The ultimate goal of differential expression analysis is to select genes whose expression values are significantly different between two or more groups of samples. Statistical tools are available for the following types of analysis:
The type of statistical tools available to the user are dependent on the number of groups specified during the Preparing Datasets process. If more complicated analyses are needed, you can download the raw CEL files or the normalized data for analysis using the statistical package of your choice. See "Downloading a Dataset".
If you have grouped the arrays in your dataset into only two groups, you can perform parametric, non-parametric, or 2-way ANOVA statistical analysis.
The parametric analysis is a two-sample t-test assuming equal variances and is executed using the R function t.test. This test is considered parametric because it assumes that the distribution of expression values is normal within each group. However, expression data is often not distributed normally and there are often not enough observations to assume that the central limit theorem applies.
A non-parametric test does not depend on the distribution of the expression data. The Wilcoxon rank sum test is invoked when you specify a non-parametric test. This analysis is done in R using the function wilcox_test from the coin package. When the sample size is under 50, the exact p-value is used, otherwise a normal approximation is calculated. The parametric t-test is more powerful when the data is truly normally distributed, but the non-parametric test is robust for data that is not normally distributed.
Use a two-way ANOVA Analysis to input factors or use factors from the array attributes in a two-way analysis of variance. You can test for four different effects; main effect of factor 1, main effect of factor 2, the interaction effect between factor 1 and factor 2, or the overall model effect. To test for the interaction effect or the overall model effect, a regression model is used that contains the main effects for both factor 1 and factor 2 plus the interaction effect, a true two-way ANOVA. To test for main effects, the interaction effect is not included in the model. F-statistics are reported in all cases. Factors that are entered as character values are treated as categorical, and factors that are entered as numerical values are treated as continuous.
If you have grouped the arrays in your dataset into more than two groups, the following types of statistical analyses are available:
Use a one-way ANOVA model to compare the within-group variance and the between-group variance of selected groups. You can choose from any of the possible pair-wise contrasts (e.g., Group1 vs. Group 2) or the overall effect of group (factor effect) on the model. When there are more than four groups, you can only use the factor effect. For the pair-wise contrasts, a moderated t-statistic is used to test significance, and for factor effects, a moderated F-statistic is used. For the moderated t-statistic and F-statistic, the standard deviation of the ordinary test is "shrunk" to reflect information that is borrowed across genes (Smyth 2004).
References
Smyth GK (2004). Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments. Statistical Applications in Genetics and Molecular Biology 3(1), Article 3.
Use a two-way ANOVA Analysis to input factors or use factors from the array attributes in a two-way analysis of variance. You can test for four different effects; main effect of factor 1, main effect of factor 2, the interaction effect between factor 1 and factor 2, or the overall model effect. To test for the interaction effect or the overall model effect, a regression model is used that contains the main effects for both factor 1 and factor 2 plus the interaction effect, a true two-way ANOVA. To test for main effects, the interaction effect is not included in the model. F-statistics are reported in all cases. Factors that are entered as character values are treated as categorical, and factors that are entered as numerical values are treated as continuous.
Use a t-test with noise distribution to determine a list of genes that are differentially expressed between two groups in a replicate experiment, i.e., "high" selected line from replicate 1, "low" selected line from replicate 1, "high" selected line from replicate 2, and "low" selected line from replicate 2. This method was first introduced by Eaves et al. in 2002.
This method involves first calculating a modified t-statistic for each probe(set) for each replicate separately where the traditional sample variances are replaced with a "pooled" variance. The pooled variance is calculated for each group using a weighted mean between the observed variance and a mean local variance. The weights are 2 to 1 where the larger of the two variances is given the larger weight. To calculate the mean local variance, the data is first sorted by mean expression for each probe(set), the mean local variance is then calculated as the mean of the variances of the 250 probe(set)s immediately below the probe(set) of interest and the 250 probe(set)s immediately above the probe(set) of interest.
After t-statistics are calculated for each probe(set) and each replicate, the probe(set)s are separated into two groups. Probe(set)s are placed in the null distribution if their t-statistics show opposite signs in the two replicate experiments. The t-statistics for these experiments are used to generate a null distribution of t-statistics for p-values to be based on. Instead of individual p-values being calculated for each probe(set), an initial p-value threshold is set and it is determined whether or not probe(set)s meet this criteria. Using this method, the type I error rate (p-value) is determined by the product of the following three probabilities:
Therefore, the percentiles from the null distribution used to determine 'significance' can be calculated for a specific error rate by taking the square root of the fraction, the probability of having the two t-statistics showing the same direction of differential expression divided by the specified error rate. A gene is considered significant if the observed t-statistic for each replicate is larger than the threshold t-statistic determined from the null distribution for that replicate. Exact p-values are not reported for this statistical method, and therefore, multiple testing corrections cannot be implemented.
References
Eaves IA, Wicker LS, Ghandour G, Lyons PA, Peterson LB, Todd JA, Glynne RJ (2002). Combining mouse congenic strain and microarray gene expression analyses to study a complex trait: The NOD model of type1 diabetes. Genome Research 12:232-243.