels of the two or more drugs at a plurality of time points; receiving, by the at least one processor, response data indicative of measurements of a therapeutic outcome variable at the plurality of time points; determining, using the at least one processor, from the response data and the exposure data, a response function that relates the therapeutic outcome to the exposure levels of the two or more drugs; optimising, using the at least one processor, the response function with respect to the exposure levels to determine optimised exposure levels for the subject; and generating, using the at least one processor, an optimised dosing regimen based on the optimised exposure levels.

Description

OPTIMISATION OF COMBINATION DRUG THERAPIES

Technical Field

The present invention relates, in general terms, to optimisation of combination drug therapies, for example for treatment of cancers such as colorectal cancer. It will be appreciated that the invention has applicability to treatment of a wide variety of medical conditions.

Background

Designing multi-drug regimens often involves target-and synergy prediction-based drug selection, and subsequent dose escalation to achieve the maximum tolerated dose (MTD) of each drug. This approach may improve efficacy, but usually not optimally, and often substantially increases toxicity. Drug interactions depend on many pathways in the omics networks, further complicating the design process. The extremely large drug-dose parameter space cannot be reconciled using conventional approaches, which are largely based on prediction. This barrier at least partially accounts for the low response rates that are observed with conventional mono-and combinatorial chemotherapy.

For example, colorectal carcinoma (CRC) is the third most common cancer in men (663,000 cases, 10.0%of all cancer cases) and the second most common cancer in women (571,000 cases, 9.4%of all cancer cases) worldwide. The lifetime risk of developing CRC is approximately 1 in 20 (5.1%) . Numerous cancer therapies such as 5-fluorouracil (5-FU) , irinotecan, oxaliplatin, bevacizumab, cetuximab, and panitumumab, and the oral drug capecitabine have been effective against CRC. Several combinations of these drugs, such as FOLFOX (leucovorin, 5-FU, and oxaliplatin) , FOLFIRI (leucovorin, 5-FU, and irinotecan) , and XELOX (oxaliplatin and capecitabine) , with or without a monoclonal antibody, have been reported to improve CRC treatment outcomes. However, the efficacy of current chemotherapeutic agents against CRC has reached a plateau. The chemotherapy response rate is about 25%. The 5-year survival rate of patients with advanced CRC has remained <8%due to the development of resistance to treatment. With regards to more recently developed therapies, tyrosine kinase inhibitors can potentially avoid chemotherapy-induced cytotoxicity. Targeted agents can potentially overcome chemotherapy resistance and enhance patient response localized or advanced cancer. Despite their promising potential, these inhibitors have benefited only certain patient populations with CRC.

There thus remains a need for a way to optimise combination therapies for use in treating medical conditions such as CRC.

Summary

The present disclosure provides a method of optimising a combination drug therapy comprising two or more drugs administrable to a subject, the method comprising:

receiving, by at least one processor, exposure data indicative of measurements of a sample of a subject to whom the two or more drugs have been administered at an initial dosing regimen, the measurements being of exposure levels of the two or more drugs at a plurality of time points;

receiving, by the at least one processor, response data indicative of measurements of a therapeutic outcome variable at the plurality of time points;

determining, using the at least one processor, from the response data and the exposure data, a response function that relates the therapeutic outcome to the exposure levels of the two or more drugs;

optimising, using the at least one processor, the response function with respect to the exposure levels to determine optimised exposure levels for the subject; and

generating, using the at least one processor, an optimised dosing regimen based on the optimised exposure levels.

The response function may be a polynomial function of the exposure levels.

In certain embodiments, the response function is:

or a time-integrated version thereof, where R is the response data at time t, N is the number of drugs, and c _i (t) is the exposure level of drug i at time t.

In certain embodiments, the exposure levels are blood serum concentrations, blood plasma concentrations, urine concentrations, hair concentrations, or saliva concentrations of the respective drugs.

In certain embodiments, the exposure levels are varied by fewer than (M ²+3M+2) /2 sets of variations of drug doses of the initial dosing regimen, and preferably without varying drug doses of the initial dosing regimen.

The method may further comprise treating the subject according to the optimised dosing regimen.

The present disclosure also provides a system for optimising a combination drug therapy comprising two or more drugs administrable to a subject, the system comprising:

at least one processor; and

computer-readable storage having stored thereon instructions for causing the at least one processor to perform a method as disclosed herein.

The present disclosure also provides a non-transitory computer-readable storage medium having instructions stored thereon for causing at least one processor to perform a method as disclosed herein.

a receiving unit that is configured to:

receive exposure data indicative of measurements of a sample of a subject to whom the two or more drugs have been administered at an initial dosing regimen, the measurements being of exposure levels of the two or more drugs at a plurality of time points; and

receive response data indicative of measurements of a therapeutic outcome variable at the plurality of time points; and an optimisation unit that is configured to:

determine, from the response data and the exposure data, a response function that relates the therapeutic outcome to the exposure levels of the two or more drugs;

optimise the response function with respect to the exposure levels to determine optimised exposure levels for the subject; and

generate an optimised dosing regimen based on the optimised exposure levels.

The response function may be a polynomial function of the exposure levels, such as:

The exposure levels may be blood serum concentrations, blood plasma concentrations, urine concentrations, hair concentrations, or saliva concentrations of the respective drugs.

The present disclosure also provides a method of optimising a combination drug therapy comprising two or more drugs administrable to a subject, the method comprising:

measuring, at a plurality of time points, exposure levels of the two or more drugs in a sample of a subject to whom the two or more drugs have been administered at an initial dosing regimen;

measuring a therapeutic outcome variable at the plurality of time points;

determining, from the measurements of the exposure levels and the therapeutic outcome variable, a response function that relates the therapeutic outcome variable to the exposure levels of the two or more drugs;

optimising the response function with respect to the exposure levels to determine optimised exposure levels for the subject; and

generating an optimised dosing regimen based on the optimised exposure levels.

The exposure levels may be varied by fewer than (M ²+3M+2) /2 sets of variations of drug doses of the initial dosing regimen, and preferably without varying drug doses of the initial dosing regimen.

Brief description of the drawings

Embodiments of the present invention will now be described, by way of non-limiting example, with reference to the drawings in which:

Figure 1 is a flow diagram of a method for optimising a combination therapy according to certain embodiments.

Figure 2 is a block architecture of a system for optimising a combination therapy according to certain embodiments.

Figure 3 shows an optimisation flow according to certain embodiments. (a) Based on dose response curves of drug x, the calibration regimen (CR) dose of drug x are determined. All rats are treated with the CR on day 1 and day 7. (b) The highly variable tumor response rates of all rats are measured and correlated with the corresponding drug dose inputs. (c) Based on the drug-dose values and the tumor response rate of individual rat, the phenotypic response surface (PRS) platform was applied to obtain the individually optimized regimen (IOR) for each rat. (d) The subject-specific IOR regimen is subsequently administered on day 14 and day 24 to comprehensive converge to the best tumor response rate.

Figure 4 shows experimental results from an optimisation method according to certain embodiments. (a) The tumor responses of the control group during days 1-3 are shown (n=3) . No apparent efficacy is observed. Tumor sizes were normalized to the tumor size of individual rats measured at day 0. (b) The CR regimen was applied on day 1 and day 7 and the normalized tumor size is shown (n=5) . Tumor sizes were normalized to the tumor size of individual rats measured at day 0. The IOR regimen was applied on day 14 and the tumor sizes were normalized to the tumor size of the individual rat measured at day 0 (n=5) . (c) A waterfall plot based on the normalized tumor size deducted by the normalized average tumor size of the control group is shown for IOR1, IOR2, IOR3, IOR4, and IOR5. (d) The response rate based on the normalized tumor size for all 5 subjects from days 9-13 is shown (average rate = 0.0276, S. D. =0.0183) . The green dash line is the averaged response rate of the control group (average rate = 0.0576, S.D. = 0.0204) (e) The tumor sizes normalized to the tumor size of the individual rat measured at day 13 are shown for the IOR group (n=5) . The control group average tumor size during the course of treatment is shown. (f) The response rate based on the normalized tumor size for all 5 subjects from days 14-30 is shown (average rate = 0.00776, S.D. = 0.00291) .

Figure 5 shows dynamic responses of Phenotypic response surface (PRS) . Optimized drug-drug interactions of IOR1, IOR2, IOR3, IOR4, and IOR5 on day 13 are shown. Optimal dosing parameters are indicated by a yellow marker. (a) IOR1: Optimized drug interaction PRS plots for adriamycin-cisplatin, herceptin-cisplatin, and gemcitabine-cisplatin are shown. (b) IOR1: Optimized drug interaction PRS plots for herceptin-adriamycin, gemcitabine-adriamycin, and gemcitabine-herceptin are shown. (c) IOR2: Optimized drug interaction PRS plots for adriamycin-cisplatin, herceptin-cisplatin, and gemcitabine-cisplatin are shown. (d) IOR2: Optimized drug interaction PRS plots for herceptin-adriamycin, gemcitabine-adriamycin, and gemcitabine-herceptin are shown. (e) IOR3: Optimized drug interaction PRS plots for adriamycin-cisplatin, herceptin-cisplatin, and gemcitabine-cisplatin are shown. (f) IOR3: Optimized drug interaction PRS plots for herceptin-adriamycin, gemcitabine-adriamycin, and gemcitabine-herceptin are shown. (g) IOR4: Optimized drug interaction PRS plots for adriamycin-cisplatin, herceptin-cisplatin, and gemcitabine-cisplatin are shown. (h) IOR4: Optimized drug interaction PRS plots for herceptin-adriamycin, gemcitabine-adriamycin, and gemcitabine-herceptin are shown. (i) IOR5: Optimized drug interaction PRS plots for adriamycin-cisplatin, herceptin-cisplatin, and gemcitabine-cisplatin are shown. (j) IOR5: Optimized drug interaction PRS plots for herceptin-adriamycin, gemcitabine-adriamycin, and gemcitabine-herceptin are shown.

Figure 6 shows that tumor treatment response is mediated by time-dependent drug interaction terms. Normalized tumor sizes are plotted against drug-drug interaction terms as a function of time for IOR1 to IOR5. A shift between drug synergism and antagonism is observed over time, demonstrating the need for dynamic modulation of combination therapy to maintain optimized treatment outcomes. (a) The impact of adriaymicin-gemcitabine interactions on the normalized tumor size over time is shown. (b) The impact of adriaymicin-cisplatin interactions on the normalized tumor size over time is shown. (c) The impact of adriaymicin-herceptin interactions on the normalized tumor size over time is shown. (d) The impact of gemcitabine-cisplatin interactions on the normalized tumor size over time is shown. (e) The impact of gemcitabine-herceptin interactions on the normalized tumor size over time is shown. (f) The impact of cisplatin-herceptin interactions on the normalized tumor size over time is shown.

Figure 7 shows that linear, quadratic, and drug interaction terms govern tumor treatment efficacy. The 15 outlined terms identify the linear relation of the drug dose, the quadratic relation of the drug dose, as well as drug-drug interactions. The numerical subscripts serve as drug identifiers: 1: adriamycin, 2: gemcitabine, 3: cisplatin, 4: herceptin. (a) IOR1 terms are shown for day 13. (b) IOR2 terms are shown for day 13. (c) IOR3 terms are shown for day 13. (d) IOR4 terms are shown for day 13. (e) IOR5 terms are shown for day 13.

Figure 8 shows that minimizing the sum of the linear, quadratic, and drug interaction terms optimizes combination therapy. The contributions to the tumor size response based on the sum of the linear terms, quadratic terms, and the drug-drug interaction terms are plotted for IOR1, IOR2, IOR3, IOR4, and IOR5 as a function of time.

Figure 9 shows a schedule of drug administration and tumor measurements. Two groups of rats were investigated. For the control group, 3 rats were inoculated with tumor cells and received no treatment throughout the trial. For the IOR group, 5 rats were inoculated with tumor cells, treated twice with the CR regimen on day1 and day7, and then treated twice with IOR regimens on day14 and day24. Tumor sizes were recorded daily. Drug doses in serum after the first treatment were recorded for 9 time points.

Figure 10 shows safety investigations of the individualized therapies. (a) Neutrophil quantification on day 21 and day 31. (b) Alanine aminotransferase (ALT) levels on day 21. (c) Comparison of ALT values against tumor size. Data are represented as mean ± standard deviation for each group.

Figure 11 shows drug plasma concentration for each IOR subject during the first 64 hours after initial CR treatment.

Figure 12 shows bar plots of blood serum drug concentration for each IOR subject for day 1 to day 6 following initial CR treatment.

[Rectified under Rule 91, 26.03.2020]
Figure 13 shows daily tumor sizes and serum drug doses. (a) adriamycin serum dose, (b) gemcitabine serum dose, (c) cisplatin serum dose, (d) herceptin serum dose and (e) tumor size (normalized to day 0) was recorded for each rat in IOR group. 15 data sets were generated from the 13 days (from day 1 to day 13 as indicated in the shaded area) of measurements with interpolation to generate individualized PRS for each rat, which was then applied to determine the individualized optimal regimen on day 14.
Figure 14 shows results of the statistical analysis of rat IOR4.

Detailed description

The present invention is predicated on the realisation that exposure levels (e.g., drug plasma level or drug serum level) of drugs in a multi-drug combination therapy can be optimised on an individual level to provide the optimal therapeutic effect to a subject suffering from a medical condition, without requiring a large number of variations in drug dose levels for the optimisation process, contrary to prior art approaches that measure response for multiple dosing levels. The optimised exposure levels obtained according to the invention can be used to infer an optimal dosing regimen, on an individualised basis, for the subject. Advantageously, this can be done with a greatly reduced number of dosing modulations, or even, in at least some cases, no dosing modulations at all. A further advantage of the present invention is that it may be implemented independently of knowledge pertaining to drug synergism.

In general terms, the method according to certain embodiments comprises a calibration phase, in which variations in exposure level are monitored at the same time as variations in response to a combination therapy are monitored, such that a relationship between response and exposure level can be derived. The variations in exposure level may be, but need not be, induced by variation in the dose of one or more drugs of the combination therapy. Following the calibration phase, a modified dosing regimen may be applied. The exposure level and response may continue to be monitored, and calibration may continue to be performed over time to dynamically adjust the dosing regimen. The calibration may use a sliding window approach, for example, such that the N most recent measurements are used for calibration, where N is the minimum number of measurements needed to obtain the coefficients of the function describing the relationship between response and exposure level.

Referring initially to Figure 1, a method 100 of optimising a combination drug therapy comprising two or more drugs administrable to a subject comprises a first step 102 of receiving exposure data indicative of measurements of a sample of a subject to whom the two or more drugs have been administered at an initial dosing regimen. The measurements are of exposure levels of the two or more drugs at a plurality of time points. For example, the measurements may be obtained by measuring blood serum concentrations or blood plasma concentrations of the two or more drugs.

As used herein, “exposure level” refers to the concentration of a drug in the body of a subject, for example as measured in a blood sample or other sample extracted from the subject. This is to be contrasted with “dosing level” , which refers to the concentration of a drug when administered to the subject.

The exposure data may be received by at least one processor of a computing device or set of computing devices. For example, the exposure data may be provided on a storage medium that is physically connected to the computing device, or may be transmitted to the computing device via a network interface. In some embodiments, the computing device may be, or may be connected to, a diagnostic device that includes components for analysing patient samples (such as blood samples, saliva samples, urine samples, etc. ) , and determining concentrations of one or more drugs in the patient samples, these concentrations then being provided as measurements of exposure levels to the at least one processor.

The exposure data are time series data of the exposure levels of the two or more drugs. For example, if there are four drugs in the combination therapy, then the exposure data will comprise four time series c _i (t) , where i=1, …, 4, each time series representing a succession of concentration measurements at a plurality of time points (which may or may not be evenly spaced) . The concentration measurements may represent drug serum level or drug plasma level, for example.

At step 104, response data are received (e.g., by the at least one processor) . The response data are indicative of measurements of a therapeutic outcome variable at the plurality of time points (i.e., the same times at which the exposure levels are measured) . The therapeutic outcome variable may be any one of a number of clinically relevant quantities that are indicative of efficacy of the combination therapy. For example, if the combination therapy is for use in treatment of a solid tumour, one such therapeutic outcome variable may be tumour size. In another example, the therapeutic outcome variable may be a level of a biomarker that is associated with a lymphoid neoplasm.

More generally, the following methods of measuring therapeutic outcome may be used:

(1) Use of hair, fecal matter, sweat, mucus, cheek swabs, earwax, tears, sperm, skin cells or scrapes, and other excretions or biological materials to screen for markers for tumor treatment response, including proteins and protein fragments, cell, blood, and nucleic acids (e.g., small interfering RNA (siRNA) , microRNA (miRNA) , long noncoding RNA, DNA, exosomes, and other classes of ribosomal and deoxyribosomal nucleic acids) ;

(2) Patient body temperature, blood pressure, pupil dilation, body weight, fluid intake or brain waves, electrochemical readings of the brain, cardiac signals, excretion, and palpation;

(3) Blood draws to monitor levels of circulating tumor markers (e.g., cytokines, antibodies, serum proteins, electrolytes, hematocrit levels, and general protein and biological markers) that serve as indicators for tumor treatment response;

(4) Urine analysis to monitor levels of electrolyte, protein, possible presence of blood, or other markers that serve as indicators for tumor treatment response-additional markers include proteins and protein fragments, cell, and nucleic acids (e.g., siRNA, miRNA, long noncoding RNA, DNA, exosomes, and other relevant nucleic acids) ;

(5) Sputum analysis to assess number of sperms for infertility treatment and for relevant markers associated with tumor treatment response (e.g., proteins and protein fragments, cell, blood, and nucleic acids, such as siRNA, miRNA, long noncoding RNA, DNA, exosomes, and other classes of ribosomal and deoxyribosomal nucleic acids) ;

(6) Saliva analysis to assess for relevant markers associated with tumor treatment response (e.g., proteins and protein fragments, cell, blood, and nucleic acids, such as siRNA, miRNA, long noncoding RNA, DNA, exosomes, and other classes of ribosomal and deoxyribosomal nucleic acids) ;

(7) Use of imaging techniques, such as X-ray, PET, CT, CAT, MRI (e.g., conventional MM, functional MRI, or other types of MRI) , fluorescence spectroscopy, near-infrared spectroscopy, Raman spectroscopy, fluorescence correlation spectroscopy, acoustic imaging techniques, microscopy of tissue, biopsy, and other imaging techniques to monitor tumor size or to monitor fluid and blood flow to and from a tumor as an indicator for tumor treatment response, or blood flow to and from an area of the body (e.g., brain, heart, and so forth) as an indicator of general treatment response;

(8) Image processing techniques to quantify tumor treatment response from imaging techniques (e.g., pixel counting, heat maps, or other techniques) -image processing techniques also can include image analysis for hematoxylin and eosin staining or other cell or tissue stains to quantify tumor response, fluorescent marker quantification to assess tumor response, and quantification of biopsy (e.g., fine needle aspiration) samples and other relevant biological materials to quantify tumor treatment response; and

(9) Skin analysis for accessing color, lipid, and blood circulation for cosmetic treatments.

Returning to Figure 1, the method 100 includes a further step 106 of determining (e.g., by the at least one processor) , from the response data and the exposure data, a response function that relates the therapeutic outcome to the exposure levels of the two or more drugs.

For example, the response function may be a polynomial function of the exposure levels. In particular, it has been found that use of a quadratic response function is able to efficiently generate optimised dosing regimens for combination therapy. Step 106 may therefore include fitting the response data to the following function:

where R represents the response data as a function of time t, and c _i (t) is the exposure level of drug i at time t. The response function R may also be referred to herein as a phenotypic response surface (PRS) .

The coefficients of the terms of R may be determined in any suitable fashion. For example, a multidimensional curve fitting algorithm may be used to determine the coefficients. An example implementation of a multidimensional curve fitting algorithm may be found in the fitnlm function of MATLAB (MathWorks, Natick, MA) or the nls function of the R statistical programming platform (www. r-project. org) .

In some embodiments, an integral version of Equation (1) may be used to derive a response function as follows:

where T ₁ and T ₂ are start and end times of an initial treatment regimen. It will be noted that in Equation (2) , the coefficients are time-independent. This is because, during the initial, calibration stage of the method 100, it is assumed that the coefficients remain constant. The coefficients in Equation (2) may be determined by fitting response data R by multidimensional fitting (for example) , as before.

The coefficients, x ₀, x _i, y _ii and z _ij, define the interactions of drugs with both the molecular mechanisms (genetics, proteomics transcriptomics, and metabolomics, etc. ) and unique physiological behavior (metabolism, immune system and pharmacokinetics, etc. ) of a biological system ranging from cells, to animals, to human patients.

Based on the PRS correlation in Equation (1) or (2) , a rationally developed, small number of calibration assays (in vitro, preclinical, or human) can be used in concert for deterministically identifying these coefficients and immediately prescribing a globally optimal treatment course. For example, in an in vitro search of potent drug-dose combinations from a pool of 14 drugs, Equation 1 has 120 coefficients. Instead of carrying out 6 billion high throughput tests, 120 experiments can tell us the optimized regimens ranked by efficacy. In an in vivo setting, only a very small number of data points are available, especially in the case of personalized therapy. In other words, a large amount of training data is not available for in vivo testing. The PRS equation (1) or (2) enables immediate implementation of the optimized drug doses at a given time, t, and can dynamically re-optimizes these doses during treatment to adjust for mechanistic (e.g. genomics, proteomics, transcriptomics, etc. ) , physiological, and treatment regimen changes in personalized medicine. As the approach described herein is model-free, the implementation is agnostic to the class of drugs used or indication being treated.

The aberrant pathways in diseased cells will make the omics networks depart from their normal functions, which will propagate to organs and to the entire body. Identifying the disease mechanisms and tracing their interactions with cellular and physiological functions are overwhelmingly complex. After drug treatment is applied, how the drugs interplay with cascade cellular and physiological mechanisms to reach therapeutic purposes is at least equally complex. Accordingly, the simplified nature of Equation (1) or (2) , and the ability to determine a dosing regimen from it based on relatively small amounts of data, is particularly advantageous.

Once the coefficients of Equation (1) or (2) are determined, the method 100 may include a step 108 of optimising (e.g., using the at least one processor) , the response function R with respect to the exposure levels c _i (t) to determine optimised exposure levels for the subject. In particular, the coefficients determined from step 106 are held constant, and any suitable multidimensional optimisation algorithm may be used to determine values

that provide a local or global maximum or minimum of R. In one example, if R represents tumour size, the optimisation operation at step 108 may comprise finding values

that give a global minimum for R.

The optimisation operation at step 108 may make use of any suitable multivariate optimisation algorithm, for example a gradient-based method such as steepest descent, or a heuristic method such as a genetic algorithm, particle swarm optimisation, or simulated annealing.

At step 110, the method 100 includes generating (e.g., using the at least one processor) an optimised dosing regimen based on the optimised exposure levels

Once the optimised dosing regimen is generated, the method may comprise treating the subject according to the optimised dosing regimen.

The method 100 may be iterative. For example, after treating the subject according to the optimised dosing regimen, one or more further rounds of measurements may be made of exposure levels and corresponding response. These further measurements may be combined with previous measurements, and previously derived coefficients from Equation (2) , to derive a new set of coefficients, and to then determine a new set of optimised values

for a new optimised dosing regimen. This process may be repeated, with the most recent N exposure level and response measurements being used at each iteration, in a sliding window approach.

Since Equation (2) includes (M ²+3M+2) /2 unknowns (i.e., the coefficients) , at least that number of observations is required to determine them. Accordingly, should it not be possible to perform enough modulations of drug doses to vary the c _i sufficiently to obtain the minimum number of required exposure level measurements, the method 100 may comprise simply taking further exposure level measurements (e.g., further blood draws to obtain drug serum levels) , without modifying any doses in the dosing regimen, as discussed above. If for some reason it becomes impractical to take such measurements, in some embodiments, it may be possible to use population-wide PK data as a proxy, or to use alternative techniques for providing additional data, such as imputation, interpolation or data augmentation.

Turning to Figure 2, a system 200 for optimising a combination therapy includes at least one processor 202 in communication with computer-readable storage 204. The at least one processor 202 is also in communication with one or more input/output devices such as a display 206 (which may be a touch-screen display capable of both input and output functions, for example) and one or more interfaces 208 (e.g., USB interfaces, network interfaces and the like) for enabling the system 200 to communicate with one or more external devices. For example, at least one of the interfaces 208 may enable the system 200 to communicate with one or more diagnostic devices that measure exposure levels of two or more drugs in a sample of the subject, to thereby obtain exposure data, and/or with one or more diagnostic devices that measure or otherwise obtain response data indicative of values for one or more therapeutic outcome variables as described above. If the system 200 is integrated with the one or more diagnostic devices, one such interface 208 may be a local bus connection, for example.

The computer-readable storage 204 may have stored thereon a receiving unit 214 that is configured to receive the exposure data and the response data as described above with reference to

steps

102 and 104 of method 100, and an optimisation unit 216 that is configured to: determine, from the response data and the exposure data, a response function that relates the therapeutic outcome to the exposure levels of the two or more drugs; optimise the response function with respect to the exposure levels to determine optimised exposure levels for the subject; and generate an optimised dosing regimen based on the optimised exposure levels; as described above with reference to

steps

106, 108 and 110 of method 100. In this sense, the receiving unit 214 and optimisation unit 216 are software modules stored on computer-readable storage 204 and configured to carry out their respective functions. However, it will be appreciated that in some embodiments, the receiving unit 214 and optimisation unit 216 may instead be standalone components (separate from storage 204) comprising hardware or a combination of software and hardware.

Example

An example of a method of optimising a combination therapy will now be described, with reference to an experiment conducted on a genetically homogeneous rat population inoculated with colorectal cancer (CRC) cells, and a combination of four drugs: adriamycin, gemcitabine, cisplatin, and herceptin. The four compounds are not typically used as monotherapies towards colorectal cancer, or in combination with other drugs. Among the 4 drugs, cisplatin, adriamycin, and gemcitabine are chemo agents. They target TopoII and DNA replication enzymes. Herceptin is an antibody, which targets the EGFR receptor ERB2. Combinatorial application of these agents can potentially exert beneficial effects and promote their anti-CRC efficacy.

Using method 100, a novel combination therapy (AGCH: adriamycin, gemcitabine, cisplatin, and herceptin) , was dynamically optimized to increase the treatment response rate using rat models (Figure 3) . Of note, these four compounds are not typically used as monotherapies towards CRC, or in combination with other drugs. Method 100 agnostically optimizes the combination of these four drugs to reconcile the best dosages modulated over time, independent of target or mechanistic biology. Following the initial administration of AGCH at 1/4 MTD (maximum tolerated dose) of each drug to each rat, which also served as the calibration period for the PRS coefficients of Equation (1) , a substantial level of variability was observed between the treated rats during the initial calibration period, even when using the genetically homogeneous rats and cancer cell line for the study. Upon PRS implementation, each rat was treated by the individually optimized regimen (IOR) obtained via method 100. The tumor response in each rat was actionably converged such that all rats responded to treatment. Importantly, all rat tumors collapsed in a uniform fashion to reveal a universally potent and collective treatment response. In order to achieve this outcome, this work demonstrates the substantial changes to drug dose and individualized dose modulation that are required for each rat. The method 100 successfully reconciled these differences to result in collective agnostic optimization of first-order, second-order, and drug-drug interaction terms of the PRS equation (1) that resulted in optimized treatment responses for all rats, despite subject-specific drug antagonism. In effect, the method 100 successfully uncovered the foundation for why population-averaged drug administration results in low response rates, and actionably overcame this barrier to mediate optimized multi-drug treatment.

Results

Calibration: 1/4 Maximum tolerated dose regimen (1/4 MTDR) and individually optimized regimen (IOR)

In this study, a rat model (Crl: NIH-Foxn1 ^rnu, Charles River) was used to test a new antitumor regimen (AGCH: Cisplatin, Adriamycin, Herceptin, and Gemcitabine) to treat CRC. Each rat was inoculated subcutaneously at the rear right flank with HT-29 colon cancer cells (1 × 10 ⁶) in 0.1 mL of PBS. The tumor size served as the primary efficacy indicator.

Based on the MTDs obtained from the literature (Table 1) , the 1/4 MTD regimen was developed by combining the 1/4 MTD of each of the 4 drugs. The 1/4 MTD regimen was as follows: cisplatin, 1.5 mg/kg; adriamycin, 1.5 mg/kg; herceptin, 82.7 mg/kg; and gemcitabine, 30.0 mg/kg. The IOR was determined using PRS technology for each rat according to the protocol described in the materials and methods section. The weight and dosing level of each rat in IOR group are listed in Table 2.

The study included 2 groups of rats. The 3 rats in the control group (C1-C3) were treated with the same volume (0.1 mL) of phosphate-buffered saline (PBS) . The 5 rats in the individually optimized regimen (IOR) group (IOR1-IOR5) were treated by 1/4 MTD doses for each drug in the morning of day 1 and day 7. The 5 rats were treated by IOR in the morning of

day

14 and 24. The tumor sizes were measured in the afternoon of every day (Figure 9) .

Individually Optimized Regimens (IOR) markedly enhance tumor treatment response

The normalized tumor size is the tumor size of a rat measured at a specific day of interest divided by the tumor size at day 0 (Table 2) . To provide more insight into the high degree of variability in PBS treatment response between rats C1-C3 during the 30-day treatment period that subsequently required management by PRS, tumor response normalized to the tumor size of each rat at day 0 were plotted (Figure 4a) . During days 0-3, the tumor response increased in a linear fashion with time. During days 3-9, tumor experienced regress (C1) and slow response (C2 and C3) . From days 9-30, tumors of rats C1 and rats C2 have linearly response rate. Rat C3 had much faster tumor response rate after day 9 and started to fizzle on day 18.

The normalized tumor sizes of rats IOR1-5 and the average response of the control group were plotted (Figure 4b) . These rats also exhibited highly diverse responses while under treatment with 1/4 MTD regimens. During days 0-3, tumor response increased in a linear fashion. During days 3-9, as previously observed with rats C1-3, tumor response exhibited an unsteady/high variable state, where tumor response occurred between days 3-5, and regression was clearly observed for rats IOR1, IOR2, and IOR4 between days 5-9 (Figure 4b) . During days 9-13, tumor responses resumed with an average normalized tumor response rate of 0.0276/day (SD=0.0183) . Among the five rats, only rat IOR4 had a clearly favorable response to the 1/4 MTD regimen (Figure 4d) . A waterfall plot was analyzed to demonstrate the variability in each subject’s response to 1/4 MTD treatment, and the resulting use of the IOR regimen to optimize the time-dependent, dose-dependent, and subject-specific responses to treatment efficacy (Figure 4c) . In the waterfall figure, the normalized averaged tumor size of the control group was used as the reference. In this plot, IOR administration results in a substantial increase in efficacy.

It is widely recognized that combination chemotherapy results in highly variable treatment outcomes between patients and response rates of ～25%. The inability to pinpoint optimized doses in the combination to accommodate genetics related human heterogeneity and patient-specific physiological responses to therapy combination results in implicitly suboptimal treatment efficacy and could be the reason for low response rate under 1/4 MTD treatment (Figure 4d) . Among the 5 rats, the response rates of

Rat

3 and 5 are close to that of the control group (green dash line) . Only IOR4 has the best response rate. Remarkably, upon IOR implementation, the derived optimal doses for each rat resulted in all IOR rats responding to treatment with all rats collapsing towards a uniform normalized tumor response rate (Figure 4e) . Furthermore, the rats uniformly converged towards the average tumor response rate of 0.00776/day (SD=0.00291) , which was similar to the response rate of IOR4, the best among all five rats under 1/4 MTD treatment (Figure 4f) . The averaged tumor response rate of the IOR group from day 14 to day 30 was about 13.5%of the tumor response rate of the control group from day 9 to day 30 (Figure 4a and 4f) .

Dynamic Responses of the Phenotypic Response Surface (PRS)

To demonstrate how dose ratios can substantially affect the subject-specific nature at any given time during treatment, PRS drug interaction surfaces based on the prospective treatment of the IOR cohort were plotted. For a 4-drug regimen, 6 drug-drug interaction surfaces are created, with the horizontal axes showing the drug doses and the vertical axis representing the normalized tumor size. As such, the PRS visualizes tumor size variations as they correlate with drug doses based on experimental validation, not estimation or prediction. Importantly, this plot implicitly represents the integration of disease mechanisms (e.g. genomics, proteomics, transcriptomes, etc. ) as well as physiology and drug behavior for a specific subject. The PRS plots continuously varied during the three days following 1/4 MTD regimen administrations on day 7. These surfaces can change rapidly during treatment and PRS-mediated identification of these surfaces as they undergo dynamic changes during the course enables continuous optimization during the course of treatment.

The PRS plots for each of the 5 IOR rats at day 13 are shown, with the yellow markers denoting the IOR that administrated on day 14 (Figure 5) . From these surfaces, the PRSs of Rat, 1, 2 and 4 are different but have similar patterns. However, the PRSs of Rat 3 are similar to those of

Rat

1, 2 and 4, but adriamycin-cisplatin interaction is different from that of

Rat

1, 2 and 4. Rat 5 have different patterns from that of the other 4 rats. The tumor response rates of

Rat

3, 5 are higher than the response rates of the other three rats in IOR group (Figure 4d) .

Linear, quadratic, and drug-drug interaction terms of the PRS equation (1)

The phenotypic outputs were obtained based on the PRS platform by optimizing the drug and dose inputs according to Equation 1, with one coefficient, x ₀, and 14 terms for a 4-drug combination. Not all of the terms contribute to tumor response at all the time, and the drug-drug interactions terms can be either synergistic or antagonistic. However, all of these terms must be considered in order to achieve global optimization, and at least 15 experimental assays are required to solve for these terms. In experimental terms, this means that predictive analysis (e.g. drug-drug interactions) cannot substitute experimental validation. Most importantly, PRS can guide the search of the IOR doses of the drugs and eventually lead the intricate balances of 15 terms to the most desired tumor responses for all the tested subjects. Using method 100 to identify this set of 15 coefficients and terms is the foundation of deterministic optimization during the dynamic treatment regimen.

Each term in Equation 1 consists of a coefficient multiplied by the concentrations c _i, c _i ², or c _ic _j. The dose of each drug is an independent variable and could be freely adjusted during the course of the study. The values of coefficients x _i, y _ii, and z _ij reflect the changes in the phenotypic outputs (e.g. tumor size) , which are a function of subject genomics, proteomics and metabolomics, and other –omics mechanisms, as well as drug-physiology interactions (Table 3) . Hence, these coefficients are cross-correlated and dependent on time and the physiological conditions of each test subject. Terms associated with c _i are contributed by the linear drug effects on tumor response. Terms associated with c _i ² are contributed by the quadratic drug effects on tumor response. Terms associated with c _ic _j are contributed by the drug-drug interaction (synergistic or antagonistic) effects on tumor response. The actual increase or decrease in tumor size is associated with the sum of all 15 products of coefficients and concentrations. Therefore, synergism and antagonism, which are often represented by drug-drug interactions, constitute only a portion of the factors that impact tumor response.

The drug-drug interactions that dictate synergism and antagonism are time- dependent

By integrating each term in Eq. 1 from day 0 to day 13 and normalizing to the tumor size at day 0, the sum is the normalized tumor size at day 13. From day 0 to day 13, rats IOR1-IOR5 were given the 1/4 MTD regimen. The dynamic behavior of the drug-drug interaction terms and their impact on tumor size were analyzed for day 7 to day 13 (Figure 6) . Day 7 was the second treatment of 1/4 MTD regimen. The synergism or antagonism between two drugs depends on multiple factors including the specific subject being treated. For the drug-drug interaction term, if the value is negative and will reduce the tumor size, representing drug synergy. If the value is positive, these 2 drugs will be antagonistic. For the same rat, the drug-drug interactions are not all synergetic (negative values) or all antagonistic (positive values) . The magnitudes of the drug-drug interactions became pronounced except IOR 3 after day 9. The tumor response rate of each rat from day 9 to day 13 was almost constant (Figure 3d) .

Tumor response contributed by the linear, quadratic, and drug-drug interaction terms

All 15 terms of IOR1 (Figure 7a) , IOR2 (Figure 7b) , IOR3 (Figure 7c) , IOR4 (Figure 7d) , and IOR5 (Figure 7e) , are plotted where i = 1, 2, 3, and 4 for adriamycin, gemcitabine, cisplatin, and herceptin, respectively. All 15 PRS terms are either positive or negative, with similar magnitudes, so that the predictive analysis only based on drug-drug interaction terms cannot give a correct population-wide estimation of the resulting efficacy and or toxicity. At day 13, the linear terms have no contributions to the tumor response. Taking z ₁₂ as an example, a negative reading indicates synergism between

drugs

1 and 2 at day 13 for rat IOR1 (Figure 7a) . Conversely, z ₁₂ is antagonistic in IOR5 (Figure 7e) . Furthermore, the patterns of the 15 PRS terms (coefficients multiplied by the drug doses) of IOR1, 2, 3, and 4 are similar. The signs of these terms of IOR5 are opposite to those in other rats. The PRS analysis of terms revealed the substantial variability in the contribution of their combinations towards tumor treatment response between the subjects. Nonetheless, augmented AI-PRS implementation agnostically minimized the sum of all 15 terms to optimize efficacy across all subjects.

Tumor response contributed by the sums of linear, quadratic and drug-drug interaction terms

The sum of the linear, quadratic, and drug-drug interaction terms for each rat was plotted (Figure 8) . Prior to day 14, the rats were treated by 1/4 MTD regimen. As previously established, the treatment response is governed by all 15 terms of the 4 drug combinatorial regimen. Substantial variability in the contribution of these terms towards tumor treatment response was observed for

days

6, and 7, for each subject. For example, the sum of the linear terms contributed more towards tumor treatment response during day 6 for IOR2, IOR3 and IOR5 compared to IOR1 and IOR4. Day 7 was the second treatment with 1/4 MTD regimen. After day 7, the tumor responses of all rats depend on the sum of the quadratic and drug-drug interaction terms. The signs of the sum of quadratic and drug-drug interactions terms are always opposite. The signs may switch between day 8 to day 10. Hence, the synergism and antagonism among drugs are dynamic and not a universal property of drug pairs. During day 11-13, the sum of drug-drug interaction terms of IOR1, IOR2, IOR3 and IOR4 are all negative (synergetic) . Only IOR 5 had antagonistic drug-drug interactions and also has the highest tumor response rate (Figure 4d) .

Safety study

To verify the safety of the IOR therapy approach used in this study, we investigated 2 important biomarkers, namely the blood neutrophil levels and the serum alanine aminotransferase (ALT) levels after IOR administration. After the third treatment (day 21) , the neutrophil levels increased significantly in the IOR compared to those in the control group. However, after the fourth treatment (day 31) , no significant differences were observed in the neutrophil levels of the two groups (Figure 11a) . Furthermore, the serum ALT levels were monitored after the third treatment to assess liver toxicity. The control and IOR showed similar variations in ALT levels (Figure 11b) . A correlation of the tumor size on day 21 normalized to day 13 with the serum ALT levels for the control and IOR cohorts further revealed no apparent toxicity of the AGCH combination (Figure 11c) . As such, the rats treated by IOR did not exhibit any apparent liver toxicity. The substantially reduced tumor sizes coupled with unimpaired liver function and absence of prolonged neutrophil level changes suggested that the IOR was simultaneously efficacious and well tolerated (Figure 11c) .

Methods

Rat model

Ten rats (Crl: NIH-Foxn1 ^rnu, Charles River) were randomly distributed into 2 groups, the control group (C1, C2, C3, C4, C5) and IOR group (IOR1, IOR2, IOR3, IOR4, IOR5, ) . Each rat was inoculated subcutaneously at the rear right flank with HT-29 colon cancer cells (1 × 10 ⁶) in 0.1 mL of PBS to induce tumor formation according to an established protocol. 3 weeks after tumor inoculation (designated as day 0) , C4 and C5 were removed from the study due to early mortality unrelated to treatment. Note: the nude rats were purchased from Charles Rivers and shipped overseas. After such a long travel with shipping stress, two of the immune incompetent rats were weak and died several days after arrival. The IOR group received 4 treatments on day1, day7, day14 and day 24 (Table 2) . On day 1 and day 7, the IOR group was treated with the 1/4 MTD regimen, which consisted of 1.5 mg/kg cisplatin, 1.5 mg/kg adriamycin, 82.7 mg/kg herceptin and 30.0 mg/kg gemcitabine (Sigma-Aldrich, Tables 1 and 2) . The data obtained from the rats in control group (solvent-containing group) were used as baseline/background reference for deduction. The data obtained from experimental rats subtracted the baseline reference will then use for further analysis. The tumor size was measured via optical Vernier. The tumor size and drug plasma concentration were measured in first 64 hours (Figure 12) and every day for the first seven days (Figure 13) . On day 14 and day 24, each rat in the IOR group was treated with the individually optimized regimen (IOR) , which was determined by the PRS platform with serum drug doses and tumor sizes measured from day 1 to day13 (IOR1 shown in Table 5) . The tumor sizes for all of the rats were continuously monitored until day 30 (Figures 3a and 3b) .

Individually optimized regimen (IOR) determined by PRS platform

According to the PRS equation (Equation 1) , a minimum of 15 tests with different drug–dose ratios were needed to determine the 15 coefficients. During the first 13 days, all of the 5 IOR rats were treated with the 1/4 MTD regimen. Based on the area under the cure of drug plasma levels and corresponding tumor sizes for each rat (Figure 13a-d) and the measured tumor sizes (Figure 13e) , 15 data sets were generated from the 13 day’s measurements with the help of interpolation, The information was used to determine the PRS coefficients for all IOR rats (Table 3) . After the coefficients of PRS equation being determined, the IOR doses administered on day 14 day 24 of the 5 rats that mediate optimal tumor response are listed (Table 2) . The tumor sizes of the IOR group were recorded until day 30 (Figure 3) .

The computer codes used to determine the coefficients of the quadratic algebraic equation for fitting the PRS surface are available in MATLAB.

Safety Study

Blood samples were collected in 10%heparin from the retro-orbital vein and diluted in an equal volume of PBS containing 0.5%bovine serum albumin (BSA) . Neutrophils were washed in PBS containing 0.5%BSA, counted, and re-suspended using an IDEXX ProCyte Dx hematology analyzer (IDEXX Laboratories Inc., Westbrook, ME, USA) , according to the manufacturer’s protocol (Figure 10) .

Statistical Analysis

The IOR cohort was statistically examined using nonlinear least-squares regression. Matlab ^TM software was applied to examine the statistics using the fitnlm function. The results of the statistical analysis of rat IOR4 were discussed and plotted in Figure 14. The computer codes used for the statistical analysis are available in MATLAB ^TM.

Table 1. Documented maximum tolerate doses for cisplatin, adriamycin, herceptin and gemcitabine

References

(1) http: //www. bdipharma. com/MSDS/Teva/Cisplatin_MSDS. pdf

(2) Cancer Chemother Pharmacol. 1999; 43 (1) : 1-7.

(3) http: //datasheets. scbt. com/sc-200923. pdf

(4) Proc Natl Acad Sci USA. 2006 Nov 7; 103 (45) : 16649-54.

(5) http: //www. gene. com/download/pdf/MSDS_herceptin_vials440mg. pdf

(6) http: //www. bdipharma. com/MSDS/Hospira/Gemcitabine%202-10. pdf

(7) Cancer Res. 2005 Oct 15; 65 (20) : 9510-6

Table 2. (a) Tumor size, CR and IOR for each IOR rat. (b) Weights of both control and IOR groups

(a)

(b)

Table 3. Optimized coefficients of 5 IOR rats at day14

Table 4. IOR dose and MTD dose

Table 5. Data sets interpolated from these 13 day’s measurements were applied to construct the PRS of IOR1 and determine the optimal individualized regimen for IOR1 on day 14.

It will be appreciated that many further modifications and permutations of various aspects of the described embodiments are possible. Accordingly, the described aspects are intended to embrace all such alterations, modifications, and variations that fall within the spirit and scope of the appended claims.

Throughout this specification and the claims which follow, unless the context requires otherwise, the word “comprise” , and variations such as “comprises” and “comprising” , will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps.

The reference in this specification to any prior publication (or information derived from it) , or to any matter which is known, is not, and should not be taken as an acknowledgment or admission or any form of suggestion that that prior publication (or information derived from it) or known matter forms part of the common general knowledge in the field of endeavour to which this specification relates.

Claims

A method of optimising a combination drug therapy comprising two or more drugs administrable to a subject, the method comprising:

receiving, by at least one processor, exposure data indicative of measurements of a sample of a subject to whom the two or more drugs have been administered at an initial dosing regimen, the measurements being of exposure levels of the two or more drugs at a plurality of time points;

receiving, by the at least one processor, response data indicative of measurements of a therapeutic outcome variable at the plurality of time points;

determining, using the at least one processor, from the response data and the exposure data, a response function that relates the therapeutic outcome to the exposure levels of the two or more drugs;

optimising, using the at least one processor, the response function with respect to the exposure levels to determine optimised exposure levels for the subject; and

generating, using the at least one processor, an optimised dosing regimen based on the optimised exposure levels.
A method according to claim 1, wherein the response function is a polynomial function of the exposure levels.
A method according to claim 2, wherein the response function is:

or a time-integrated version thereof, where R is the response data at time t, N is the number of drugs, and c _i (t) is the exposure level of drug i at time t.
A method according to any one of claims 1 to 3, wherein the exposure levels are blood serum concentrations, blood plasma concentrations, urine concentrations, hair concentrations, or saliva concentrations of the respective drugs.
A method according to any one of claims 1 to 4, wherein the exposure levels are varied by fewer than (M ²+3M+2) /2 sets of variations of drug doses of the initial dosing regimen, and preferably without varying drug doses of the initial dosing regimen.
A method according to any one of claims 1 to 5, further comprising treating the subject according to the optimised dosing regimen.
A system for optimising a combination drug therapy comprising two or more drugs administrable to a subject, the system comprising:

at least one processor; and

computer-readable storage having stored thereon instructions for causing the at least one processor to perform a method according to any one of claims 1 to 5.
A non-transitory computer-readable storage medium having instructions stored thereon for causing at least one processor to perform a method according to any one of claims 1 to 5.
A system for optimising a combination drug therapy comprising two or more drugs administrable to a subject, the system comprising:

a receiving unit that is configured to:

receive exposure data indicative of measurements of a sample of a subject to whom the two or more drugs have been administered at an initial dosing regimen, the measurements being of exposure levels of the two or more drugs at a plurality of time points; and

receive response data indicative of measurements of a therapeutic outcome variable at the plurality of time points; and an optimisation unit that is configured to:

determine, from the response data and the exposure data, a response function that relates the therapeutic outcome to the exposure levels of the two or more drugs;

optimise the response function with respect to the exposure levels to determine optimised exposure levels for the subject; and

generate an optimised dosing regimen based on the optimised exposure levels.
A system according to claim 9, wherein the response function is a polynomial function of the exposure levels.
A system according to claim 10, wherein the response function is:

or a time-integrated version thereof, where R is the response data at time t, N is the number of drugs, and c _i (t) is the exposure level of drug i at time t.
A system according to any one of claims 9 to 11, wherein the exposure levels are blood serum concentrations, blood plasma concentrations, urine concentrations, hair concentrations, or saliva concentrations of the respective drugs.
A method of optimising a combination drug therapy comprising two or more drugs administrable to a subject, the method comprising:

measuring, at a plurality of time points, exposure levels of the two or more drugs in a sample of a subject to whom the two or more drugs have been administered at an initial dosing regimen;

measuring a therapeutic outcome variable at the plurality of time points;

determining, from the measurements of the exposure levels and the therapeutic outcome variable, a response function that relates the therapeutic outcome variable to the exposure levels of the two or more drugs;

optimising the response function with respect to the exposure levels to determine optimised exposure levels for the subject; and

generating an optimised dosing regimen based on the optimised exposure levels.
A method according to claim 13, wherein the response function is a polynomial function of the exposure levels.
A method according to claim 14, wherein the response function is:

or a time-integrated version thereof, where R is the response data at time t, N is the number of drugs, and c _i (t) is the exposure level of drug i at time t.
A method according to any one of claims 13 to 15, wherein the exposure levels are blood serum concentrations, blood plasma concentrations, urine concentrations, hair concentrations, or saliva concentrations of the respective drugs.
A method according to any one of claims 13 to 16, wherein the exposure levels are varied by fewer than (M ²+3M+2) /2 sets of variations of drug doses of the initial dosing regimen, and preferably without varying drug doses of the initial dosing regimen.
A method according to any one of claims 13 to 17, further comprising treating the subject according to the optimised dosing regimen.