We are also given as input a set of drugs that selleck chemical Volasertib are available for anticancer treatment. In the context of personalized medicine we would like to assign markers to a drug to identify the pa tient subpopulation with the best response rates. Again, to be precise, the marker assignment to each drug is represented by a barcode or Boolean vector Yj , where yjl 1 if marker l is used to inform the treat ment with drug j and 0 otherwise. A drug to sample protocol fj is used to inform the treatment options, where fj 1 indicates to consider drug j as a treat ment option for sample i and fj 0 otherwise. For ex ample, Figure 1 illustrates the protocol where fj 1 if the sample and the drug share a marker in common. Once the treatment options are determined for each sample, we then apply a patient protocol g to choose the personalized therapies for each patient.

For example, Figure 1 illustrates the protocol g indicating the treatment with the drug with highest expected response rate among the treatment options identified for each patient. Another possibil ity is to treat with the c drugs with the higher response rates among those suggested for each patient. The current approach to targeted therapies is to assign markers to drugs based either on the target for which the drug was developed or some preliminary study suggesting an increase response rate in patients having the marker. We take a more general approach where the markers are assigned to drugs to maximize the response rate to therapy.

To this end, we define the following optimization problem Find the drug marker assignments Yj, the drug to sample protocols fj and sample protocol g that maximize the over all response rate O. Response model To calculate O we require the probability GSK-3 that each pa tient responds to a drug when the drug is used as a sin gle agent and some quantification of drug interactions. In the simplest scenario where there are no drug interac tions, the probability Pi that a patient responds to is per sonalized therapy is given by the probability that it responds to at least one of the drugs on its personalized combination where eij 1 if drug j is included in the personalized ther apy of patient i and pij is the probability that patient i re sponds to drug j when the latter is used as a single agent.

When interactions are present we can improve on after adding correction terms accounting for two drug interactions and so on However, for most combinations we do not have a quan titative estimate of how these interactions definitely affect the re sponse rate. For the purpose of illustrating our methodology, we will use the non interacting drugs ap proximation in our simulations. Response by marker approximation In the clinical practice we cannot test the response of each cancer patient to each approved anticancer drug. However, we can estimate the response rate to a drug depending on the present/absence of the markers assigned to that drug.