# Algorithms for Drug Sensitivity Prediction
## 4 Predictive Models
### Integrated Functional and Genomic Characterization-Based Models
For two drugs \(d_{1}\) and \(d_{2}\), the biologically-motivated constraints can be described as:C1: If \(K(d_{1},S_{T})\preceq K(d_{2},S_{T})\), then \(R(d_{1})\leq R(d_{2})\) C2: If \(K(d_{1},S_{T})\succeq K(d_{2},S_{T})\), then \(R(d_{1})\geq R(d_{2})\)  
where \(\preceq\) denotes component-wise inequality. Note that the entries of \(K\) are in the normalized range of \([0,1]\). If any target \(T_{\xi}\) is a tumor suppressor (anti-oncogene), then \(K(d,T_{\xi})\) can be substituted by \(1-K(d,T_{\xi})\), and the same constraints C1 and C2 will apply. C1 essentially states that if inhibiting a number of oncogenic target proteins has blocked tumor proliferation signaling pathways, then inhibiting more oncogenic target proteins will not open any path that has already been blocked. C2 captures the fact that if a set of oncogenic target protein inhibitions is unsuccessful in blocking the paths of a circuit, then a reduced number of target protein inhibitions among the inhibiting oncogenic proteins cannot block all of the proliferation paths. Note that the oncogenic or tumor suppressor behavior of the targets for each tumor culture can be elucidated from an RNA interference (siRNA) screen [107]. The application of the constraints on the full set of drug targets \(S_{T}\) will be ineffective, as there will be few pairs of drugs that will satisfy the component-wise monotonic relationship. However, we can utilize the fact that cancers are often driven by smaller sets of drivers, and inhibiting a set of driver targets can result in reduced proliferation of the tumor. For a particular tumor, there can be multiple sets of such blocks that can reduce proliferation. Thus, a search for a smaller set \(S_{T_{0}}\) of \(T_{0}\) targets among the set \(S_{T}\) that will follow the constraints \(C_{1}\) and \(C_{2}\) can be constructed. The gene expression information can be used to remove oncogenic targets that are not expressed. To arrive at the optimal set of targets, a binarized target set has to be considered and a sequential floating forward search utilized for selecting the set \(S_{T_{0}}\)[32]. Once the set \(S_{T_{0}}\) is generated for the cell culture, the goal is to generate the prediction \(R(\tilde{D}_{N})\) where \(D_{N}\) denotes the target pattern for a new drug or drug combination. A search for the set of subset drugs \(b_{1},b_{2},\cdots,b_{s_{1}}\) from the training set that satisfies \(K(b_{i},S_{T_{0}})\preceq D_{N}\) for \(i\in\{1,2,\cdots,s_{1}\}\) is performed. Similarly, a search for the set of superset drugs \(p_{1},p_{2},\cdots,p_{s_{2}}\) from the training set that satisfies \(K(p_{i},S_{T_{0}})\succeq D_{N}\) for \(i\in\{1,2,\cdots,s_{2}\}\) is executed. Based on the biological constraints C1 and C2, the sensitivity \(R(\tilde{D}_{N})\) can be assumed to satisfy the following inequality:  
\[\max(R(b_{1}),R(b_{2}),\cdots,R(b_{s_{1}})\leq R(\tilde{D}_{N})\leq\min(R(p_{ 1}),R(p_{2}),\cdots,R(p_{s_{2}}) \tag{15}\]  
Subsequent enhancements to the modeling framework constituted (a) integration of genetic information in the prediction framework to remove false positive targets [31].