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: /nrclinonc

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 Personalized Therapy

Targeted therapies Aggarwal S (2010) Nat Rev Drug Discov

Drug combinations are needed Number of drugs Overall response rate (%)

Y1Y1 Y2Y2 Y3Y3 Y4Y4 X1X1 X2X2 X3X3 X4X4 X5X5 Samples/markersDrugs/markers Personalized cancer therapy: Input information X i sample barcode Y i drug barcode(supported by some empirical evidence, not necessarily optimal, e.g. Viagra)

Y1Y1 Y2Y2 Y3Y3 Y4Y4 X1X1 X2X2 X3X3 X4X4 X5X5 f j (X i,Y j ) drug-to-sample protocol e.g., suggest if the sample and the drug have a common marker Samples/markersDrugs/markers Drug-to-sample protocol fj(Xi,Yj)fj(Xi,Yj)

Y1Y1 Y2Y2 Y3Y3 Y4Y4 X1X1 X2X2 X3X3 X4X4 X5X5 Samples/markersDrugs/markers Sample protocol g sample protocol e.g., Treat with the suggested drug with highest expected response fj(Xi,Yj)fj(Xi,Yj) g

Y1Y1 Y2Y2 Y3Y3 Y4Y4 X1X1 X2X2 X3X3 X4X4 X5X5 Samples/markersDrugs/markers Optimization 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. Overall response rate (O) fj(Xi,Yj)fj(Xi,Yj) g

Drug-to-sample protocol f j Boolean function with K j =|Y j | inputs K j number of markers used to inform treatment with dug j

From clinical trials we can determine q 0jk the probability that a patient responds to treatment with drug j given that the cancer does not harbor the marker k q 1jk 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 q ljk 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 d i suggested drugs, and the expected probabilities of respose p* ij Sort the suggested drugs in decreasing order of p* ij Select the first C i =max(d i,c) drugs

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

Add/remove marker Change function (Kj,fj)(Kj,fj) (K j,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 IC50 ij, 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: p ij Drug concentration reaching the cancer cells  Drug concentration to achieve response ( IC50 ij ) Probability density Treatment drug concentration (fixed for each drug) p ij probability that the concentration of drug j reaching the cancer cells of type i is below the drug concentration required for response  models drug metabolism variations in the human population

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)

K j =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