Furthermore, we cannot exclude that for large c the simulated annealing algorithm gets trapped in local optima and that for the actual global optimal d does increases with increasing c. In any event this discrep ancy should motivate future work to obtain theoretical estimates for together d based on the patterns of correlations between the response rates and the ability of the simulating annealing algorithm to reach the global optimum. In Table 1 we report the effective drug catalog for the small pharmacokinetic variations case and maximum combination size c 3 drugs. In addition, we report whether those drugs were included in the catalogs for c 1 and 2, showing the percent of samples treated when included and otherwise.

Most drugs in the c 3 catalog are also in cluded in the c 1 and 2 catalogs, indicating that there is a core set of drugs that is relevant independent of the max imum combination size allowed. The percentage of sam ples treated with a given drug in the catalog increases from c 1 to 3. This effect can be explained by the fact that, as we allow combinations of more drugs, a drug can be in cluded in personalized combinations as a second or third choice. We note that in some instances the marker assigned to a drug coincides with what expected given the known drug target. For example, the marker TP53 wt is suggested to inform the treatment with nutlin 3a. This makes sense because nutlin 3a releases TP53 from the inhibition by its negative regulator MDM2 and the out come of nutlin 3a treatment is modulated by the TP53 status.

In another case, the marker BRAF V600E is assigned to the BRAF inhibitor PLX4720. The marker KRAS G12D is assigned to another BRAF inhibi tor, AZ628, which still makes sense because KRAS is just upstream of BRAF in the RAS/RAF/MAPK/ERK signal ing pathway. In another case, the marker ERBB2 0 and the Boolean func tion are assigned to the ERBB2/EGFR inhibitor BIBW2992, which again makes sense since ERBB2 inhibitors are expected to be more effective in the presence of ERBB2 amplifications. However, GSK-3 in most instances the rela tion between the assigned marker/Boolean function and the known target is not obvious. The best example is the assignment of a tissue type as a marker, rather than the status of the gene coding for the target or another gene in the same pathway. Conclusions We have proposed a methodology that optimizes the as signment of companion biomarkers to drugs to achieve the highest possible response rate with the minimal add to your list tox icity. The outcome of our methodology is an optimal drug catalog, the assignment of optimal biomarkers to each drug and a treatment decision protocol where a drug is used to treat a patient when the latter is positive for the drug companion biomarker.