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