Optimization of personalized therapies for anticancer treatment

Abstract

Background: As today, there are hundreds of targeted therapies for the treatment of cancer, many of which have companion biomarkers that are in use to inform treatment decisions. If we would consider this whole arsenal of targeted therapies as a treatment option for every patient, very soon we will reach a scenario where each patient is positive for several markers suggesting their treatment with several targeted therapies. Given the documented side effects of anticancer drugs, it is clear that such a strategy is unfeasible.

Results: Here, we propose a strategy that optimizes the design of combinatorial therapies to achieve the best response rates with the minimal toxicity. In this methodology markers are assigned to drugs such that we achieve a high overall response rate while using personalized combinations of minimal size. We tested this methodology in an in silico cancer patient cohort, constructed from in vitro data for 714 cell lines and 138 drugs reported by the Sanger Institute. Our analysis indicates that, even in the context of personalized medicine, combinations of three or more drugs are required to achieve high response rates. Furthermore, patient-to-patient variations in pharmacokinetics have a significant impact in the overall response rate. A 10 fold increase in the pharmacokinetics variations resulted in a significant drop the overall response rate.

Conclusions: The design of optimal combinatorial therapy for anticancer treatment requires a transition from the one-drug/one-biomarker approach to global strategies that simultaneously assign makers to a catalog of drugs. The methodology reported here provides a framework to achieve this transition.

Figure 1

Optimization of personalized therapies. 1- We are given as input a set of patients, Boolean vectors reporting the markers status on each patient (X) and a set of drugs available for treatment. 2- A Boolean vector reporting the markers that will be used to inform treatment is specified for each drug (Y). 3- Drugs are suggested for the treatment of each patient using a drug-to-sample protocol depending on the sample and drug markers (f_j(X_i,Y_j)). In this example a drug is suggested for the treatment of a patient whenever they share at least one marker. 4- Finally, a sample protocol is used to specify the treatment to each patient (g). In this example the best treatment for each sample is selected. Finally, we optimize the marker assignments to drugs (Y_j), the drug-to-sample protocols (f_j(X_i,Y_j)) and the sample protocol (g) to obtain the maximum overall response rate, as represented in the figure by the arrow.

Figure 2

Boolean functions and operations among them. a) Boolean functions with one input. Functions with a dashed line are not considered because the output is independent of the input. b) Boolean functions with two inputs. Functions with a dashed line are not considered because the output is independent of at least one input. c) An example showing the removal of the right marker (B) from function (2,2), which can be either result into function (1,0) or (1,1). Since function (1,0) is excluded then the function (1,1) is always chosen. d) Same example but removing the left marker (A). e) All mappings from (2,b) to (1,b’) following removal of the right (B) marker. f) All mappings from (2,b) to (1,b’) following removal of the left marker. e) All mappings from (1,b) to (2,b’) following the addition of a marker. For simplicity, we have chosen the reverse of the right-marker removal (panel e) as the mapping for the marker addition.

Figure 3

Comparison between the imputed and reported logIC50 data. The solid line represents the case when the imputed and reported values coincide.

Figure 4

Convergence of the simulated-annealing algorithm for the in silico study. The overall response rate (as estimated with the by-marker approximation, O*) as a function of the number of initial conditions tried.

Figure 5

Predictions of the in silico study. Model predictions as a function of the maximum combination size allowed for two values of the pharmacokinetic variations parameter σ. a) The overall response rate. b) Number of drugs used for the treatment of at least one sample.

Figure 6

Pseudocode for the simulated-annealing algorithm. *This step is introduced to avoid the accumulation of markers in drugs that are not used for treatment.