Subclass mapping: identifying common subtypes in independent disease data sets

Abstract

Whole genome expression profiles are widely used to discover molecular subtypes of diseases. A remaining challenge is to identify the correspondence or commonality of subtypes found in multiple, independent data sets generated on various platforms. While model-based supervised learning is often used to make these connections, the models can be biased to the training data set and thus miss inherent, relevant substructure in the test data. Here we describe an unsupervised subclass mapping method (SubMap), which reveals common subtypes between independent data sets. The subtypes within a data set can be determined by unsupervised clustering or given by predetermined phenotypes before applying SubMap. We define a measure of correspondence for subtypes and evaluate its significance building on our previous work on gene set enrichment analysis. The strength of the SubMap method is that it does not impose the structure of one data set upon another, but rather uses a bi-directional approach to highlight the common substructures in both. We show how this method can reveal the correspondence between several cancer-related data sets. Notably, it identifies common subtypes of breast cancer associated with estrogen receptor status, and a subgroup of lymphoma patients who share similar survival patterns, thus improving the accuracy of a clinical outcome predictor.

Figure 1. Subclass mapping (SubMap) methodology. Two independent data sets, A and B, are clustered separately, compared and integrated.

(a) Candidate subclasses are defined by clustering A and B (predetermined phenotype can also be used). Marker genes of each candidate subclass in A (A_i) are selected, and mapped onto a gene list ranked according to their differential expression with respect to a subclass of B (B_j). Their over-representation at the top of the ranking is evaluated using the enrichment score (ES_AiBj), and significance is assessed as a nominal p-value, p_AiBj, by randomly permuting sample class labels in B. This process is repeated by interchanging the role of A and B to compute ES_BjAi and p_BjAi. (b) Mutual enrichment information, p_AiBj and p_BjAi, are combined using the Fisher inverse chi-square statistic, F_ij. Its significance is estimated based on a null distribution for the F_ij generated by randomly picking the nominal-p from corresponding null distributions for ES_AiBj and ES_BjAi. After multiple hypothesis testing (MHT) correction, p-values for F_ij are summarized in the subclass association (SA) matrix. Clustering of the SA matrix reveals subclasses common to A and B.

Figure 2. Example 1: Multiple tissue types.

(a) SubMap was applied to two data sets, Multi-A and Multi-B, containing multiple tissue types: breast (Br), prostate (Pr), lung (Lu), and colon (Co). Bonferroni-corrected p-values for breast, prostate, lung, and colon tissues were 0.002, 0.002, 0.002, and 0.002, respectively. (b) Each tissue type in Multi-B was removed before applying SubMap. Only subsets of the same tissue type were significantly associated (Bonferoni-corrected p<0.05). The p-values for “Multi-A-Br and Multi-B-Lu (left-upper)”, “Multi-A-Lu and Multi-B-Br (left-bottom)”, and “Multi-A-Co and Multi-B-Br (right-bottom)” are 0.330, 0.547, and 0.517, respectively

Figure 3. Example 2: Common subtypes of Diffuse Large B-cell Lymphoma (DLBCL).

SubMap was applied for three subclasses of DLBCL pre-determined in DLBCL-A and DLBCL-B data sets. Bonferroni-corrected p-values for “oxidative phosphorylation (OxPhos)”, “B-cell response (BCR)”, and “host response (HR)” subtypes were 0.008, 0.001, and 0.001, respectively. The association for the pair of DLBCL-A-BCR and DLBCL-B-OxPhos was not significant (p = 0.362).

Figure 4. Example 3: Common subtypes of breast cancer associated with estrogen receptor (ER) status.

(a) Candidate subclass labels were assigned using hierarchical clustering in Breast-A and Breast-B data sets independently. (b) Subclass association (SA) matrix for Breast-A and Breast-B. Bonferroni-corrected p-values for the combinations of “A₁ and B₂”, “A₁ and B₄“, “A₂ and B₁”, “A₃ and B₁”, and “A₃ and B₃” were 0.070, 0.002, 0.023, 0.001, and 0.055, respectively (FDR-corrected p-values of 0.014, 0.001, 0.008, 0.001, and 0.014, respectively). *: ER status is missing for one case.

Figure 5. Example 4: Survival prediction in Diffuse Large B-cell lymphoma (DLBCL) data sets.

(a) Subclass association (SA) matrix for the comparison between DLBCL-C and DLBCL-D data sets. Bonferroni-corrected p-values for the pairs of “C₃ and D₂” and “C₄ and D₃” were 0.002 and 0.002, respectively, (b) Survival prediction models were built using DLBCL-C and applied to DLBCL-D. Kaplan-Meier survival curves for the predicted groups in DLBCL-D are shown. Left: Prediction model was trained using all cases in DLBCL-C (n = 58), and tested on all cases in DLBCL-D (n = 129). Middle: Survival prediction using only cases from “matched” subclasses. Model was trained using C₃ ∪ C₄ samples (n = 25) and tested in D₂ ∪ D₃ (n = 61). The survival separation was better than that in the left panel in spite of having fewer samples. Right: survival prediction using only cases from “unmatched” subclasses. Model was trained using C₁ ∪ C₂ (n = 33) and tested in D₁ ∪ D₄ (n = 68). The numbers of events were 61, 22, and 39 for all (D₁ ∪ D₂ ∪ D₃ ∪ D₄), “matched” (D₂ ∪ D₃), and “unmatched” (D₁ ∪ D₄) patients, respectively. p-values were calculated using the log-rank test. DFS: disease free survival.