Statistical adjustment of signal censoring in gene expression experiments

Motivation: Numerical output of spotted microarrays displays censoring of pixel intensities at some software dependent threshold. This reduces the quality of gene expression data, because it seriously violates the linearity of expression with respect to signal intensity. Statistical methods based on typically available spot summaries together with some parametric assumptions can suggest ways to correct for this defect. Results: A maximum likelihood approach is suggested together with a sensible approximation to the joint density of the mean, median and variance—which are typically available to the biological end-user. The method ‘corrects’ the gene expression values for pixel censoring. A by-product of our approach is a comparison between several two-parameter models for pixel intensity values. It suggests that pixels separated by one or two other pixels can be considered independent draws from a Lognormal or a Gamma distribution

Novel statistical approaches for non-normal censored immunological data: analysis of cytokine and gene expression data

Background: For several immune-mediated diseases, immunological analysis will become more complex in the future with datasets in which cytokine and gene expression data play a major role. These data have certain characteristics that require sophisticated statistical analysis such as strategies for non-normal distribution and censoring. Additionally, complex and multiple immunological relationships need to be adjusted for potential confounding and interaction effects. Objective: We aimed to introduce and apply different methods for statistical analysis of non-normal censored cytokine and gene expression data. Furthermore, we assessed the performance and accuracy of a novel regression approach in order to allow adjusting for covariates and potential confounding. Methods: For non-normally distributed censored data traditional means such as the Kaplan-Meier method or the generalized Wilcoxon test are described. In order to adjust for covariates the novel approach named Tobit regression on ranks was introduced. Its performance and accuracy for analysis of non-normal censored cytokine/gene expression data was evaluated by a simulation study and a statistical experiment applying permutation and bootstrapping. Results: If adjustment for covariates is not necessary traditional statistical methods are adequate for non-normal censored data. Comparable with these and appropriate if additional adjustment is required, Tobit regression on ranks is a valid method. Its power, type-I error rate and accuracy were comparable to the classical Tobit regression. Conclusion: Non-normally distributed censored immunological data require appropriate statistical methods. Tobit regression on ranks meets these requirements and can be used for adjustment for covariates and potential confounding in large and complex immunological datasets

STATISTICAL ANALYSIS OF GENE EXPRESSION MICROARRAYS

This manuscript is composed of two major sections. In the first section of the manuscript we introduce some of the biological principles that form the bases of cDNA microarrays and explain how the different analytical steps introduce variability and potential biases in gene expression measurements that can sometimes be dificult to properly address. We address statistical issues associated to the measurement of gene expression (e.g., image segmentation, spot identification), to the correction for back-ground fluorescence and to the normalization and re-scaling of data to remove effects of dye, print-tip and others on expression. In this section of the manuscript we also describe the standard statistical approaches for estimating treatment effect on gene expression, and briefly address the multiple comparisons problem, often referred to as the big p small n paradox. In the second major section of the manuscript, we discuss the use of multiple scans as a means to reduce the variability of gene expression estimates. While the use of multiple scans under the same laser and sensor settings has already been proposed (Romualdi et al. 2003), we describe a general hierarchical modeling approach proposed by Love and Carriquiry (2005) that enables use of all the readings obtained under varied laser and sensor settings for each slide in the analyses, even if the number of readings per slide vary across slides. This technique also uses the varied settings to correct for some amount of the censoring discussed in the first section. It is to be expected that when combining scans and correcting for censoring, the estimate of gene expression will have smaller variance than it would have if based on a single spot measurement. In turn, expression estimates with smaller variance are expected to increase the power of statistical tests performed on them