Development Classification using Helmert Contrast

A simple but powerful tool for extracting temporal patterns is found in contrasts: linear combinations of gene expression over time. Contrasts usually but not always have their coefficients summing to zero. An example of the use of contrasts can be seen in Lonnstedt et al where samples were taken from cells at 0.5, 1, 4 and 24 h after stimulation with a growth factor and contrast patterns were used to categorize genes into late and early responders. Symth used contrasts in the univariate linear model setting and used F-statistic for testing whether there is any change in gene expression levels over time. This approach assumes that the samples are independent and so would be appropriate for cross-sectional data.

Post-hoc contrast analysis is widely used for small time series experiments (those in which a few time points were sampled) a post-hoc contrast analysis. This technique has been applied to microarray studies. A set of orthogonal contrast vectors is applied to the data matrix to test specific hypotheses regarding the pattern of group differences. Our goal is to characterize the time patterns so we have applied the Helmert contrasts which test for changes across time by comparing expression at each time point to all preceding time points. Another way of finding the changes in age development is to use the standard Helmert contrasts which are shown in the following table.


The designs have been labeled as “Design-X” where X represented the time point which is compared to the average of the preceding time points. They measure the rate of change between the time point X and the all the preceding time points.