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Optimization of personalized therapies for
anticancer treatment
Alexei Vazquez
The Cancer Institute of New Jersey
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Human cancers are heterogeneous
Meric-Bernstam, F. & Mills, G. B. (2012) Nat. Rev. Clin. Oncol. doi:10.1038/nrclinonc.2012.127
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Beltran H et al (2012) Cancer Res
DNA-sequencing of aggressive prostate cancers
Human cancers are heterogeneous
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Personalized cancer therapy
Meric-Bernstam F & Mills GB (2012) Nat Rev Clin Oncol
PersonalizedTherapy
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Targeted therapies
Aggarwal S (2010) Nat Rev Drug Discov
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Drug combinations are needed
Number of drugs
Ove
rall
resp
onse
rat
e (%
)
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Y1
Y2
Y3
Y4
X1
X2
X3
X4
X5
Samples/markers Drugs/markers
Personalized cancer therapy: Input information
Xi sample barcodeYi drug barcode(supported by some empirical evidence,
not necessarily optimal, e.g. Viagra)
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Y1
Y2
Y3
Y4
X1
X2
X3
X4
X5
fj(Xi,Yj) drug-to-sample protocol
e.g., suggest if the sample and the drug have a common marker
Samples/markers Drugs/markers
Drug-to-sample protocol
fj(Xi,Yj)
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Y1
Y2
Y3
Y4
X1
X2
X3
X4
X5
Samples/markers Drugs/markers
Sample protocol
g sample protocol
e.g., Treat with the suggested drug with highest expected response
fj(Xi,Yj)g
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Y1
Y2
Y3
Y4
X1
X2
X3
X4
X5
Samples/markers Drugs/markers
Optimization
Find the drug marker assignments Yj, the drug-to-sample protocols fj and sample protocol g that maximize the overall response rate O.
Ove
rall
resp
onse
rat
e (O
)
fj(Xi,Yj)g
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Drug-to-sample protocol
fj Boolean function with Kj=|Yj| inputs
Kj number of markers used to inform treatment with dug j
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From clinical trials we can determine
q0jk the probability that a patient responds to treatment with drug j given that the cancer does not harbor the marker k
q1jk the probability that a patient responds to treatment with drug j given that the cancer harbors the marker k
Estimate the probability that a cancer i responds to a drug j as the mean of qljk over the markers assigned to drug j, taking into account the status of those markers in cancer i
Sample protocol
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Sample protocol: one possible choice
Specify a maximum drug combination size c
For each sample, choose the c suggested drugs with the highest expected response (personalized drug combination)
More precisely, given a sample i, a list of di suggested drugs, and the expected probabilities of respose p*ij
Sort the suggested drugs in decreasing order of p*ij
Select the first Ci=max(di,c) drugs
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Overall response ratenon-interacting drugs approximation
In the absence of drug-interactions, the probability that a sample responds to its personalized drug combination is given by the probability that the sample responds to at least one drug in the combination
Overall response rate
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Add/remove marker
Change function(Kj,fj) (Kj,f’j)
Optimization
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• S=714 cancer cell lines• M*=921 markers (cancer type, mutations,
deletions, amplifications). • M=181 markers present in at least 10 samples• D=138 drugs
• IC50ij, drug concentration of drug j that is needed to inhibit the growth of cell line i 50% relative to untreated controls
• Data from the Sanger Institute: Genomics of Drug Sensitivity in Cancer
Case study
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Case study: empirical probability of response: pij
Drug concentration reaching the cancer cells
Drug concentration to achieve response(IC50ij)
Pro
bab
ility
de
nsi
tyTreatment drug concentration(fixed for each drug)
pij probability that the concentration of drug j reaching the cancer cells of type i is below the drug concentration required for response
models drug metabolismvariations in the humanpopulation
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Case study: response-by-marker approximation
By-marker response probability:
Sample response probability, response-by-marker approx.
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Case study: overall response rate
Response-by-marker approximation(for optimization)
Empirical(for validation)
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• Kj=0,1,2• Metropolis-Hastings step
– Select a rule from (add marker, remove marker, change function)
– Select a drug consistent with that rule– Update its Boolean function– Accept the change with probability
• Annealing– Start with =0 0=0– Perform N Metropolis-Hastings steps N=D +, exit when =max =0.01, max=100
Case study: Optimization with simulated annealing
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Case study: convergence
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Case study: ORR vs combination size
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Case study: number of drugs vs combination size
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Outlook
• Efficient algorithm, bounds
• Drug interactions and toxicity
• Constraints– Cost– Insurance coverage
• Bayesian formulation