Other research groups have already proposed the idea of data integration, but most groups have only investigated the integration of clinical and microarray data. Tibshirani and colleagues 19 proposed such a framework by reducing the microarray data to one variable, addable to models based on clinical characteristics such as age, grade, and size of the tumor. Nevins and colleagues 20 combined clinical risk factors with metagenes (that is, the weighted average expression of a group of genes) in a tree-based classification system. Wang et al. combined microarray data with knowledge on two clinicopathological variables by defining a gene signature only for the subset of patients for whom the clinicopathological variables were not sufficient to predict outcome 21.

A further evolution can be seen in studies in which two omics data sources are simultaneously considered, in most cases microarray data combined with proteomics or array CGH data. Much literature on such studies involving data integration already exists. However, the current definition of the integration of high-throughput data sources as it is used in the literature differs from our point of view.

In a first group of integration studies, heterogeneous data from different sources were analyzed sequentially; that is, one data source was analyzed while the second was used as confirmation of the found results or for further deepening the understanding of the results 22. Such approaches are used for biological discovery and a better understanding of the development of a disease, but not for predictive purposes. For example, Fridlyand and colleagues 23 found three breast tumor subtypes with a distinct CNV pattern based on array CGH data. Microarray data were subsequently analyzed to identify the functional categories that characterized these subtypes. Tomioka et al. 24 analyzed microarray and array CGH data of patients with neuroblastoma in a similar way. Genomic signatures resulted from the array CGH data, while molecular signatures were found after the microarray analysis. The authors suggested that a combination of these independent prognostic indicators would be clinically useful.

The term data integration has also been used as a synonym for data merging in which different data sets are concatenated at the database level by cross-referencing the sequence identifiers, which requires semantic compatibility among data sets 2526. Data merging is a complex task due to, for example, the use of different identifiers, the absence of a 'one gene-one protein' relationship, alternative splicing, and measurement of multiple signals for one gene. In most studies, the concordance between the merged data sets and their interpretation in the context of biological pathways and regulatory mechanisms are investigated. Analyses of the merged data set by clustering or correlating the protein and microarray data can help identify candidate targets when changes in expression occur at both the gene and protein levels. However, there has been only modest success from correlation studies of gene and protein expression. Bitton et al. 27 combined proteomics data with exon array data, which allowed a much more fine-grained analysis by assigning peptides to their originating exons instead of mapping transcripts and proteins based on their IDs.

Our definition for the combination of heterogeneous biological data is different. We integrate multiple layers of experimental data into one mathematical model for the development of more homogeneous classifiers in clinical decision support. For this purpose, we present a kernel-based integration framework. Integration occurs within the patient domain at a level not so far described in the literature. Instead of merging data sets or analyzing them in turn, the variables from different omics data are treated equally. This leads to the selection of the most relevant features from all available data sources, which are combined in a machine learning-based model. We were inspired by the idea of Lanckriet and colleagues 28. They presented an integration framework in which each data set is transformed into a kernel matrix. Integration occurs on this kernel level without referring back to the data. They applied their framework to amino acid sequence information, expression data, protein-protein interaction data, and other types of genomic information to solve a single classification problem: the classification of transmembrane versus non-transmembrane proteins. In this study by Lanckriet and colleagues, all considered data sets were publicly available. This requires a computationally intensive framework for determining the relevance of each data set by solving an optimization problem. Within our set-up, however, all data sources are derived from the patients themselves. This makes the gathering of these data sets highly costly and limits the number of data sets, but guarantees more relevance for the problem at hand.

We previously investigated whether the prediction of distant metastasis in breast cancer patients could be improved when considering microarray data besides clinical data 29. In this manuscript, we consider not only microarray data but also high-throughput data from multiple biological levels. Three different strategies for clinical decision support are proposed: the use of individual data sets (referred to as step A); an integration of each data type over time by manually calculating the change in expression (step B); and an approach in which data sets are integrated over multiple layers in the genome (and over time) by treating variables from the different data sets equally (step C).

We apply our framework to two cases, summarized in Table 1. In the first case on rectal cancer, tumor regression grade, lymph node status, and circumferential margin involvement (CRM) are predicted for 36 patients based on microarray and proteomics data, gathered at two time points during therapy. The second case on prostate cancer involves microarray and copy number variation data from 55 patients. Tumor grade, stage, metastasis, and occurrence of recurrence were available for prediction 3031.

Kernel methods are a group of algorithms that can handle a very wide range of data types, such as vectors, sequences, networks, and so on. They map the data x from the original input space to a high dimensional feature space with the mapping function Φ(x). This embedding into the feature space is performed by a mathematical object K(x_k, x_l), called a 'kernel function'. This function efficiently computes the inner product ⟨Φ(x_k), Φ(x_l)⟩ between all pairs of data items x_k and x_l in the feature space, resulting in the kernel matrix. The size of this matrix is determined only by the number of data items, whatever the nature or the complexity of these items. For example, a set of 100 patients each characterized by 6,913 gene expression values is still represented by a 100 × 100 kernel matrix 40. The representation of all data sets by this real-valued square matrix, independent of the nature or complexity of the data to be analyzed, makes kernel methods ideally positioned for heterogeneous data integration.

Any symmetric, positive semidefinite function is a valid kernel function, resulting in many possible kernels - for example, linear, polynomial, and diffusion kernels. They all correspond to a different transformation of the data, meaning that they extract a specific type of information from the data set. In this paper, the normalized linear kernel function:

where is used instead of the linear kernel function . With the normalized version, the values in the kernel matrix will be bounded because the data points are projected onto the unit sphere while these elements can take very large values without normalization. Normalizing is thus required when combining multiple data sources to guarantee the same order of magnitude for the kernel matrices of the data sets.

A kernel algorithm for supervised classification is the SVM developed by Vapnik 41 and others. Contrary to most other classification methods and due to the way data are represented through kernels, SVMs can tackle high dimensional data (for example microarray data). Given a training set of N samples with feature vectors x_k ∈ Rⁿ and output labels y_k ∈ {-1, +1}, the SVM forms a linear discriminant boundary y(x) = sign[W^TΦ(x)+b] in the feature space with maximum distance between samples of the two considered classes, with w representing the weights for the data items in the feature space and b the bias term. This corresponds to a non-linear discriminant function in the original input space. A modified version of SVM, LS-SVM, was developed by Suykens et al. 34. On high dimensional data sets, this modified version is much faster for classification because a linear system instead of a quadratic programming problem needs to be solved.

The constrained optimization problem for an LS-SVM has the following form:

subject to:

with e_k the error variables, tolerating misclassifications in cases of overlapping distributions, and γ the regularization parameter, which allows tackling the problem of overfitting. It has been shown that regularization seems to be very important when applying classification methods on high dimensional data 42.

In many two-class problems, data sets are skewed in favor of one class such that the contribution of false negative and false positive errors to the performance assessment criterion are not balanced. We therefore used a weighted LS-SVM in which a different weight ζ_k is given to positive and negative samples in order to account for the unbalancedness in the data set 5. The objective function changes into:

with

and N_P and N_N representing the number of positive and negative samples, respectively.

Univariate feature selection techniques are computationally simple but do not incorporate feature-feature interactions. However, due to small sample size limitations, multivariate approaches are often not appropriate for discovering the underlying complex, multivariate correlations. Because it has been shown that univariate gene selection methods lead to good and stable performances across many cancer types and yield in many cases consistently better results than multivariate approaches 43, we used the method DEDS (differential expression via distance synthesis) 44. This technique is based on the integration of different univariate test statistics via a distance synthesis scheme because features highly ranked simultaneously by multiple statistics are more likely to be differentially expressed than features highly ranked by a single test statistic. The statistical tests combined are ordinary fold changes, ordinary t-statistics, SAM (significance analysis for microarrays) statistics and moderated t-statistics. DEDS is available as a BioConductor package in R.

We applied DEDS to the microarray data sets as well as the genomics data set. From our experience, DEDS is less appropriate for data with a limited set of features (data not shown). Since the proteomics data on rectal cancer contain only 90-92 cancer-related proteins, one test statistic suffices, for which we chose the Wilcoxon rank sum test.

To determine the optimal number of features, we use a leave-one-out (LOO) cross-validation approach in which we increase the number of included features iteratively according to the obtained feature ranking but in which we do not include more features than the number of samples in the data set on which the optimal number of features is determined, as discussed by Li and Yang 45. Besides the number of features, the parameters of the kernel method (parameter γ for LS-SVM with normalized linear kernel) also need to be selected. This selection occurs on a k-dimensional grid with k - 1 the number of data sets included. We considered 40 possible values for γ, ranging from 10^-4 to 10⁶ on a logarithmic scale. In each LOO iteration, a sample is left out, feature selection is performed on the remaining n - 1 samples, and models are built for all possible combinations of parameters on this grid. Each model with the instantiated parameters is evaluated on the left out sample. This whole procedure is repeated for all samples. The model parameters are chosen corresponding to the model with the highest LOO area under the receiver operating characteristic (ROC) curve (AUC). If multiple models have the same AUC, the model with the lowest balanced error rate and an as high as possible sum of sensitivity and specificity is chosen. For each considered outcome, the AUC of the best performing model is compared with the AUC of the other models using the method of Hanley and McNeil 46. The final features are chosen as those that occurred most often in the top rankings determined in each LOO iteration.

Three kinds of model building strategies are proposed, different in the degree of integration. Figure 1 shows these strategies in more detail. The data sets are represented as matrices with rows corresponding to patients and columns corresponding to genes, proteins, or CNVs. The matrices representing microarray or genomics data are larger than those for the proteomics data to emphasize the difference in dimensionality.

All three strategies were applied to the microarray and proteomics data sets of rectal cancer. For the prostate cancer data set, however, only two strategies were applicable due to a lack of measurements repeated over time. For all models the parameters were trained according to the same approach, which makes the corresponding LOO results comparable for each outcome separately.

Using the methodologies shown in Figure 1, models were built using microarray and proteomics data of 36 rectal cancer patients at two time points during therapy for the prediction of three outcomes registered at the moment of surgery: a tumor regression grading system (WHEELER) and two prognostic factors, pathologic N stage at surgery (pN-STAGE) and the circumferential margin involvement (CRM). The models with the highest AUC, lowest balanced error rate and an as high as possible sum of sensitivity and specificity are shown in Table 2. The step A models are MT₀ (model based on microarray data at T₀), MT₁ (model based on microarray data at T₁), PT₀ (model based on proteomics data at T₀), and PT₁ (model based on proteomics data at T₁). The step B models consist of MT₀-T₁ (model based on change in gene expression between T₀ and T₁) and PT₀-T₁ (model based on change in protein abundances between T₀ and T₁). Finally, the step C models comprise MT₀₁ (model based on microarray data at both time points), PT₀₁ (model based on proteomics data at both time points), MPT₀ (model based on microarray and proteomics data at T₀), MPT₁ (model based on microarray and proteomics data at T₁), all possible combinations of three data sets (using the same name convention), and MPT₀₁ (model based on all data (microarray and proteomics data at both time points)). The numbers of genes and proteins were chosen to optimize the LOO performance of the LS-SVM models. The features selected most often in the 36 LOO iterations are listed and discussed. For each outcome, the ROC curve of the best model was compared with the ROC curves of all other models 46. The P-values of these significance tests are reported as well.

Table 2 shows the LS-SVM models for the considered combinations of data sets to predict WHEELER, pN-STAGE, and CRM with the optimal number of genes and proteins selected with DEDS and the Wilcoxon rank sum test, respectively. The corresponding ROC curves are shown in Additional data file 1. The performance of the models based on three data sets is given in Additional data file 2. Due to the slightly, but not significantly, better performance for each outcome of one model based on three data sets compared to models based on two data sets, we report the results for the best model combining two data sets. Such models would only require a sample to be taken at one time point (MPT₀, MPT₁) or one technology to be applied on two time points (MT₀₁, PT₀₁). For the prediction of WHEELER, the expression of 25 genes and 12 proteins at T₁ was best, although not significantly, with an AUC of 0.9269. Also for pN-STAGE, combining both data sets at T₁ using the expression of 21 genes and 14 proteins resulted in the best LOO AUC of 0.9870. This performance is significantly better than all step A and B models as well as PT₀₁. Finally, the inclusion of 7 genes and 33 proteins at T₁ led to an AUC of 0.9630 for the prediction of CRM. Four models based on only one data type perform significantly worse compared to MPT₁. For all outcomes, none of the selected proteins are a product of the selected genes.

The contribution of the genes and/or proteins in rectal or colorectal cancer that were selected most often in the LOO iterations of MPT₁ and predicted most accurately WHEELER, pN-STAGE, or CRM are shown in Table 3. A protein important for CRM, for example, is the epidermal growth factor receptor (EGFR), involved in signaling pathways affecting cellular growth, differentiation, and proliferation. This protein represents one of the most promising targets allowing progress in colorectal cancer treatment. It has been suggested that EGFR polymorphisms as well as polymorphisms of other genes active in the EGFR pathway may be potential indicators of radiosensitivity in patients with rectal cancer treated with chemoradiation 49. In colorectal cancer, pro-inflammatory cytokines such as interleukin-1 beta and interleukin-6 may be accountable for the overexpression of Cox-2, important in the early stage and for progression 50. Transforming growth factor alpha, down-regulated in our patients with a good responsiveness to preoperative therapy, is implicated in metastatic spread of colon cancer cells 51. The expression of interleukin-8 is associated with induction and progression of colorectal carcinoma and the development of colorectal liver metastases 52. In our data set, it is down-regulated in the group of patients with no lymph nodes found at surgery. Finally, elevated carcinoembryonic antigen and cancer antigen 19-9 are related to poor outcome in colorectal cancer 53. Their levels are low in patients with no lymph nodes, while carcinoembryonic antigen is also less expressed in patients with a negative CRM, that is, belonging to the class of 'responders'. A complete list of the genes and proteins chosen by the models MPT₁ are shown, for each outcome separately, in Additional data file 3. The predictions seem to depend on mainly different subsets of features. The gene encoding PAI-2 is important for both WHEELER and CRM, while the proteins important for two of the three outcomes are interleukin-4, ferritin, apolipoprotein H, epidermal growth factor, matrix metalloproteinase-2, and lymphotactin. Notably, these genes and proteins were also selected by the other models based on microarray and/or proteomics data at T₁, although the specific feature ranking depends on the number of features included. Some of these genes and proteins were also included in the models based on data at T₀.

The same methodology was applied to microarray and genomics data of 55 patients with prostate cancer. Table 4 shows the results for the prediction of the grade and stage of the tumor (GRADE and STAGE), as well as the tumors that metastasized to distant lymph nodes (METASTASIS) or that recurred (RECURRENCE). Because the data were gathered at one time point, only step A and C models are applicable. The step A models are represented as M (model based on microarray data) and G (model based on genomics data), and the step C model based on both microarray and genomics data as MG. Also, after having optimized the essential number of features to be included using a LOO cross-validation, the final genes and CNVs were selected based on their position and number of occurrences in the 55 LOO rankings.

We obtained similar results as for rectal cancer. Combining gene expression with measurements at the DNA level (MG) led, for all four outcomes, to an improvement in classification accuracy and was significant in some cases (Table 4). For the prediction of GRADE, six genes and eight CNVs selected with DEDS resulted in an AUC of 0.9006. For STAGE, 42 genes and 22 CNVs were needed for a performance of 0.8528. The model MG for the prediction of METASTASIS had an AUC of 0.9868 when fusing the expression of 18 genes with 3 CNVs. Finally, the prediction of RECURRENCE was most difficult, with an AUC of 0.7857 when combining 32 genes and 2 CNVs. Additional data file 1 shows the ROC curves of the models listed in Table 4.

Several genes and CNVs have been selected by MG and are known to be involved in, and important for, prostate cancer (Table 5). The gene ALOX15B is a suppressor of prostate tumor development 54 and in this data set is down-regulated in tumors of high-grade and in tumors that recurred. Both SFRP4 and CXCL14 on the other hand are inhibitors of prostate tumor growth 5556. SFRP4 is up-regulated in tumors of high-grade, and CXCL14 in tumors of advanced stage. A small deletion involving chromosomal band 21q22.3 fuses all coding exons of ERG to androgen-related sequences in the promoter of the prostate-specific TMPRSS2 gene. This chromosomal rearrangement is a highly prevalent oncogenic alteration in prostate tumor cells and leads to an aberrant expression of the ERG proto-oncogene, important for early prostate carcinogenesis 57. In this data set, ERG is overexpressed in tumors in which the cancer metastasized to distant lymph nodes. It has been shown that this genetic biomarker is a strong prognostic factor for disease recurrence, and can be used for early detection and outcome prediction in prostate cancer 58. VAV3, an oncogene involved in development and progression of prostate cancer, is up-regulated in tumors that metastasized 59. It has previously been shown that strong overexpression of TIAM1 is significantly associated with disease recurrence and a decreased disease-free survival 60. Also, JAG1 is significantly associated with recurrence 61 and plays a role in cell growth, progression, and metastasis. In this data set, both genes are up-regulated in the group of tumors that recurred. Finally, several germline mutations or variants in RNASEL have been observed among hereditary prostate cancer cases, indicating that polymorphic changes within the RNASEL gene may be associated with increased risk of familial but not sporadic prostate cancer 62. A list of all the genes and CNVs selected by the models MG are shown in Additional data file 3. As for rectal cancer, the outcomes for prostate cancer seem to be characterized by mainly different sets of features. Five genes overlap between at least two outcomes (ERG, AHSG, SEMA4G, F5, and ALOX15B), while the same holds for four CNVs of the genes GPD1L, KCTD12, SMYD5, and TRO.

To assess the benefit of our kernel-based integration approach over standard data fusion techniques, we implemented an ensemble approach in which each data set gives rise to a separate LS-SVM classifier. These individual LS-SVM models were built similarly to the step A models, with the same number of genes, proteins or CNVs selected as included in the best models MPT₁ and MG. Subsequently, as a late integration step, the continuous outputs of these models were added.

For the study on rectal cancer, the AUC values of the ensemble models integrating the microarray and proteomics data set gathered at T₁, and the corresponding AUC values of the best model obtained with our strategy (MPT₁) are shown in Table 6. The P-values of the significance tests comparing the ROC curves are reported as well 46. For CRM, our strategy was significantly better than the ensemble approach at a significance level of 0.05. For WHEELER and pN-STAGE, the AUC values did not differ significantly. Similarly for the study on prostate cancer, the AUC values of MG were compared with the AUC values of the ensemble models combining microarray and genomics data (Table 6). For all four outcomes, the AUC of MG was better than the AUC of the ensemble models, although being significantly better for RECURRENCE only.

We additionally verified whether, in both cases, data from multiple layers of molecular biology were complementary. After mapping the entities of the data sets based on their entrez gene IDs, we investigated the correlation between the microarray and proteomics data of rectal cancer on the one hand, and between the microarray and genomics data of prostate cancer on the other hand. Using the Spearman correlation coefficient, there was no significant correlation for rectal cancer between the abundances of the 90-92 proteins and their corresponding transcripts at a significance level of 0.05. The microarray and genomics data sets for prostate cancer were slightly more correlated. While for GRADE the 6 genes selected by the model MG did not correlate with their DNA expression, 2 of the 42 selected genes for STAGE were significantly correlated (P < 0.05). For METASTASIS and RECURRENCE, there was a significant correlation for one and three genes, respectively. The regions, with involved CNVs selected from the genomics data, were also compared with the regions in which the selected genes from the microarray data were located. For the majority of regions, there was no overlap. For the other regions with the same rough chromosomal location, the genes selected by both data sets were different.