Error Distribution for Gene Expression Data

Abstract

We present a new instance of Laplace's second Law of Errors and show how it can be used in the analysis of data from microarray experiments. This error distribution is shown to fit microarray expression data much better than a normal distribution. The use of this distribution in a parametric bootstrap leads to more powerful tests as we show that the t-test is conservative in this setting. We propose a biological explanations for this distribution based on the Pareto distribution of the variables used to compute the log ratios.

Performance of Gene Selection and Classification Methods in a Microarray Setting: A Simulation Study

“…For the skewness parameter κ we chose values of 0.5 (skewed to the left) and 1.2 (skewed to the right). They are similar or a bit more extreme than estimates found by Purdom and Holmes (2005) for several microarrays from published microarray experiments. Their estimates range from 0.792 to 1.174.…”

“…We wish to examine the effect of such a deviation on the performance of the selection and classification methods. Purdom and Holmes (2005) propose the use of the asymmetric Laplace distribution for microarray data. It is more peaked compared to the normal distribution.…”

“…Secondly, in the Van Sanden et al (2007) study the normal distribution has been used as the underlying distribution in the simulation procedure. It has been shown (Purdom and Holmes, 2005), however, that microarrays do not always follow the normal distribution. Thus, we considered the symmetric Laplace distribution as a long-tailed alternative.…”

Application of Esscher Transformed Laplace Distribution in Microarray Gene Expression Data

“…This method is widely used in microarray experiments as this removes the intensity dependence in log 2 (R i /G i ) values, where R i is the red dye intensity (Cy3) and G i (Cy5) is the green dye intensity for the i th gene . The same dataset was used to fit asymmetry Laplace distribution in Purdom and Holmes (2005).…”

“…An error distribution of gene expression datasets was approximated by two distributions by taking log-normal in the bulk of microarray spot intensities and a power law in the tails (Hoyle, Rattray, Jupp, & Brass, 2002). The gene expression was also fitted by using an asymmetric Laplace distribution (Purdom & Holmes, 2005). However, in order to take outliers into account, the Cauchy distribution has been used for estimating gene expressions using data from multiple-laser scans (Khondoker, Glasbey, & Worton, 2006), and the Laplace mixture model was introduced as a long tailed alternative to the normal distribution (Bhowmick, Davison, Goldstein, & Ruffieux, 2006).…”