Berrar D. et al. - Practical Approach to Microarray Data Analysis

If a binomial distribution is used, the probability of having x genes in F in a set of K randomly picked genes is given by the classical formula of the binomial probability in which the probability of extracting a gene from F is estimated by the ratio of genes in F present on the chip M / N and the corresponding p-value can be respectively calculated as:

and

The main difference between the binomial and hypergeometric distributions is that the binomial models a sampling with replacement. Thus, selecting a gene involved in F should not influence the probability of selecting another gene involved in F. However, in our experiments, we do sampling without replacement since when a gene is picked, we cannot pick it again and the set of unpicked genes in F is reduced by one, thus changing the probability of future picks from F. Because of this, the two distributions behave a bit differently. For example, one cannot use the hypergeometric to calculate the probability of having x > M genes since this would be equivalent to picking more F genes than there are on the microarray. However, the expression of the binomial probability density function will still provide a meaningful probability since in sampling with replacement one gene can be picked more than once and it is possible to pick more F genes than present on the microarray. However, the expression of the binomial probability density function will still provide a meaningful probability since in sampling with replacement one gene can be picked more than once and it is possible to pick more F genes than present on the microarray. Unfortunately, the computation of the hypergeometric distribution is not feasible for lists longer than K > 150 genes. However, for such large values, the hypergeometric distribution tends to behave like a binomial. In consequence, the binomial formula in Equation 18.3 can be used to compute the p-values.

Alternative approaches include a Chi-square test for equality of proportions (Fisher and van Belle, 1993) and Fisher’s exact test (Man et al., 2000). For the purpose of applying these tests, the data can be organized as shown in Table 18.2. The dot notation for an index is used to represent the summation on that index.

316 Chapter 18

The p-value corresponding to a particular occurrence is calculated as the sum of all probabilities in this table lower than the observed probability corresponding to the observed combination (Man et al., 2000).

Finally, Audic and Claverie (1997) have used a Poisson distribution and a Bayesian approach to calculate the probability of observing a given number of tags in SAGE data. As noted by Man et al. (2000), this approach can be

The p-values are calculated as a cumulative probability density function (cdf) as follows (Audic and Claverie, 1997; Man et al., 2000):

Extensive simulations performed by Man et al. compared the Chi-square test for equality of proportions with Fisher’s exact test and Audic and Claverie’s test and showed that the Chi-square test has the best power and

as well as the binomial test. Fisher’s exact test is required when the sample size is small and the chi-square test cannot be used. For a typical microarray experiment with genes on the chip and selected genes, the binomial approximates very well the hypergeometric and is used instead. For small, custom microarrays (fewer than 200 genes), the is used. The program calculates automatically the expected values and uses Fisher’s exact test when becomes unreliable (expected values less than 5). Thus, the choice between the three different models is automatic, requiring no statistical knowledge from the end-user.

We did not implement Audic and Claverie’s test because: i) it has been shown that is at least as good (Man et al., 2000), and ii) while very appropriate for the original problem involving ESTs, the use of a Poisson distribution may be questionable for our problem.

The exact biological meaning of the calculated p-values depends on the list of genes submitted as input. For example, if the list contains genes that are upregulated and mitosis appears more often than expected,

the conclusion may be that the condition under study stimulates mitosis (or more generally, cell proliferation) in a statistically significant way. If the list contains genes that are downregulated and mitosis appears more often than expected (exactly as before), then the conclusion may be that the condition significantly inhibits mitosis.

4.DISCUSSION

Onto-Express has been applied to a number of publicly available data sets. For example, a microarray strategy was recently used by van ‘t Veer et al. to identify 70 genes that can be used as a predictor of clinical outcome for breast cancer (van’t Veer et al., 2002). A subsequent analysis revealed that several key mechanisms such as cell cycle, cell invasion, metastasis, angiogenesis and signal transduction genes were significantly upregulated in cases of breast cancer with poor prognosis. However, as shown below, a comprehensive global analysis of the functional role associated with the differentially regulated genes has revealed novel biological mechanisms involved in breast cancer. Using the global strategy provided by OntoExpress the 231 genes significantly correlated with breast cancer prognosis were categorized into 102 different biological processes. Seventy-two of these groups had significant p-values (p < 0:05). Of these 72 groups, only 17 are represented by two or more members of the same biological pathway. These encompass most of the processes postulated to be indicative of poor prognosis including cell cycle, cell invasion, metastasis, and signal transduction (van’t Veer et al., 2002). Interestingly, angiogenesis, cell cycle control, cell proliferation, and oncogenesis, are not significantly represented (p > 0:05) but a host of novel pathways were identified. These included protein phosphorylation, a common cellular response to growth factor stimulation and anti-apoptosis (apoptosis = programmed cell death). Both are believed to be intimately linked, acting to preserve homeostasis and developmental morphogenesis. Clearly, these processes can impact cancer. This data is used as a sample data set at: http://vortex.cs.wayne.edu. We invite the readers to login and use Onto-Express to analyze the data themselves in the light of the information provided in (van’t Veer et al., 2002).

4.1Utility, Need, and Impact

A tool such as Onto-Express can be used in two different ways. Many microarray users embark upon “hypotheses generating experiments” in which the goal is to find subsets of genes differentially regulated in a given condition. In this context, Onto-Express can be used to analyze and interpret the results of the experiment in a rigorous statistical manner (see section 3).

However, another major application is in experiment design. An alternative to the “hypotheses generating experiments” is the “hypothesis driven experiments” in which one first constructs a hypothesis about the phenomenon under study and then performs directed experiments to test the hypothesis. Currently, no two chips offer exactly the same set of genes. There is a natural tendency to select the chip with the most genes but this may not necessarily be the best choice and certainly, not the most cost effective. When a hypothesis of a certain mechanism does exist, we argue that one should use the chip(s) that best represent the corresponding pathways. Onto-Express can suggest the best chip or set of chips to be used to test a given hypothesis. This can be accomplished by analyzing the list of genes on all existing arrays and providing information about the pathways and biological mechanisms covered by the genes on each chip. If chip A contains 10,000 genes but only 80 are related to a given pathway and chip B contains only 400 genes but 200 of them are related to the pathway of interest, the experiment may provide more information if performed with chip B instead of A. This can also translate into significant cost savings.

An early version of Onto-Express was first made available in February 2002 (Khatri et al., 2002). In the period February-June, our user base grew to 590 valid registered users from 47 countries. The web traffic analysis shows a daily average of 74.28 page views by 18.28 unique visitors (including the weekend). Onto-Express has also been mentioned in several news articles (Janssen, 2002; Tracy, 2002; Uehling, 2002). Version 1 of Onto-Express is available free of charge at: http://vortex.cs.wayne.edu. This version constructs functional profiles for the cellular role, cellular component, biological process and molecular function as well as biochemical function and chromosome location. Version 2 of Onto-Express adds the computation of the statistical significance of the results.

4.2Other Related Work and Resources

A tremendous amount of genetic data is available on-line from several public databases (DBs). NCBI provides sequence, protein, structure and genome DBs, as well a taxonomy and a literature DB. Of particular interest are UniGene (non-redundant set of gene-oriented clusters) and LocusLink (genetic loci). SWISS-PROT is a curated protein sequence DB that provides high-level annotation and a minimal level of redundancy (Bairoch and Apweiler, 2000). Kyoto Encyclopedia of Genes and Genomes (KEGG) contains a gene catalogue (annotated sequences), a pathway DB containing a graphical representation of cellular processes and a LIGAND DB (Kanehisa and Goto, 2000; Kanehisa et al., 2000; Ogata et al., 1999).

GenMAPP is an application that allows the user to create and store pathways in a graphic format, includes a multiple species gene database and allows a mapping of a user’s expression data on existing pathways (Dahlquist et al., 2002). Other related databases and on-line tools include: PathDB (metabolic networks) (Waugh et al., 2000), GeneX (NCGR) (source independent microarray data DB; Mangalam et al., 2001), Arrayexpress (EBI, 2001a), SAGEmap (Lash et al., 2000), (EBI, 2001a), ArrayDB (NHGRI, 2001), ExpressDB (Aach et al., 2000), and Stanford Microarray Database (Sherlock et al., 2001; Stanford, 2001). Two meta-sites containing information about various genomic and microarray on-line DBs are (Shi, 2001) and (CNRS, 2001).

Data format standardization is necessary in order to automate data processing (Brazma, 2001). The Microarray Gene Expression Data Group (MGED) is working to standardize the Minimum Information About a Microarray Experiment (MIAME), the format (MAGE) and ontologies and normalization procedures related to microarray data (Brazma et al., 2001; EBI, 2001b). Of particular interest is the Gene Ontology (GO) effort which aims to produce a dynamic, controlled vocabulary that can be applied to all organisms even as knowledge of gene and protein roles in cells is accumulating and changing (Ashburner et al., 2000; Ashburner et al., 2001). Expression profiles of genes across tissues can be obtained with tissue microarrays (Kononen et al., 1998; Bubendorf et al., 1999a; Bubendorf et al., 1999b; Schraml et al., 1999;Sallinen et al., 2000; Moch et al., 2001; Nocito et al., 200la; Nocito et al., 2001b; mousses et al., 2002). Other techniques allowing a high-throughput screening includes the Serial Analysis of Gene Expression (SAGE) (Velculescu et al., 1995) and PowerBlots (Biosciences, 2002). Although such techniques have very high throughput when compared with techniques such as Northern blots or RT-PCR, they still require a considerable amount of laboratory effort. Data mining of the human dbEST has been used previously to determine tissue gene expression profiles (Bortoluzzi et al., 2000; Hishiki et al., 2000; Hwang et al., 2000; Sese et al., 2001; Vasmatzis et al., 1995).

5.CONCLUSION

In contrast to the approach of looking for key genes of known specific pathways or mechanisms, global functional profiling is a high-throughput approach that can reveal the biological mechanisms involved in a given condition. Onto-Express is a tool that translates the gene expression profiles showing how various genes are changed in specific conditions into functional profiles showing how various functional categories (e.g., cellular functions) are changed in the given conditions. Such profiles are constructed

based on public data and Gene Ontology categories and terms. Furthermore, Onto-Express provides information about the statistical significance of each of the pathways and categories used in the profiles allowing the user to distinguish between cellular mechanisms significantly affected and those that could be involved by chance alone.

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