Our approach has two steps. In STEP 1, we infer pseudo-exons using multiple probe intensities. In STEP 2, we identify pseudo-exons that are differentially expressed between two groups of samples. In STEP 1, for each probe, we first compute the average of the difference in probe intensities between the two groups of samples. Then, based on the similarity of probe intensities and probe adjacency on the gene sequence, we merge probes into clusters that represent one pseudo-exon. In STEP 2, we test if the pseudo-exons are differentially expressed between the two groups of samples. The expression value from a pseudo-exon is treated as an entity in the current analysis, comparable to the gene expression from a complete probe set in customary analyses of gene expression data. The selected pseudo-exons are interpreted as an indication of alternative splicing at this region of the gene between the two comparison groups.

For illustrative purposes, we applied the above method to predict splice variants between the normal cerebellum and medulloblastoma tumor samples, which included both non-metastatic and metastatic tumors. In STEP 1, using a significance level of 0.05 in the t-test, we identified 10,838 pseudo-exons out of a total of 142,580 (7129 × 20) probes that represent the 7,129 probe sets on the Hu6800 GeneChip^®. In STEP 2, we compared the difference in expression values between the two groups for each pseudo-exon. The histogram of Z-scores from these tests is shown in Figure 2. With the significance threshold of the Z-score set to 4.8 (equivalent to one false positive error in the discovery), we discovered 811 pseudo-exons, derived from 577 genes, were significantly different between normal cerebellum and medulloblastoma tumor samples. Note that for some genes more than one pseudo-exon was selected.

Following the same procedure, we predicted splice variants between the non-metastatic and the metastatic medulloblastomas. We identified 8,319 pseudo-exons, thirteen of which were significantly different between non-metastatic and metastatic medulloblastomas (Table 1). Instead of conducting validation in a biological experiment, we searched two genome browsers for supportive evidence for our prediction. We input the thirteen genes in Table 1 into the Integrated Genome Browser (IGB) from Affymetrix 7 to see whether the probes in the identified pseudo-exons were positioned on separate exons within the same gene, which is a pre-requisite for alternative splicing. For further consistency, we checked whether the predicted pseudo-exons were reported as splice variants in the UCSC Human Genome Browser 8 under the track named "mRNA sequences from GenBank". In the IGB, we found four out of thirteen genes with predicted alternatively spliced pseudo-exons resided on different exons. These four genes were glutaredoxin (GLRX), carboxypeptidase N polypeptide 1 (CPN1), Keratin 7 (KRT7) and killer cell lectin-like receptor subfamily C member 3 (KLRC3). For instance, we predicted the last three probes for GLRX were within one pseudo-exon. In IGB, based on RefSeq information, these three probes are on a different exon. We searched alternatively transcribed variants deposited in GenBank in the "mRNA sequences from GenBank" track in UCSC Human Genome Browser for the genes confirmed by IGB. All of them except for CPN1 have at least two transcript sequences in the GenBank database. At least one of these sequences lack the region that we predicted to be alternatively spliced, and at least one of these sequences contain the predicted region. We also searched PubMed for reported splice variants for the thirteen identified genes. Five of out of the thirteen genes were reported in the literature to have splice variants. They are nitric oxide synthase 1 (NOS1) 9, low density lipoprotein receptor (LDLR) 10, thrombopoietin (THPO) 11, Down syndrome critical region gene 1 (DSCR1) 12, paired box gene 2 (PAX2) 13.

To compare our method with the Hu et al's, we implemented their method and applied it to our dataset. When comparing normal cerebellum and medulloblastomas samples using Hu et al's method, we inferred 31 alternatively spliced genes with the selection criterion used by Hu et al in their paper (Table 2). Among these 31 genes, seven overlapped with the findings from our approach (Table 3). For four of them, D87119_at, U14971_at, U29953_rna1_at, X04828_at, the locations of the alternative splicing were consistent between the two methods. In the comparison between non-metastatic and metastatic medulloblastoma samples, we did not find any gene that was alternatively spliced by Hu et al's method. We also investigated the effect of different selection criteria in Hu et al's method (i.e. the R threshold, which is the ratio of the probe intensity in a tissue over the mean of the probe intensities in the remaining nine tissue types for the same probe). Table 4 shows the relation between the 577 genes predicted by our approach and the genes selected with different R thresholds in Hu's approach. Numbers of predicted alternatively spliced genes increase as smaller R values (less stringent) are used.

We checked both IGB and UCSC Human Genome Browsers for supportive evidence for the seven predicted alternatively spliced variants in Table 3. We found four genes that had predicted pseudo-exons located on separate exons according to IGB and alternative spliced mRNA from GenBank in UCSC Human Genome Browser. They are guanine nucleotide binding protein alpha inhibiting activity polypeptide 2 (GNAI2), ribosomal protein S9 (RPS9), activated leukocyte cell adhesion molecule (ALCAM), and minichromosome maintenance deficient 7 (MCM7). There are splicing variants reported in PubMed literature for ALCAM 14.

Our empirical dataset consists of GeneChip^® Hu6800 expression array data from sixty-nine medulloblastoma samples and four cerebellum samples as normal controls. Among the medulloblastoma samples, forty-two are from non-metastatic tumors and twenty-seven are from metastatic tumors. There are 7,129 probe sets in the Hu6800 expression array, and twenty probes in each probe set.

In this step, we merge probes within a gene into clusters that represent pseudo-exons. First, we compute the difference in probe hybridization intensity between two groups of samples for each probe. Then, for each gene, we merge probes into clusters based on the similarity of the differences in probe intensity (between the two groups of samples) and the probe adjacency on the genome sequence. For a gene, let Y_{(i, 1)}, and n₁ be the probe intensity for the ith probe in sample group 1, variance, and sample size, respectively. Similarly, Y_{(i, 2)}, and n₂ are for the sample group 2. Within the gene, the index i increases from the direction of the 5' end to the 3' end. We start with the first probe from the 5' end and compute:

where is the mean of probe intensities. If the absolute value of t_i does not exceed the threshold value at the significance level α = 0.05, we merge the ith probe with the (i+1)th probe to generate a pseudo-exon. The resulting pseudo-exon becomes the new ith probe in the next iteration of the t-test. The pseudo-exon extends with each iteration until the results of the t-test become significant or reach the last probe within a probe set. If t_i exceeds the significance threshold value, we do not merge the ith probe with the (i+1)th probe, but start generating a new pseudo-exon from this (i+1)th probe, using the same iteration procedure. After we finish the last probe at the 3' end, we may either have several pseudo-exons or only one pseudo-exon (i.e. the entire probe set) if every t-statistic within a probe set is not significant.

For each pseudo-exon, we determine whether there is a difference in hybridization intensity between the two groups x₁ and x₂. Our null hypothesis is that, for any pseudo-exon, the difference in probe intensity between the two groups is zero. If we reject the null hypothesis for a pseudo-exon, meaning that the hybridization intensities between the two groups are significant different for that pseudo-exon, we then infer that there is a splice variant between the two groups of samples for the corresponding region within the gene.

In the same vein as Li and Wong's model to analyze gene expression at the probe level 15, we propose a multiplicative heterogeneity factor model to associate the probe intensities of a pseudo-exon directly with the covariate, i.e. group indictor x_k:

where Y_jik is the hybridization intensity for the ith probe in the jth pseudo-exon in the kth sample, N is the number of probes in the jth pseudo-exon, δ_k and λ_k are heterogeneity factors for normalization,x_k is the group indicator for the kth sample, β_j is the coefficient for jth pseudo-exon, φ_ji is the multiplicative probe-specific parameter for ith probe in jth pseudo-exon, and ξ is random variation term. To avoid making any distributional assumptions, we applied estimating equation techniques to estimate the coefficients and their standard errors for making statistical inferences 16171819.