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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 Human cancers are heterogeneous DNA-sequencing of aggressive prostate cancers Beltran H et al (2012) Cancer Res Personalized cancer therapy Personalized Therapy Meric-Bernstam F & Mills GB (2012) Nat Rev Clin Oncol Targeted therapies Aggarwal S (2010) Nat Rev Drug Discov Overall response rate (%) Drug combinations are needed Number of drugs Personalized cancer therapy: Input information Samples/markers Drugs/markers X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Xi Yi sample barcode drug barcode (supported by some empirical evidence, not necessarily optimal, e.g. Viagra) Drug-to-sample protocol Samples/markers X1 Drugs/markers fj(Xi,Yj) 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 Sample protocol Samples/markers Drugs/markers g X1 fj(Xi,Yj) Y1 X2 Y2 X3 Y3 X4 Y4 X5 g sample protocol e.g., Treat with the suggested drug with highest expected response Optimization Overall response rate (O) Samples/markers Drugs/markers g X1 fj(Xi,Yj) Y1 X2 Y2 X3 Y3 X4 Y4 X5 Find the drug marker assignments Yj, the drug-tosample protocols fj and sample protocol g that maximize the overall response rate O. Drug-to-sample protocol fj Boolean function with Kj=|Yj| inputs Kj number of markers used to inform treatment with dug j Sample protocol From clinical trials we can determine q0jk q1jk the probability that a patient responds to treatment with drug j given that the cancer does not harbor the marker k 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: 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 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 Optimization Add/remove marker Change function (Kj,fj) (Kj,f’j) Case study • 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 Probability density 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 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 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) Case study: Optimization with simulated annealing • 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 – Perform N Metropolis-Hastings steps – +, exit when =max 0=0 N=D =0.01, max=100 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