Optimization of personalized therapies for anticancer treatment Alexei Vazquez The Cancer Institute of New Jersey.

Optimization of personalized therapies for

anticancer treatment

Alexei Vazquez

The Cancer Institute of New Jersey

Human cancers are heterogeneous

Meric-Bernstam, F. & Mills, G. B. (2012) Nat. Rev. Clin. Oncol. doi:10.1038/nrclinonc.2012.127

Beltran H et al (2012) Cancer Res

DNA-sequencing of aggressive prostate cancers

Human cancers are heterogeneous

Personalized cancer therapy

Meric-Bernstam F & Mills GB (2012) Nat Rev Clin Oncol

PersonalizedTherapy

Targeted therapies

Aggarwal S (2010) Nat Rev Drug Discov

Drug combinations are needed

Number of drugs

Ove

rall

resp

onse

rat

e (%

)

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)

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)

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

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

Drug-to-sample protocol

fj Boolean function with Kj=|Yj| inputs

Kj number of markers used to inform treatment with dug j

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

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

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

Add/remove marker

Change function(Kj,fj) (Kj,f’j)

Optimization

• 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

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

Case study: response-by-marker approximation

By-marker response probability:

Sample response probability, response-by-marker approx.

Case study: overall response rate

Response-by-marker approximation(for optimization)

Empirical(for validation)

• 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

Case study: convergence

Case study: ORR vs combination size

Case study: number of drugs vs combination size

Outlook

• Efficient algorithm, bounds

• Drug interactions and toxicity

• Constraints– Cost– Insurance coverage

• Bayesian formulation