Optimization of personalized therapies for anticancer treatment
- Alexei Vazquez^{1}Email author
https://doi.org/10.1186/1752-0509-7-31
© Vazquez; licensee BioMed Central Ltd. 2013
Received: 3 July 2012
Accepted: 26 March 2013
Published: 12 April 2013
Abstract
Background
As today, there are hundreds of targeted therapies for the treatment of cancer, many of which have companion biomarkers that are in use to inform treatment decisions. If we would consider this whole arsenal of targeted therapies as a treatment option for every patient, very soon we will reach a scenario where each patient is positive for several markers suggesting their treatment with several targeted therapies. Given the documented side effects of anticancer drugs, it is clear that such a strategy is unfeasible.
Results
Here, we propose a strategy that optimizes the design of combinatorial therapies to achieve the best response rates with the minimal toxicity. In this methodology markers are assigned to drugs such that we achieve a high overall response rate while using personalized combinations of minimal size. We tested this methodology in an in silico cancer patient cohort, constructed from in vitro data for 714 cell lines and 138 drugs reported by the Sanger Institute. Our analysis indicates that, even in the context of personalized medicine, combinations of three or more drugs are required to achieve high response rates. Furthermore, patient-to-patient variations in pharmacokinetics have a significant impact in the overall response rate. A 10 fold increase in the pharmacokinetics variations resulted in a significant drop the overall response rate.
Conclusions
The design of optimal combinatorial therapy for anticancer treatment requires a transition from the one-drug/one-biomarker approach to global strategies that simultaneously assign makers to a catalog of drugs. The methodology reported here provides a framework to achieve this transition.
Keywords
Cancer Personalized medicine Targeted therapy Combinatorial therapyBackground
Personalized cancer therapy has been proposed as the next battle in the war on cancer and targeted therapies as the new warfare machinery [1]. Targeted therapies are designed to treat cancers carrying specific molecular alterations. In turn these molecular alterations can be used as companion biomarkers to inform the decision of using, or not using, the targeted therapy to treat a patient [2]. For example, in the context of breast cancer, the level of the receptor tyrosine kinase HER2/neu is used to select trastuzumab (Herceptin; Genentech) as adjuvant therapy [3].
By design, a targeted therapy is expected to be effective in a subset of cancer patients (e.g., trastuzumab in HER2/neu positive breast cancer patients). However, even within this subset, the long-term response may be reduced. Some patients may initially respond to the targeted therapy but later on regress due to the occurrence of secondary molecular alterations. For example, in the context of melanoma, cancers with the BRAF(V600E) mutation can be treated with vemurafenib (Zelboraf, Plexxikon) resulting in outstanding response [4]. However, in about one year most patients regress due to upregulation of compensatory pathways [5, 6]. The molecular background of a cancer can also modulate the response to a targeted therapy, even when treatment is suggested by the biomarker. For example, as a difference with melanoma patients, colon cancer patients harbouring the same BRAF(V600E) mutation show a very limited response to vemurafenib [7]. One mechanism explaining this difference is the feedback activation of EGFR upon treatment with vemurafenib and the fact that EGFR levels are higher in colon cancer than in melamoma cells [8].
Although targeted therapies may fail as single agents, they can still be effective when used in combination with other agents. Combinatorial therapy is a rational approach to overcome the failure of single drugs [9]. One hypothesis is that one agent in the combination can cover for the caveats of other agents, increasing the response rate [10]. As for the case of single agents, biomarkers can be used to inform the inclusion of targeted therapies in a drug combination, which we name personalized combinatorial therapy.
The shift from single drug targeted therapy to combinatorial personalized therapies introduces a new challenge. As today, there are hundreds of targeted therapies with their associated biomarkers, some of which are already in use to inform treatment decisions. If we would consider the whole arsenal of targeted therapies as a treatment option for every patient, very soon we will reach a scenario where each patient is positive for several markers suggesting their treatment with several targeted therapies [11]. Given the documented side effects of anticancer drugs, it is clear that such a strategy is unfeasible. A new strategy is needed to optimize the design of combinatorial therapies to achieve the best respond rates with the minimal toxicity. In this work we introduce a methodology to achieve this goal.
Results and discussion
The current approach to targeted therapies is to assign markers to drugs based either on the target for which the drug was developed or some preliminary study suggesting an increase response rate in patients having the marker. We take a more general approach where the markers are assigned to drugs to maximize the response rate to therapy. To this end, we define the following optimization problem:
Find the drug marker assignments Y_{ j }, the drug-to-sample protocols f_{ j }and sample protocol g that maximize the overall response rate O.
Response model
In this equation values of J_{ jk }<0 will result in response rates higher than what expected if the drugs do not interact (synergy) while values of J_{ jk }>0 will result in response rates lower than what expected if the drugs do not interact (antagonism). We note that antagonism could take place at the level of pharmacodynamics (antagonism at the cellular level) or at the level of pharmacokinetics (antagonism at the drug metabolism level) and the latter may result in increased toxicity.
We are aware of documented examples of drug interactions in the context of cancer treatment [12]. However, for most combinations we do not have a quantitative estimate of how these interactions affect the response rate. For the purpose of illustrating our methodology, we will use the non-interacting drugs approximation (Eq. 1) in our simulations.
Response-by-marker approximation
In short, the probability that a given patient i responds to a given drug j is approximated by the estimated fraction of patients that responds to that drug within the group of patients having the same status as patient i for the markers assigned to drug j.
Finding the optimal personalized combinations
We need some procedure to find the optimal treatment combinations. In the Methods section we report a simulated annealing algorithm that performs an exploration of the space of markers assigned to drugs and drug-to-sample protocols with a gradual increased bias towards improvements on the overall response rate. Although this algorithm may not find the optimal solution, it can provide a good approximation to hard computational problems [13].
Updating the drug-to-sample protocols
During the optimization procedure we need to explore different marker assignments to drugs and different choices of drug-to-sample protocols. To this end we need some precise representation of the Boolean functions and the transformations among them. The drug-to-sample protocols are represented by a Boolean function f_{ j }(X_{ i },Y_{ j }) that returns 0 (do not suggest) or 1 (suggest) depending on the status of the markers assigned to the drug on a given sample. For computational convenience it is easier to write the Boolean functions as ${f}_{j}\left({X}_{i},{Y}_{j}\right)={f}_{j}\left({X}_{i{l}_{1}},\dots ,{X}_{i{l}_{{K}_{j}}}\right)$, where K_{ j } is the number of markers assigned to drug j, ${l}_{j1},\dots {l}_{{K}_{j}}$ is the list of markers assigned to drug j and f_{ j } is a Boolean function of K_{ j }inputs. Given K markers there are 2^{k} possible input states (x_{1},…,x_{k}), which can be enumerated as follows: $a\left(x\right)={\displaystyle \sum _{k=1}^{K}{x}_{k}{2}^{k-1}}$. For each of these input states we can set the output o_{ a }to 0 or 1. We can enumerate the Boolean functions with K inputs using the mapping $b\left(o\right)={\displaystyle \sum _{a=0}^{{2}^{K}-1}{o}_{a}{2}^{a-1}}$. Therefore, we can represent every Boolean function with two indexes (K,b), the first one denoting the number of inputs and the second one the specific Boolean function with K-inputs.
To explore different Boolean functions we change the function, add a new marker or remove one marker. When changing a Boolean function, (K,b)→(K,b’), a new function is selected at random among all considered Boolean functions with the same number of inputs. When removing a marker, (K,b)→(K-1,b’), if the drug has one marker then we remove it, the drug will have no markers assigned and, therefore, it will not be considered for the treatment of any patient. If the drug has two markers assigned then we remove one of the two markers and use the transformations illustrated in Figure 2c and d. For example, in Figure 2c we start with the function (2,2) and remove the B (right) input. For this function the output is always 0 when the A (left) input is 1 but the output can be 0 or 1 when the A input is 0. Therefore, (2,2) can be mapped to (1,0) or (1,1) after removing the B input. Since the output of (1,0) is independent of the input state it is not considered. A similar reasoning can be applied to obtain the mappings for function (2,2) when removing the A marker instead (Figure 2d). Applying this approach to every (2,b) function we obtain the mappings in Figure 2e and f. Finally, if a marker is added, (K,b)→(K+1,b’), then we use the mappings in Figure 2g, which are the reverse of (K-1,b’)→(K,b) removing the A (left) input. In all cases, when more that one choice is available we choose one of them with equal probability.
Case study
For each cell line the cancer subtype and the status of 47 cancer related genes was also reported, including somatic mutations and copy number alterations. We use as markers the observation of a specific cancer type (e.g., breast cancer), somatic mutations (e.g., TP53:wild-type, TP53:R175H, TP53:R248Q, etc.), and copy number alterations (gene:-, gene:0, gene:+ for deletion, normal and amplification, respectively). This procedure resulted in 921 markers. Among those, we retained 181 markers that are observed in at least 10 cell lines.
To each cell line we associate a sample that is fully composed of that cell line. We assume that different drugs are used at different treatment doses because they are active at different concentration ranges. The mean logIC50 of a drug across cancer cell lines is a good estimate of the typical concentration for the drug activity in this in vitro setting. Thus, for each drug we set the treatment log-concentration y_{ j }=mean(logIC50)_{ j }+logh, where h represents the fold change in the dose. Values of h below 1 represent low dose therapy, while those above 1 represent high dose therapy. In average, cancer cells have IC50s that are about 2 fold lower than those of normal cells [15]. Based on this we assume that the highest tolerated dose is h=2, and that is the dose used for treatment.
We assume that due to variations in drug delivery the actual log-dose reaching the cancer cells, denoted by Z_{ j }, is different from y_{ j }. Pharmacokinetic variables generally follow a normal distribution after a log-transformation [16] and, therefore, we assume that Z_{ j }(the log-dose) is a random variable following a normal distribution, with mean y_{ j }and variance σ. Here σ models variations associated with drug pharmacokinetics in patients. Pharmacokinetic parameters characterizing the steady state plasma drug concentrations and drug clearance rates can vary as much as 2–10 fold [17, 18]. To model such variations we will use σ=1,10.
where erfc(x) is the complementary error function. When the cell line logIC50_{ ij } is much higher than the treatment dose reaching the cancer cells (logIC50_{ ij }-y_{ j }>>σ) then p_{ ij }≈0. In contrast, when the cell line logIC50_{ ij }is much lower than the treatment dose reaching the cancer cells (logIC50_{ ij }-y_{ j }<<σ) then p_{ ij }≈1.
To test a more realistic scenario, we are not going to use the response probabilities in (Eq. 6). Instead, we are going to use the response by-marker approximation in (Eq. 5). To this end, given a drug and its assigned markers, we divide the cell lines into groups depending on the status of those markers, and estimate the response probability of q(j,s) as the average of p_{ ij }over all cell lines in that group. To avoid biases from small group sizes, we set q(j,s)=0 for any group with less than 10 samples.
We do not have an estimate of the possible interactions between the 138 drugs in this in silico study. We assume that the drugs do not interact and we approximate the response to a personalized drug combination by (Eq. 1), but replacing p_{ ij } by the response by-marker approximation (Eq. 5).
In the optimization problem defined above we could attempt to optimize the marker assignments to drugs, the drug-to-sample protocols f_{ j }(X_{ i },Y_{ j }) and the sample protocol g. However, to reduce the computational complexity of the problem, we will impose the sample protocol g_{best,c}, assign at most two markers to each drug and optimize over marker assignments to drugs and the drug-to-sample protocols.
We note that in this study we count with the actual response probability of each cell line to each drug. Therefore, we can use as input the optimal personalized combinations obtained by using the response by-marker approximation (Eq. 5) and then calculate the overall response rate using the original cell line response rates (Eq. 6).
We note that not all drugs are included in the treatment of at least one sample, resulting in a smaller effective drug catalog (Figure 5b). For all the maximum combination sizes tested, less than 80 out of 138 (58%) of the drugs are needed. Furthermore, beyond personalized combinations of three drugs, we observe a decrease in the number of needed drugs as we increased the maximum allowed combination size (Figure 5b). This observation suggests that the need for only 58% of the drugs will hold for larger combination sizes. We note that the decrease of the needed drugs is unexpected. For example, if the response rates were independent identically distributed random variables then the probability that a drug is selected for the treatment of a samples is c/d, the probability that a drug is selected for the treatment of at least one sample is 1-(1-c/d)^{s} and the average number of drugs used for the treatment of at least one sample is d* = d[1 − (1 − c/d)^{ s }]. Therefore, for independent identically distributed response rates d* increases monotonically with increased the combination size c. The departure from this expectation in Figure 5b could be due to the existence of correlations in the response rates of different drugs when treating different cells lines. Furthermore, we cannot exclude that for large c the simulated-annealing algorithm gets trapped in local optima and that for the actual global optimal d* does increases with increasing c. In any event this discrepancy should motivate future work to obtain theoretical estimates for d* based on the patterns of correlations between the response rates and the ability of the simulating-annealing algorithm to reach the global optimum.
The catalog of drugs in the optimized personalized combinatorial therapies
% of samples treated | K | f | Markers | Target | |||
---|---|---|---|---|---|---|---|
c | 1 | 2 | 3 | 3 | 3 | 3 | 3 |
Embelin | 0.7 | 5.9 | 31.5 | 2 | 13 | lung: small_cell_carcinoma,TP53:wt | XIAP |
Nutlin-3a | 4.1 | 8.0 | 24.5 | 2 | 11 | TP53:wt,RB1:wt | MDM2 |
Bicalutamide | 1.3 | 3.9 | 21.4 | 2 | 11 | ALK:wt,KRAS:0 | Androgen receptor (ANDR) |
XMD8-85 | 1.0 | 5.7 | 19.5 | 2 | 9 | CDKN2A:wt,malignant_melanoma | ERK5 (MK07) |
Shikonin | 1.7 | 1.7 | 11.8 | 1 | 2 | TP53:wt | unknown |
NVP-BEZ235 | 0.6 | - | 8.0 | 2 | 4 | PTEN:wt,EZH2:wt | PI3K (Class 1) and mTORC1/2 |
CI-1040 | 1.8 | 3.8 | 7.6 | 2 | 6 | malignant_melanoma,TP53:p.R273H | MEK1/2 |
EHT 1864 | 1.1 | 3.5 | 7.1 | 1 | 2 | lung: small_cell_carcinoma | Rac GTPases |
BMS-754807 | - | 4.1 | 7.0 | 2 | 14 | neuroblastoma,KRAS:p.G12V | IGF1R |
PLX4720 | 0.8 | 3.5 | 6.9 | 2 | 13 | BRAF:p.V600E,MSH2:wt | BRAF |
BX-795 | 0.7 | 5.7 | 6.3 | 2 | 14 | glioma,KRAS:+ | TBK1, PDK1, IKK, AURKB/C |
AKT inhibitor VIII | 2.4 | 5.6 | 6.3 | 2 | 9 | lung: NSCLC: adenocarcinoma,EGFR:wt | AKT1/2 |
AZD6482 | 3.8 | 6.2 | 6.3 | 1 | 2 | glioma | PI3Kb (P3C2B) |
RDEA119 | 3.9 | 7.4 | 6.0 | 2 | 13 | malignant_melanoma,BRCA1:0 | MEK1/2 |
MS-275 | 4.9 | 5.9 | 5.9 | 2 | 6 | lung: small_cell_carcinoma,RB1:wt | HDAC |
BI-D1870 | 0.7 | 1.7 | 5.3 | 2 | 14 | CCND1:0,MYCN:0 | RSK1/2/3/5, PLK1, AURKB |
MG-132 | 1.4 | - | 5.2 | 1 | 2 | glioma | Proteasome |
FH535 | 1.5 | 3.6 | 5.0 | 2 | 14 | breast,CCND1:+ | unknown |
Docetaxel | 2.8 | 1.3 | 4.6 | 2 | 9 | upper_aerodigestive_tract,EGFR:wt | Microtubules |
CGP-60474 | - | 2.8 | 4.3 | 1 | 2 | CDKN2a(p14):p.? | CDK1/2/5/7/9 |
AS601245 | 1.7 | 2.5 | 4.2 | 2 | 7 | ovary,osteosarcoma | JNK |
NVP-TAE684 | 1.5 | 3.8 | 4.2 | 1 | 1 | APC:wt,stomach | ALK |
Epothilone B | 1.3 | 1.4 | 4.1 | 2 | 7 | PIK3CA:p.E545K,TP53:p.R248W | Microtubules |
Camptothecin | 2.9 | 3.8 | 4.1 | 2 | 7 | AML,lymphoblastic T cell leukaemia | TOP1 |
Vorinostat | 4.1 | 5.7 | 4.1 | 1 | 2 | MYCN:+ | HDAC inhibitor Class I, IIa, IIb, IV |
A-443654 | 1.4 | 3.6 | 4.1 | 1 | 1 | SMAD4:wt | AKT1/2/3 |
PD-0325901 | 1.1 | 2.1 | 3.9 | 2 | 11 | large_intestine,VHL:0 | MEK1/2 |
RO-3306 | 1.5 | 3.2 | 3.9 | 2 | 11 | cervix,MYCL1:0 | CDK1 |
17-AAG | 2.2 | 2.2 | 3.8 | 2 | 6 | STK11:wt,MET:0 | HSP90 |
S-Trityl-L-cysteine | 1.1 | 3.5 | 3.8 | 1 | 1 | FBXW7:wt | KIF11 |
ZM-447439 | 0.1 | 1.3 | 3.6 | 2 | 7 | lung: NSCLC: large cell,RB1:- | AURKB |
Vinblastine | 1.4 | 2.2 | 3.2 | 2 | 13 | upper_aerodigestive_tract,IDH1:0 | Microtubules |
Paclitaxel | 0.1 | 2.5 | 3.2 | 2 | 11 | oesophagus,TSC1:wt | Microtubules |
AICAR | 0.6 | 1.7 | 2.9 | 1 | 1 | KDM6A:wt | AMPK agonist |
BIBW2992 | 1.4 | 2.2 | 2.9 | 1 | 1 | ERBB2:0 | EGFR, ERBB2 |
JNK-9L | - | - | 2.7 | 1 | 2 | AML | JNK |
BAY 61-3606 | 1.0 | 2.1 | 2.7 | 1 | 2 | Ewings sarcoma | SYK |
AMG-706 | - | - | 2.7 | 1 | 2 | Ewings sarcoma | VEGFR, RET, c-KIT, PDGFR |
AZ628 | - | 2.2 | 2.5 | 2 | 9 | KRAS:p.G12D,FGFR3:0 | BRAF |
BMS-536924 | - | 1.1 | 2.5 | 2 | 7 | KRAS:+,MDM2:+ | IGF1R |
JW-7-52-1 | 1.1 | 1.7 | 2.5 | 1 | 2 | stomach | MTOR |
Elesclomol | 1.0 | 3.5 | 2.4 | 2 | 8 | bladder,TSC1:wt | HSP70 |
Pyrimethamine | 0.8 | 3.5 | 2.4 | 1 | 2 | pancreas | Dihydrofolate reductase (DHFR) |
KIN001-135 | 0.3 | 0.7 | 2.2 | 1 | 1 | MET:+ | IKKE |
Dasatinib | - | - | 2.0 | 2 | 13 | Renal cell carcinoma,NRAS:0 | ABL, SRC, KIT, PDGFR |
ABT-888 | 1.5 | 2.5 | 1.7 | 2 | 11 | lymphoid_neoplasm other,CDK4:0 | PARP1/2 |
BI-2536 | 2.9 | 3.1 | 1.7 | 2 | 2 | CDKN2A:p.0?,MYC:0 | PLK1/2/3 |
IPA-3 | - | - | 1.7 | 1 | 2 | B cell lymphoma | PAK |
WO2009093972 | 1.5 | 2.0 | 1.7 | 1 | 2 | soft tissue other | PI3Kb |
Methotrexate | 1.7 | 4.2 | 1.5 | 2 | 8 | lymphoblastic leukemia,GNAS:wt | Dihydrofolate reductase (DHFR) |
Roscovitine | 0.1 | 3.1 | 1.5 | 1 | 2 | Burkitt lymphoma | CDKs |
FTI-277 | 1.4 | 1.4 | 1.5 | 1 | 2 | thyroid | Farnesyl transferase (FNTA) |
PAC-1 | 1.5 | 1.5 | 1.5 | 1 | 2 | Burkitt lymphoma | CASP3 activator |
CCT018159 | 1.3 | 3.5 | 1.4 | 2 | 14 | osteosarcoma,PTEN:0 | HSP90 |
PF-4708671 | 0.7 | 0.8 | 1.4 | 2 | 13 | Myeloma,BRCA1:wt | p70 S6KA |
TW 37 | 0.8 | 1.1 | 1.4 | 2 | 6 | MLH1:wt,APC:0 | BCL-2, BCL-XL |
MK-2206 | 1.3 | 1.4 | 1.4 | 1 | 2 | endometrium | AKT1/2 |
JNK Inhibitor VIII | - | - | 0.3 | 1 | 2 | AML | JNK |
Obatoclax Mesylate | - | - | 0.1 | 2 | 2 | RB1:-,CDK6:+ | BCL-2, BCL-XL, MCL-1 |
We note that in some instances the marker assigned to a drug coincides with what expected given the known drug target (Table 1, Markers and Target columns). For example, the marker TP53:wt (i.e., TP53 wild-type) is suggested to inform the treatment with nutlin-3a. This makes sense because nutlin-3a releases TP53 from the inhibition by its negative regulator MDM2 and the outcome of nutlin-3a treatment is modulated by the TP53 status [19]. In another case, the marker BRAF:V600E is assigned to the BRAF inhibitor PLX4720 [20]. The marker KRAS:G12D is assigned to another BRAF inhibitor, AZ628, which still makes sense because KRAS is just upstream of BRAF in the RAS/RAF/MAPK/ERK signaling pathway [21]. In another case, the marker ERBB2:0 (i.e., normal ERBB2 copy number) and the Boolean function (1,1) (i.e., suggest in the absence of the marker) are assigned to the ERBB2/EGFR inhibitor BIBW2992, which again makes sense since ERBB2 inhibitors are expected to be more effective in the presence of ERBB2 amplifications [22]. However, in most instances the relation between the assigned marker/Boolean-function and the known target is not obvious. The best example is the assignment of a tissue type as a marker, rather than the status of the gene coding for the target or another gene in the same pathway.
Conclusions
We have proposed a methodology that optimizes the assignment of companion biomarkers to drugs to achieve the highest possible response rate with the minimal toxicity. The outcome of our methodology is an optimal drug catalog, the assignment of optimal biomarkers to each drug and a treatment decision protocol where a drug is used to treat a patient when the latter is positive for the drug companion biomarker. The application of the treatment decision protocol for every drug in the catalog results in optimal personalized combinatorial therapies for every patient.
An interest future direction is the investigation of the impact of drug interactions. We expect that the optimization approach will favor drugs that synergize with many other drugs in the catalog relative to those that do not interact or antagonize with other drugs in the catalog. At the end, the interplay between manifesting a high response rate in a group of patients and the degree of synergy (or absence of antagonism) with other drugs in the catalog will determine the suitability of a given drug for its use in personalized combinations. The challenge will be to estimate of the degree of synergy/antagonism between current anticancer drugs.
Our methodology is entirely based on estimated response rates given a marker. The latter can be estimated from clinical trails testing each anticancer drug as a single agent, where all patients enrolled are tested for a set of predefined biomarkers. Using this information we can estimate the overall response rate given a marker, for each of the markers considered. In second step, we should select a cohort of patients where the status of all these biomarkers has been determined. This cohort could be, in principle, the union of all cohorts where the drugs were tested as single agents. Using the mutation status of each gene and the estimated response rates given a marker we can estimate the response rate of each patient in an approximate manner. With those estimates at hand we can then apply the methodology introduced here and make a prediction for the optimal drug catalog, the assignment of optimal biomarkers to each drug and a treatment decision protocol where a drug is used to treat a patient when it is positive for the drug marker. Finally, the predicted personalized combinatorial therapy should be tested in a two arms clinical trial to determine how it performs compared to the standard of care.
The optimization scheme introduced here can be generalized in several directions. We can improve the response rate calculation including drug interactions, provided the direction and the magnitude of those interactions is given. Our approach is also suitable for the inclusion of genetic markers affecting drug metabolism [2]. These markers can be included in the optimization scheme as well, provided we specify a model for their impact on the response rate. Further generalizations are also needed to model toxicity. However, these generalizations will result in more complicated models with more parameters, many of which will be difficult to quantify. In the mean time, the simplifications introduced here allow us to implement the personalized combinatorial therapies approach in the clinical context, by routinely sequence a subset of genes on each patient enrolled in clinical trials.
Methods
Simulated annealing algorithm
In our simulations we have chosen the parameters T=10,000d, dt=d, β_{0}=0 and d β=0.01.
The simulated-annealing algorithm can get trapped in drug marker assignments that are suboptimal. To overcome this limitation we repeat the algorithm several times and report the solution with minimum c. We did not observe significant changes from a 100 to a 1,000 repetitions. The results discussed below are obtained for 1,000 repetitions.
IC50 imputation
is the Euclidean distance between drugs based on the available data. The exploration of the parameters (α_{ sample }, α_{ drug }) in the range (1–22,1-22) resulted in Pearson Correlation Coefficients (PCCs) between imputed and actual logIC50s, when available, in the range 0.83-0.89, with a maximum of 0.89 for (α_{ sample } = 20, α_{ drug } = 3).
Author contribution
AV conceived, executed and wrote this work.
Declarations
Authors’ Affiliations
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