The patients are divided into 2Kj groups de pending on the status of those markers. We can conduct a clinical trial to estimate the newsletter subscribe response rate q of drug j for each group of patients. Once the q are known, we can estimate the response rate to any patient. To be more precise we enumerate the patient groups using the index where lj1 . ��. ljKj is the list of markers assigned to drug j and xl is the status of the l th marker. Using this nota tion we obtain the response by marker approximation In short, the probability that a given patient i responds to a given drug j is approximated by the estimated frac tion of patients that responds to that drug within the group of patients having the same status as patient i for the markers assigned to drug j.

In this equation values of Jjk 0 will result in response rates higher than what expected if the drugs do not interact while values of Jjk 0 will result in re sponse rates lower than what expected if the drugs do not interact. We note that antagonism could take place at the level of pharmacodynamics or at the level of pharma cokinetics and the latter may result in increased toxicity. The average of Pi across samples defines the overall response rate O of the personalized combinatorial therapies We are aware of documented examples of drug inter actions in the context of cancer treatment. Finding the optimal personalized combinations We need some procedure to find the optimal treatment combinations. In the Methods section we report a simu lated annealing algorithm that performs an exploration of the space of markers assigned Cilengitide to drugs and drug to sample protocols with a gradual increased bias towards improvements on the overall response rate.

Although this algorithm may not find the optimal solution, it can provide a good approximation to hard computational problems. Updating the drug to sample protocols During the optimization procedure we need to explore different marker assignments to drugs and different choices of drug to sample protocols. To this end we need some precise www.selleckchem.com/products/ganetespib-sta-9090.html representation of the Boolean func tions and the transformations among them. The drug to sample protocols are represented by a Boolean function fj that returns 0 or 1 de pending on the status of the markers assigned to the drug on a given sample. For computational convenience it is easier to write the Boolean functions as f j Xi. Y j ? f j Xil1 . ��. XilKj, where Kj is the number of markers assigned to drug j, lj1. ��lKj is the list of markers assigned to drug j and fj is a Boolean function of Kj inputs. Given K markers there are 2k possible input states, which of these input states we can set the output oa to 0 or 1. We can enumerate the Boolean functions with K inputs K using the mapping beoT ? oa2a?1.