iFad: an integrative factor analysis model for drug-pathway association inference^†

Abstract

Motivation: Pathway-based drug discovery considers the therapeutic effects of compounds in the global physiological environment. This approach has been gaining popularity in recent years because the target pathways and mechanism of action for many compounds are still unknown, and there are also some unexpected off-target effects. Therefore, the inference of drug-pathway associations is a crucial step to fully realize the potential of system-based pharmacological research. Transcriptome data offer valuable information on drug-pathway targets because the pathway activities may be reflected through gene expression levels. Hence, it is of great interest to jointly analyze the drug sensitivity and gene expression data from the same set of samples to investigate the gene-pathway–drug-pathway associations.

Results: We have developed iFad, a Bayesian sparse factor analysis model to jointly analyze the paired gene expression and drug sensitivity datasets measured across the same panel of samples. The model enables direct incorporation of prior knowledge regarding gene-pathway and/or drug-pathway associations to aid the discovery of new association relationships. We use a collapsed Gibbs sampling algorithm for inference. Satisfactory performance of the proposed model was found for both simulated datasets and real data collected on the NCI-60 cell lines. Our results suggest that iFad is a promising approach for the identification of drug targets. This model also provides a general statistical framework for pathway-based integrative analysis of other types of -omics data.

Availability: The R package ‘iFad’ and real NCI-60 dataset used are available at http://bioinformatics.med.yale.edu/group/.

Contact: hongyu.zhao@yale.edu

Supplementary Information: Supplementary data are available at Bioinformatics online.

1 INTRODUCTION

Identification of drug targets, the gene products that bind to specific therapeutic molecules, is essential for understanding drugs' action mechanism and possible side effects, and for maximizing treatment efficacy and minimizing drug toxicity. Traditional pharmaceutical research and development process is deeply rooted in the ‘one target-one drug’ mindset, which tries to interfere the pathological process through blocking an important molecular player (e.g. a specific enzyme) using a compound. Unfortunately, most drug candidates identified through high-throughput screening based on this philosophy have failed due to either poor efficacy or serious side effects (Schadt et al., 2009).

High hope has been placed on using systems biology for drug discovery through the application of novel computational methods to high-throughput genomics and proteomics data. In contrast to the traditional ‘one target-one drug’ perspective that ignores the intricate interaction among genes/proteins, systems biology approaches consider the drug effects in the global physiological environment. They may be more effective in drug discoveries because it has become apparent that most common diseases result from system-level malfunctions rather than problems with individual genes (Pujol et al., 2010). In practice, drug combination or poly-pharmacy is more commonly used in recent years to modulate multiple drug targets.

Existing computational methods for drug-target identification can be generally categorized into three classes. The first class of methods uses the classical gene expression profiling strategies to infer drug targets. For example, drug targets can be identified by comparing the mRNA responses in human cell lines induced by drugs with unknown mechanisms with a set of well understood drugs. The connectivity map project (Lamb et al., 2006) used a non-parametric rank-based pattern matching strategy based on the Kolmogorov–Smirnov statistic, which requires extensive data mining procedures. Another study (Kutalik et al., 2008) proposed a bi-clustering method, named iterative signature algorithm (ISA), to search for ‘co-modules’ representing gene–drug associations.

The second class of methods aims to integrate various types of biological data, including knowledge about bioactive molecules and their protein targets (e.g. sequences, structures and molecular mechanisms) along with the phenotypic effects of drug treatment, to deduce the probability of two proteins being bound by the same ligand (Czodrowski et al., 2009; Ecker et al., 2008; Nigsch et al., 2009). Drug docking studies have also been incorporated to measure the binding probabilities based on 3D structural complementarities (Boyce et al., 2009; Irwin et al., 2009; Kolb et al., 2009; Zavodszky and Kuhn, 2005). One disadvantage of these methods is that they only evaluate the likelihood of presumed drug-target pairs and make no inference of unknown drug targets. Campillos et al. (2008) proposed a probabilistic network to calculate the probability of two drugs sharing the same target by comparing their clinical side effects. However, this method provides limited information on the drug action mechanisms.

The third class of methods analyzes the global patterns of drug–protein interactions (Kuhn et al., 2008; Yeh et al., 2006; Yildirim et al., 2007). It is known that established gene–drug binary associations form a dense network that exhibits local clustering of similar drug types. Such networks can enhance our understanding of the physiological effects of various drugs in terms of the molecular pathways and disease categories involved. However, these ‘guilt-by-association’ methods are too coarse-grained to make quantitative inference about the effect of drugs at the system level.

In this article, we develop a coherent statistical framework to jointly analyze drug sensitivity and gene expression patterns from the same set of cell lines to infer the target pathways of drugs. Much information on these two types of data has been accumulated in the literature (Bussey et al., 2006; Ikediobi et al., 2006; Shankavaram et al., 2007; Sharma et al., 2010; Shoemaker, 2006), and if appropriately analyzed, these data may be informative for inferring drug targets. We adopt a latent factor analysis approach, where each latent factor corresponds to the activity of a specific pathway. Note that factor analysis models have been proposed for the reconstruction of gene regulatory networks and the inference of transcription factor activity profiles (Gharib et al., 2006; Meng et al., 2011; Yeh et al., 2009; Yu and Li, 2005). A previous review article (Pournara and Wernisch, 2007) compared the performance of five different factor analysis algorithms. However, these models were developed for the analysis of a single data type, i.e. gene expression data. In contrast, our proposed Bayesian sparse factor analysis model, iFad (integrative factor analysis for drug-pathway association inference), is the first effort to bring together two distinct data types in a unified framework to identify drug-target pathways. We propose and implement a modified collapsed Gibbs sampling algorithm for model inference. Our approach can also easily incorporate known pathway information to infer the ‘many-to-many’ correspondence between the two types of data. Some unique features of our model are (1) joint analysis of distinct data types; (2) a Bayesian framework to integrate prior pathway knowledge and (3) explicit consideration of the sparse nature of the drug-target pathways. Both simulation studies and applications to real NCI-60 datasets show that iFad is a promising approach for drug-target inference.

The rest of the article is organized as follows. We detail the modeling assumptions and statistical inferential procedure in Section 2. Simulations and real data analysis are described in Section 3. We conclude the article in Section 4.

2 METHODS

2.1 Model description

This section describes the statistical framework of our proposed Bayesian sparse factor analysis model, iFad and statistical inference of the model parameters. As discussed above, iFad aims to analyze paired gene expression data and drug sensitivity data generated from the same set of samples. We denote the gene expression dataset by matrix Y₁, with dimension G₁ by J, where G₁ is the number of genes and J is the sample size. The drug sensitivity dataset is denoted by matrix Y₂, with dimension G₂ by J, where G₂ is the number of drugs. Drug sensitivity is usually quantified as the ‘GI₅₀’ values, concentrations required to inhibit growth by 50% (Staunton et al., 2001). Matrices Y₁ and Y₂ are normalized (scaled to mean 0 and SD 1 for each gene/drug) before analysis.

iFad links the two matrices through the activity levels of K biological pathways (e.g. KEGG pathways), which are latent factors in our model. The rationale here is that pathway activities influence both gene expression levels and the sensitivity to drugs targeting these in these pathways. We assume that there is some prior knowledge about the gene-pathway and drug-pathway association relationships, represented by two binary matrices L₁ and L₂, with dimensions G₁ by K and G₂ by K, respectively, where L₁[g, k]=1 (or L₂[g, k]=1) indicates that the gth gene (or drug) is known to be associated with the kth pathway. This information can be retrieved from various pathway databases with different degrees of sensitivity and specificity (Bader et al., 2006; Kanehisa et al., 2010). iFad assumes that both matrices Y₁ and Y₂ are related to the common underlying pathway activity matrix X (with dimension K by J) through the following linear models:

Matrices W₁ and W₂ are the factor loading matrices describing the regulatory direction (positive or negative) and strength of the pathway activities on the gene expression levels Y₁ and drug sensitivity Y₂. The latent factor activity matrix X is shared between the two feature spaces, namely gene expression data and drug sensitivity data. Each entry in matrix X is assumed to follow a standard normal distribution. Σ₁ and Σ₂ represent the noise term added to gene expression or drug sensitivity, with mean 0 and diagonal covariance matrices Ψ₁ and Ψ₂. The precision τ_g1 (for the g₁th gene) and τ_g2 (for the g₂th drug) are modeled using a Gamma prior with shape parameters α₁, α₂ and rate parameters β₁, β₂.

In order to use the prior knowledge on the gene-pathway and drug-pathway associations (matrices L₁ and L₂), we use the spike-and-slab mixture prior (West, 2003) for the factor loading matrices W₁ and W₂. Although there exist other forms of sparsity-inducing priors (Pournara and Wernisch, 2007), the spike-and-slab prior has the advantage of easy incorporation of prior information on the connectivity structure of the loading matrix. For both W₁ and W₂, we put the following prior on each entry:

where δ₀ is the unit point mass at zero (the Dirac delta function) and π_g,k denotes the prior probability that W_g,k is non−zero. If W_g,k is non-zero, it is assumed to follow a normal distribution with mean 0 and precision τ_w. The precision τ_w can be either set to a constant or assumed to follow a Gamma prior with parameter (α_w, β_w). Usually, an auxiliary indicator variable Z_g,k is used to enable the calculation of posterior probabilities (as Z₁, W₁, π₁, L₁ and Z₂, W₂, π₂, L₂ have very similar formats except the subscript, we just listed the general formula here):

In this way, prior link matrices L₁ and L₂ are used to induce the sparsity structure of the factor loading matrices W₁ and W₂ in a flexible way, with the strength of guidance tuned conveniently by user-specified parameters η₀ and η₁. Under this setting, we can derive the prior probability of different components of the model, as well as the complete joint posterior probability (see Supplementary Materials for details).

It is worth noting that during the simulation studies in Section 3.1, both matrices Z₁ and Z₂ are unknown and are the target of inference. In contrast, for real data analysis (the NCI-60 dataset) in Section 3.2, since prior information about gene-pathway association structure is available and fairly accurate, the major interest lies in the inference of matrix Z₂, the drug-pathway association relationships.

2.2 Inference algorithm

There are many parameters to estimate for iFad. Gibbs sampling is a widely used technique to approximate the joint distribution through re-sampling. However, standard Gibbs sampler may have poor mixing due to dependence between matrices W and Z makes. Therefore, we used a modified collapsed Gibbs sampling algorithm for model inference as outlined below. Detailed derivations of the posterior conditional distributions are provided in Supplementary Materials. At the end of each sampling iteration, we add a local permutation step (Sharp et al. 2010 to address the problem of label-switching, which is also described in Supplementary Materials. We have implemented the above algorithm as the R package ‘iFad’, which is publicly available on CRAN.

3 RESULTS

We first tested the performance of iFad using simulated datasets, and then applied the method to real NCI-60 datasets to infer unknown drug-pathway associations.

3.1 Simulation study

In order to assess the performance of our proposed model, we first simulated a series of datasets to investigate the effects of different model parameter settings, as well as the various dataset properties, including sample size and noise level, among other factors.

3.1.1 Data simulation for model parameter selection

We tested eight different settings for the Gamma density parameters related to the precision of the gene/drug noise term (τ_g1, τ_g2) and the factor loading matrix (τ_w1, τ_w2), as shown in Table 1.

Table 1.

Model parameter settings considered in the simulations

Setting	αg	βg	αw	βw
1	0.7	0.3	0.7	0.3
2	0.7	0.3	σw = 1
3	1	0.1	0.7	0.3
4	1	0.1	σw = 1
5	1	0.01	0.7	0.3
6	1	0.01	σw = 1
7	1	0.005	0.7	0.3
8	1	0.005	σw = 1

α_g and β_g are the shape and rate parameters of the Gamma prior put on the precision of the noise term for both matrices Y₁ and Y₂; α_w and β_w are Gamma parameters for the precision of the non-zero elements of the factor loading matrices W₁ and W₂.

Different Gamma parameters represent different prior belief regarding the distribution of the standard deviation for the noise term/the factor loadings. Figure 1 shows the histogram of 10 000 standard deviation values randomly generated from the Gamma density with four parameter combinations tested (only the values smaller than 3 are plotted here). We first simulated two sets of data to compare the eight combinations of parameter settings, with each dataset consisting of four matrices Y₁, Y₂, π₁ and π₂, as shown in Table 2. For both datasets, we used α_g=1, β_g=0.01 and σ_w=1. For Gibbs sampling, we set the number of iteration to 30 000, with the first half discarded as burn-in period (this was chosen based on the MCMC (Markov chain Monte Carlo) trace plot). To reduce the effect of auto-correlation between adjacent iterations and the data storage burden, we only recorded the Gibbs sampling results every other 10th iteration. We ran five independent chains for Set 1 and three independent chains for Set 2, to check the consistency among multiple independent runs.

Fig. 1.

Histograms of the standard deviations sampled from the Gamma densities with different parameter settings. Note that the Gamma prior is put on the precision τ and SD = 1/sqrt(τ)

Table 2.

Data simulation for choosing model parameters

Set	K	G1	G2	J	η0 and η1		Density
					π1	π2	L1	L2	Z1	Z2
1	18	50	50	20	0.2, 0.2	0.3, 0.1	0.316	0.167	0.394	0.38
2	15	100	50	20	0.2, 0.2	0.35, 0.05	0.05	0.0067	0.235	0.353

We used the Area Under Curve (AUC) statistic [area under the receiver-operating characteristic curve (ROC) curve] to assess the inference performance of iFad. For the retained Gibbs samples after the burn-in period, we calculate the mean of each entry of matrices Z₁ and Z₂, and the ROC curve and AUC values by choosing different cutoffs and comparing the results with the true matrices Z₁ and Z₂. The ‘ROCR’ package was used for this analysis.

For general factor analysis models, there is a scale identifiability problem associated with the loading matrix W and factor matrix X, as after integrating out the latent factors, the complete density of the observed data matrix Y is a normal distribution with covariance matrix WΣ_xW′+Ψ (Pournara and Wernisch, 2007). In order to avoid this issue, for data simulation, we set matrix Σ_x to the identity matrix. We then tested eight combinations of Gamma parameters (α_g, β_g, α_w, β_w; Table 1) on two simulated datasets (as described in Table 2). We then asked how the result would be affected if η₀ and η₁ used for inference are different from that used in simulation. Hence, we chose η₀=η₁=0.2 for matrix L₁, η₀=0.15, η₁=0.05 for matrix L₂ and tested the inference algorithm again on dataset 2, which is denoted as ‘Set 3’. The results are shown in Figure 2. The red lines are the proportion of entries in matrix Z that have the same value with matrix L, representing the accuracy of prior knowledge.

Fig. 2.

AUC result of eight parameter settings for two simulated datasets. Red line is the percentage of original matching between matrices L and Z

Comparing the AUC of eight parameter settings, it can be seen that σ_w=1 usually gives more consistent result among independent chains than putting a Gamma prior on τ_w. Nevertheless, it is obvious that α_g and β_g are the major factors here. Parameter setting 6 (α_g=1, β_g=0.01 and σ_w=1) gives best result in this comparison and is used for the remaining analysis in this article. For matrix L₂ in Set 3, η₀=0.35 during simulation but 0.15 during the Gibbs sampling. We checked the overlap of the inferred non-zero entries of matrix L₂ between Sets 2 and 3 (by using cutoff 0.5 to dichotomize the posterior mean for each entry). For all the eight parameter settings, the non-zero entries inferred using η₀=0.15 are almost always a subset of those inferred using η₀=0.35 (as shown in Supplementary Fig. S1).

3.1.2 Data simulation with various patterns for model performance evaluation

After determining the appropriate model parameters, we explored how different dataset properties (e.g. sample size, confidence in the prior link matrix L, density of matrix L/Z and noise level) may influence the performance and robustness of the iFad model. Therefore, we simulated five other groups of datasets to investigate the effects of η₀ and η₁, density of the connectivity matrix, imbalanced dimension between the two feature spaces (G₁ ≠ G₂), signal-to-noise ratio (SNR) and sample size (Table 3). Regarding the simulation, matrices L₁ and L₂ are randomly generated with specified density (proportion of non-zero entries). Matrices Z₁ and Z₂ are simulated based on L₁ and L₂ with Bernoulli probability specified by η₀ and η₁. The density of Z shown in Table 3 is the average value of Z₁ and Z₂. For the SNR (Group 4), the variance of each noise term (τ_g⁻¹) was calculated as τ_g⁻¹= Var (WX[g,])/SNR = K/SNR. Three independent chains were run for each dataset in Groups 1–4, with total iteration = 30 000 and the first half as burn-in. Gibbs samples were recorded every 10th iteration. AUC results are shown in Figure 3. For Group 5, the chain usually converges slower with sample size increasing, so we tried total iteration = 10 000 (burn-in = 8000), 60 000 (burn-in = 40 000) and 100 000 (burn-in = 70 000). The AUC is plotted in Figure 4.

Table 3.

Data simulations with different properties

Set	K	G1 and G2	J	η0 and η1	Density		αg, βg
					L	Z
Group 1: the effect of different η0 and η1
1	20	100	15	0.2	0.1	0.25	1, 0.01
2	20	100	15	0.4	0.1	0.41	1, 0.01
3	20	100	15	0.3	0.1	0.34	1, 0.01
4	Same data as Set3, but used η0 and η1=0.2 for Gibbs sampling
5	Same data as Set3, but used η0 and η1=0.4 for Gibbs sampling
Group 2: the effect of density of matrices L and Z
1	20	100	15	0.2	0.01	0.21	1, 0.01
2	20	100	15	0.2	0.1	0.25	1, 0.01
3	20	100	15	0.2	0.3	0.38	1, 0.01
4	20	100	50	0.2	0.5	0.51	1, 0.01
5	20	100	50	0.2	0.7	0.61	1, 0.01
Group 3: the effect of imbalanced datasets
1	20	100	15	0.2	0.1	0.25	1, 0.01
2	20	125, 75	15	0.2	0.1	0.26	1, 0.01
3	20	150, 50	15	0.2	0.1	0.26	1, 0.01
Group 4: the effect of SNR
							SNR
1	20	100	15	0.2	0.1	0.257	2.5
2	20	100	15	0.2	0.1	0.260	5
3	20	100	15	0.2	0.1	0.257	10
4	20	100	15	0.2	0.1	0.271	100
5	20	100	15	0.2	0.1	0.247	500
6	20	100	15	0.2	0.1	0.247	1000
Group 5: the effect of sample size
1	10	50	10	0.25	0.05	0.262	1, 0.01
2	10	50	30	0.25	0.05	0.251	1, 0.01
3	10	50	50	0.25	0.05	0.247	1, 0.01
4	10	50	70	0.25	0.05	0.244	1, 0.01

Fig. 3.

AUC result of simulated data, Groups 1–4

Fig. 4.

AUC result of simulated data, Group 5

From these five groups of comparisons, it can be observed that

1. When prior information about the connectivity structure matrices Z₁ and Z₂ is fairly accurate, for example, when η₀ and η₁≤0.3, the AUC statistics are very good (Group 1, Sets 1 and 3), even if the η₀ and η₁ used for the Gibbs sampling algorithm deviated from the true values (Group 1, Sets 4 and 5). However, when η₀ and η₁ are large (Group 1, Set 2), the inference results are not satisfactory.

2. iFad performs best when the density of matrices L and Z is around 0.1–0.3 (Group 2, Sets 2 and 3); too sparse (Group 2, Set 1) or too dense (Group 2, Sets 4 and 5) connectivity structure can hamper the inference result.

3. Imbalanced dimension of the two datasets does not influence the inference result of iFad. All datasets in Group 3 achieved very good AUC statistics.

4. The SNR has an important effect. A large SNR is desired for iFad to perform well (compare Group 4, Sets 1–3 with Sets 4–6).

5. When sample size J is smaller than the total number of latent factors K, iFad cannot make accurate inference no matter how long the chain is run (Group 5, Set 1). Nevertheless, J=30 seems to be adequate for datasets with K=10 and G₁=G₂=50 (Group 5, Set 2). Increasing sample size can improve the performance of iFad (compare Sets 3 and 4 with Set 2) but requires more iterations of the Gibbs sampling.

3.2 Application of iFad: analysis of NCI-60 datasets for drug-pathway association discovery

We then applied iFad to the joint analysis of gene expression and drug sensitivity profiles of the NCI-60 cell lines. The NCI-60 project represents a comprehensive resource for various types of ‘Omics’ characterization of 60 human cancer cell lines with nine different tissue types, including RNA expression, DNA fingerprinting, DNA methylation, sequence mutation, as well as treatment response to >100 000 compounds. The gene expression and drug sensitivity data were downloaded from the CellMiner database (Shankavaram et al., 2009), with URL http://discover.nci.nih.gov/cellminer. We used ‘RNA: Affy HG-U133 (A,B)’ (44 000 probeset 2-chip set, Guanine Cytosine Robust Multi-Array Analysis (GCRMA) normalization) and ‘Drug: A4463’ for analysis.

3.2.1 Gene data preprocessing

We only used the HG-U133A chip and converted probe expression to gene expression by taking the average of the probes mapped to the same gene, resulting in a total of 12 980 genes measured across 59 cell lines (expression data of the cell line ‘LC:NCI_H23’ was unavailable). The expression data were then standardized so that for each gene, mean = 0 and SD = 1 across the 59 cell lines. As we are mainly interested in the analysis of drug response-related genes, we only kept genes that are included in either of the following two lists: first, 766 cancer-related genes (Chen et al., 2008); second, 8919 genes from the Integrated Druggable Genome Database Project (Hopkins and Groom, 2002; Russ and Lampel, 2005), downloaded from http://www.sophicalliance.com/. After this filtering, 6958 genes were retained.

3.2.2 Drug data preprocessing

The drug data are the -log10(GI₅₀) values of Sulforhodamine assay for 4463 molecules (also known as the standard agents) that have known 2D structure and have been tested at-least two times. Higher values equate to higher sensitivity of cell lines. The data are also scaled so that mean = 0 and SD = 1 for each drug. Among these 4463 molecules, we only kept the 101 drugs annotated in the CancerResource database (Ahmed et al., 2011). Little information is available about the targets or mechanisms of action for the other drugs.

3.2.3 Pathway association information

Gene-pathway and drug-pathway association data were retrieved from the KEGG MEDICUS database (Kanehisa et al., 2010). The link is http://www.genome.jp/kegg/catalog/pathway_dd.html. We compiled a list of 58 pathways that are either known to be related to cancer or have drug targets. Among the 6958 genes selected in Section 3.2.1, 1863 genes are covered by these 58 pathways and constitute the final list of genes in our real data analysis. Therefore, matrix L₁ is a binary one with dimension 1863 × 58, and the dimension of matrix L₂ is 101 × 58.

Our research objective here is to infer unknown drug-pathway associations to help better understand the mechanism of action of less well-studied compounds. We treated the pathway activity levels as latent factors in the iFad model, the gene expression data as matrix Y₁ and drug sensitivity as matrix Y₂. We compiled a list of 58 pathways (Supplementary Table S1), 1863 genes and 101 drugs for analysis, as described earlier. Gene expression data are available for 59 cell lines, representing nine different cancer types (Supplementary Table S2). Since there are only two cell lines from prostate cancer, we excluded this panel, with eight cancer types remaining for study. iFad was applied to each type, respectively, instead of using all 57 cell lines altogether, in order to avoid potential problems arising from severe cell type heterogeneity (we checked for several well-known gene–drug correlations and found that the correlation coefficient is usually much more significant when calculated using cell lines of the same type, rather than all the 57 cell lines).

For the NCI-60 analysis, the total iteration was set to 100 000 and burn-in = 70 000. For model parameters, we set η₀=η₁=0 for matrix π₁, because of high confidence in the gene-pathway association information from KEGG. For matrix π₂, we set η₁=0 and tried η₀=0.05, 0.1, 0.15, 0.2, 0.25, in order to infer unknown drug-pathway associations for various densities of matrix Z₂. Based on prior knowledge from the KEGG database, matrix L₁ has a density of 3.95%, whereas L₂ has a density of 0.51%. Figure 5 shows the distribution of the number of genes/drugs associated with each pathway for matrix L₁/L₂.

Fig. 5.

Histogram of the number of genes or drugs known to be associated with the 58 KEGG pathways as a priori

We compared the distribution of the posterior means of the entries of matrix Z₂, inferred using different values of η₀, as shown in the histograms of Supplementary Figure S2 and the quantile plots in Supplementary Figure S3. As expected, with η₀ increasing, the distribution of the posterior mean of Z₂ shifts to the right. For η₀=0.05, the number of newly inferred non-zero entries in matrix Z₂ is shown in Table 4 based on various cutoffs.

Table 4.

Number of newly inferred non-zero entries in matrix Z₂ using η₀=0.05 and various posterior probability cutoff values

Cutoff	0.2	0.25	0.3	0.35	0.4	0.45	0.5
BR	248	181	129	99	73	48	39
CNS	203	119	86	59	39	26	21
CO	276	209	167	148	121	98	81
LC	321	238	192	157	123	102	94
LE	200	122	86	66	53	41	33
ME	339	280	204	169	139	118	99
OV	261	191	154	118	96	78	63
RE	287	208	172	142	119	101	81
Union	1685	1282	1016	838	684	563	476

We took a further look at the results obtained from cutoff = 0.3, because the posterior means of non-zero entries of matrix Z₂ can reach around 0.5 (for more details, see Supplementary Table S3) at this cutoff. Figure 6 shows the association pattern in the heatmap. It can be seen that the drug-pathway interaction pattern exhibits strong cell type specificity, demonstrating the importance of conducting the analysis by separating cell line groups rather than on the entire NCI-60 panel. Supplementary Figure S4 shows the total number of drug-pathway associations in barplots. Generally speaking, the cell lines of ‘non-small cell lung cancer’ and ‘melanoma’ discovered more novel drug-pathway associations, whereas ‘leukemia’, central nervous system (‘CNS’) and ‘breast cancer’ cell lines inferred fewer new associations. One possible explanation is the difference in sample size: there are nine cell lines for ‘non-small cell lung cancer’ and ‘melanoma’, but only six cell lines for ‘leukemia’, ‘CNS’ and ‘breast cancer’.

Fig. 6.

Heatmaps showing the inferred drug-pathway association patterns. The upper panel shows the posterior mean for each entry of matrix Z₂. The lower panel is the dichotomized value using cutoff = 0.3. Rows correspond to drugs and columns correspond to pathways

We then checked whether the newly inferred drug-pathway associations are supported by biological knowledge, based on the CancerResource database (Ahmed et al., 2011) and PubMed. We chose the CancerResource database as a reference because of its comprehensiveness: it integrates drug-target information from several well-known databases, including CTD (Davis et al., 2009), PharmGKB (Hernandez-Boussard et al., 2008), TTD (Zhu et al., 2011), DrugBank (Wishart et al., 2008), as well as its own literature mining. It is worth noting that the current catalog of drug-target information is still far from complete, and the absence of specific drug-pathway associations in one database does not exclude the possibility that the interaction actually exists. Herein, we checked the inferred drug-pathway interactions using cutoff = 0.9 (with the complete list provided in Supplementary Table S4) and found that many of these associations can be validated by the CancerResource database (Table 5). For the unconfirmed associations, we checked the database CTD and found several additional validations. For example, among the ‘colon cancer’ cell line panel, drug ‘daunorubicin’ is associated with pathway ‘endometrial cancer’ with a posterior probability of 0.9547. This association is not documented in the CancerResource database, but can be confirmed by CTD. Although some drug-pathway associations are significant in more than one cell line panels (e.g. ‘doxorubicin’ acts on the ‘thyroid cancer pathway’ in both renal and ovarian cancer cell lines), most associations are still context-specific, for instance, ‘chlorambucil’ is associated with ‘melanoma pathway’ mainly in melanoma cell lines, with a high posterior probability of 0.947. In contrast, this probability is much smaller in the other cell line panels (Figure 7).

Table 5.

Drug-pathway associations inferred using iFad which have been confirmed by the CancerResource database (cutoff = 0.9)

KEGG pathway	Drug	Posterior probability	Cell line panel
Glutathione metabolism	Vincristine	0.9987	LC
ErbB signaling pathway	Mitoxantrone	0.9937	LC
Thyroid cancer	Doxorubicin	0.991	RE
Glutathione metabolism	6-Mercaptopurine	0.9867	RE
Bladder cancer	Tamoxifen	0.982	LC
VEGF signaling pathway	Carmustine	0.9803	RE
Thyroid cancer	Doxorubicin	0.9713	OV
ErbB signaling pathway	Camptothecin	0.9583	LC
Bladder cancer	Edelfosine	0.958	LC
Bladder cancer	Chlorambucil	0.9473	RE
Melanoma	Chlorambucil	0.947	ME
VEGF signaling pathway	6-Mercaptopurine	0.932	ME
Bladder cancer	Geldanamycin	0.9273	CO
Thyroid cancer	Dactinomycin	0.9263	OV
Apoptosis	Thymidine	0.923	CO
Cell cycle	Tiazofurin	0.919	LC
Drug metabolism—other enzymes	Daunorubicin	0.9157	LC
VEGF signaling pathway	Lomustine	0.9103	RE
Focal adhesion	Geldanamycin	0.91	BR
Endometrial cancer	Doxorubicin	0.909	CO
VEGF signaling pathway	Quinacrine	0.9023	RE
Base excision repair	Decitabine	0.9017	LC

BR, breast; CNS, central nervous system; CO, colon; LC, non-small cell lung cancer; LE, leukemia; ME, melanoma; OV, ovarian; RE, renal.

Fig. 7.

Cell line specificity of the ‘chlorambucil’—‘melanoma pathway’ association

We further investigated the loading matrices W₁ and W₂ for the ‘melanoma pathway’. Since there may be sign-flip during the Gibbs sampling iterations, we calculated the posterior mean of the absolute value for each entry of matrices W₁ and W₂ after the burn-in period. Figure 8 shows the heatmap of the estimated loadings of factor ‘melanoma pathway’ on its associated 63 genes (the left part) and on the 101 drugs (the right part). It can be clearly observed that when the analysis is applied to the ME panel, the factor ‘melanoma pathway’ has significant loadings on several drugs; however, these drug-pathway associations are much less evident when the analysis was performed on the other cell line types.

Fig. 8.

Posterior mean of the absolute value of matrices W₁ and W₂ (only showing the result corresponding to the ‘melanoma pathway’) for the NCI-60 data analysis, plotted by each cell line panel

4 DISCUSSION

Drug-target identification is one important problem in translational bioinformatics, as well as a crucial step in the early stage of drug discovery and development. Although there exist many different high-throughput technologies for molecular phenotype profiling, how to perform knowledge-based, informative data integration remains a major challenge. In this article, we have proposed a Bayesian sparse factor analysis model, iFad, for the joint analysis of gene expression and drug sensitivity profiles measured on the same set of cell lines. The aim is to identify the target biological pathways for drugs with unclear mechanism of action. This model allows natural incorporation of prior knowledge about the connectivity structure of biological pathways (e.g. KEGG pathway), and simultaneously relates the underlying pathway activity to both gene expression levels and drug response. Due to this sparsity formulation, the sample size needed to achieve satisfactory inference result can be much smaller than the number of features in either dataset. We demonstrate the performance of iFad first using simulation and then on the NCI-60 datasets. Real data analysis shows that our method is able to identify many cancer type-specific drug-pathway associations. One direction of great interest for future study is how to speed up the computation process, since MCMC methods are usually time-consuming when applied to high-dimensional inference.

Joint modeling of expression profiles and drug-related data represent an increasingly important and popular trend in the future. Besides the bi-clustering method ISA mentioned in Section 1 (Kutalik et al., 2008), another seminal work in this field (Chang et al., 2005) used Bayesian networks to model the gene–drug dependency, also on the NCI-60 data. Due to computational constraints of Bayesian network models, extensive feature selection was performed before the network inference. A more recent work (Chen et al., 2009) developed a linear regression model that integrates genotype and gene expression data generated under drug-free conditions of yeast segregants to predict the response to various drugs. From a statistical point of view, joint analysis of paired datasets can be achieved using a number of techniques, such as canonical correlation, bipartite graph inference, model-based clustering, etc. With the availability of more and more types of high-throughput datasets from the same panel of samples, novel statistical methods are in great need for knowledge-guided combined analysis.

Funding: National Institutes of Health (GM59507 to H.Z.) and NIH R21-GM084008 to Ning Sun.

Conflict of Interest: None declared.