Optimization of personalized therapies for anticancer treatment

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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. doi10.1038/nrclinonc.2012.127
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Human cancers are heterogeneous
DNA-sequencing of aggressive prostate cancers
Beltran H et al (2012) Cancer Res
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Personalized cancer therapy
Personalized Therapy
Meric-Bernstam F Mills GB (2012) Nat Rev Clin
Oncol
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Targeted therapies
Aggarwal S (2010) Nat Rev Drug Discov
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Drug combinations are needed
Overall response rate ()
Number of drugs
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Personalized cancer therapy Input information
Samples/markers
Drugs/markers
X1
Y1
X2
Y2
X3
Y3
X4
Y4
X5
Xi sample barcode Yi drug barcode (supported by
some empirical evidence, not necessarily
optimal, e.g. Viagra)
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Drug-to-sample protocol
Samples/markers
Drugs/markers
fj(Xi,Yj)
X1
Y1
X2
Y2
X3
Y3
X4
Y4
X5
fj(Xi,Yj) drug-to-sample protocol e.g., suggest
if the sample and the drug have a common marker
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Sample protocol
Samples/markers
Drugs/markers
g
fj(Xi,Yj)
X1
Y1
X2
Y2
X3
Y3
X4
Y4
X5
g sample protocol e.g., Treat with the suggested
drug with highest expected response
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Optimization
Samples/markers
Drugs/markers
g
fj(Xi,Yj)
X1
Y1
X2
Y2
Overall response rate (O)
X3
Y3
X4
Y4
X5
Find the drug marker assignments Yj, the
drug-to-sample protocols fj and sample protocol g
that maximize the overall response rate O.
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Drug-to-sample protocol
fj Boolean function with KjYj inputs
Kj number of markers used to inform treatment
with dug j
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Sample protocol
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
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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 pij Sort the
suggested drugs in decreasing order of
pij Select the first Cimax(di,c) drugs
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Overall response rate non-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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Optimization
Add/remove marker
Change function
(Kj,fj)
(Kj,fj)
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Case study

• S714 cancer cell lines
• M921 markers (cancer type, mutations,
  deletions, amplifications).
• M181 markers present in at least 10 samples
• D138 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

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Case study empirical probability of response pij
Drug concentration to achieve response (IC50ij)
Treatment drug concentration (fixed for each drug)
? models drug metabolism variations in the
human population
Probability density
?
Drug concentration reaching the cancer cells
pij probability that the concentration of drug j
reaching the cancer cells of type i is below the
drug concentration required for response
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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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Case study Optimization with simulated annealing

• Kj0,1,2
• 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 ?00
• Perform N Metropolis-Hastings steps ND
• ?????, exit when ??max ??0.01, ?max100

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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