Quantitative scoring of differential drug sensitivity for individually optimized anticancer therapies

We developed a systematic algorithmic solution for quantitative drug sensitivity scoring (DSS), based on continuous modeling and integration of multiple dose-response relationships in high-throughput compound testing studies. Mathematical model estimation and continuous interpolation makes the scoring approach robust against sources of technical variability and widely applicable to various experimental settings, both in cancer cell line models and primary patient-derived cells. Here, we demonstrate its improved performance over other response parameters especially in a leukemia patient case study, where differential DSS between patient and control cells enabled identification of both cancer-selective drugs and drug-sensitive patient sub-groups, as well as dynamic monitoring of the response patterns and oncogenic driver signals during cancer progression and relapse in individual patient cells ex vivo. An open-source and easily extendable implementation of the DSS calculation is made freely available to support its tailored application to translating drug sensitivity testing results into clinically actionable treatment options.


DSS derivation and calculation
The area under the curve (AUC) is the area covered between the dose-response curve (Eq. 1) and the concentration x-axis. For analytic calculation of the AUC, we derived a closed-form exact solution for the definite integral of y over the selected concentration range from 1 to 2 : where the integral function of the dose-response can be analytically expressed as ( ) = ( − ) log 1 (1 + 10 ( − ) ) + . (Eq. ) By default, we start the integration from the concentration at which the drug-response curve crosses the minimum activity level (by default, = 10%, Supplemental Figure 1B; corresponds to A min in Figure 1C): In many high-throughput screening applications, the minimum response level is set to zero for each drug (i.e. = 0). In this special case, using Eqs. 2-4, the AUC takes the following analytic form: AUC = [ 2 − + log 1 (1 + 10 ( − 2 ) ) + log 1 (1 − ) ].
After subtracting from the integrated total AUC, the area below the minimum activity level, and then dividing the remaining difference by the maximal response area, we get the basic version of the drug sensitivity score (DSS), which is effectively a normalized version of standard AUC: .
Here, min and max are the minimum and maximum concentrations, respectively, at which the drug was screened (in a typical AML screen, for instance, min = 1 nM and max = 10,000 nM, and in the CCLE screens, min = 2.5 nM and max = 8000 nM). 3 To normalize the effect of maximal response at the highest drug concentration, especially when 2 = max (default option), which many times corresponds to off-target toxicity, the DSS was further divided by the logarithm of the top asymptote : To further emphasize those drugs that obtain their response area over a relatively wide dose window, as compared to drugs that show increased response only at the higher end of the concentration range, we further modified the score: We set DSS=0 in those cases where the estimated IC50 (parameter c) is at or beyond the maximum dose level tested max , since such drug responses are often associated with off target effects that most likely are clinically irrelevant.
With each version of the DSS-score, the differential drug sensitivity score (dDSS) is calculated by subtracting the average of the control DSSs from the patient DSS, in case one or several control samples are available (e.g. the healthy bone marrow samples in the AML application).

Ranking of putative addicted kinases
To identify selective kinase targets the individual AML samples may be addicted to, we compared the sample-specific dDSS response with the target profiles of 35 kinase inhibitors overlapping between our compound panel and the compounds whose specificity was biochemically profiled in a recent kinome-wide profiling study 2 . More specifically, for each kinase target k, we calculated Kinase Inhibition Sensitivity Score (KISS) by summing the dDSS values over those kinase inhibitors i that selectively target k: Here, i goes through all those kinase inhibitors that specifically target the kinase k and whose skewness shows significant positive selectivity (p < 0.05); is the number of kinase inhibitors shown to target the kinase k on the basis of the biochemical kinase inhibitor specificities 2 . These selective drug sensitivities were used to define a putative "kinaddictome" for each patient sample -the kinases that the individual leukemia cells are likely to be addicted to, and therefore could provide important therapeutically actionable targets. The kinase sub-networks for the samples were visualized using the Cytoscape network analysis software 3 . 4

Data clustering
To reveal similarities and differences in selective drug response over the samples, differential DSS response profiles for individual drugs and samples were grouped into functionally similar drug clusters using unsupervised hierarchical clustering technique, Ward's algorithm 4 . We used here the Spearman correlation coefficients as the similarity function in the clustering algorithm, because the rank-based correlation provided relatively robust and reproducible results between different runs. The evaluation of the activity score-based clustering results was carried out using external cluster evaluation procedures, where the external benchmark drug clusters correspond to the known mode of action (MoA) classes of the drugs, if available (Supplemental Table 1). More specifically, we first determined the DSS-based drug clusters by cutting branches off the hierarchical clustering dendrogram using the "dynamicTreeCut" library 5 . These drug partitions were then compared to the MoA drug classes, excluding MoA classes with less than three drugs.

Cluster evaluation
To measure the similarity between the established MoA classes and the DSS-based drug partitions, we used adjusted version of Rand index, where the expected agreement between two random partitions is calculated by means of the generalized hypergeometric distribution 6 . The adjusted Rand index lies between 0 and 1, where 0 indicates random drug clustering and 1 that the two partitions agree perfectly. The adjusted Rand index was calculated using the Rpackage "fossil" 7 . We further validated the hierarchical clustering results using two additional cluster evaluation measures. The Jaccard index measures the similarity between the two drug partitions by calculating the size of their intersection divided by the size of the union of the two drug partitions. An index of 1 means that one of the partitions lies completely within the other, and an index of 0 indicates that the datasets have no common drugs. With the Fowlkes-Mallows index, a higher value indicates a greater similarity between the two drug partitions, and for two unrelated partitions the index approaches zero as the number of drugs increases 8 .

Implementation
The DSS calculation and data analysis pipeline was implemented in R programming language (version R-2.14.1, http://www.r-project.org/). In addition to the specific R-packages mentioned above, the following packages or libraries were used in the implementation: "xlsx" for reading and writing Excel documents, "stringr" for handling character strings, "gplots" for plotting heatmaps and histograms, "beanplot" for plotting density plots, "hopach" for calculating distances between samples and drugs, "pROC", "ROCR", "caTools" and "verification" for the ROC analysis. The R-package and its source code implementing the DSS calculations are freely available at Google code website (https://dss-calculation.googlecode.com/svn/trunk/).
Correlation Diagonal       The cell lines highlighted in yellow were selected based on the multimodal DSS3 distribution, where these four lines were highly sensitive to labatinib Labatinib response Erlotinib response