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