Introduction
We use the designation "Term-for-Term (TFT) analysis" to refer to the standard method of performing statistical analysis for overrepresentation in GO. Please see the section on Parent-Child analysis for an explanation of this name.
TFT analysis is based on the following assumptions. We are generally interesting in knowing if a subset of genes from a larger population has any special characteristics. We will define the subset as our study group. This could be a set of overexpressed genes from a microarray experiment. Note that there may be several study groups, for instance, overexpressed genes and underexpressed genes. The population group would then be defined as all genes represented on the microarray. We can then ask if the frequency of a annotation to a Gene Ontology term is different for the study group compared to the overall population.
Modified Fisher's Exact Test
Thus, we can imagine a binary random variable for each gene in the population with two mutual exclusive values: 1) The gene is annotated to the GO term in question or 2) The gene is not annotated to the GO term.
Assume the population of all genes contains M genes annotated to some term t and N genes not annotated to the term. The population thuis contains a total of M+N genes. The study set contains k genes, r of which are annotated to the term t. The hypergeometric distribution then gives the probability of sampling exactly r genes annotated term t:
Parent-Child Analysis
The Parent-Child method represents a new algorithm for identifying overrepresented Gene Ontology (GO) annotations in gene sets. While the current methods treats each term independently and hence ignores the structure of the GO hierarchy, our approach takes parent-child relationships into account. Over-representation of a term is measured with respect to the presence of its parental terms in the set. This resolves the problem that the standard approach tends to falsely detect an over-representation of more specific terms below terms known to be over-represented. Our approach comes at no additional computational complexity when compared to the standard approach.
The parent-child method is described in detail in Grossmann et al. (2007), Improved Detection of Overrepresentation of Gene-Ontology Annotations with Parent-Child Analysis (Available as an Open-Access Bioinformatics Article). A conference report from the RECOMB06 An Improved Statistic for Detecting Over-Represented Gene Ontology Annotations in Gene Sets, has appeared in Springer's Lecture Notes in Computer Science.
Multiple Testing
Since in general we will test up to thousands of GO terms for overrepresentation, we need to apply some correction for multiple testing. At present, the Ontologizer uses a classic Bonferroni correction, meaning it multiplies the nominal p-values calculated as described above by the number of tests performed. This is a very conservative form of correction for multiple testing. We can limit the number of tests performed by deciding not to test GO terms that do not annotate any genes in the population (since the study group is drawn from the population, if no genes are annotated than obviously overrepresentation of the term is impossible). Additionally, if a term annotates only one gene in the population than it is apparent that testing for overrepresentation in the study group has little meaning. Note that the number of genes in the study group annotated to the term does (and should) not need to be taken into account here.
It is possible to perform analysis on any number of groups (clusters) of genes simultaneously. The Ontologizer does not perform multiple testing correction based on the number of clusters analysed. Depending on the question posed by the user, it may or may not to be appropriate to do so.
Finally, note that Gene Ontology annotations are made to the most specific term possible. All ancestors of the term are considered to be implicitly annotated. Therefore, if we are calculating the total annotations of a term, we need to count annotations to all (more specific) descendents of the term also. Note that we need to avoid introducing "extra" (duplicate) counts if there are multiple paths from a descendent term to an ancestor term, or if two distinct descendents of a term are annotated for a certain gene. A discussion of these issues is available in Robinson et al. (2004) Gene-Ontology analysis reveals association of tissue-specific 5' CpG-island genes with development and embryogenesis. Hum Mol Genet 13:1969-78.