Kristof Engelen

Balancing false positives and false negatives for the detection of differential expression in malignancies

A basic problem of microarray data analysis is to identify genes whose expression is affected by the distinction between malignancies with different properties. These genes are said to be differentially expressed. Differential expression can be detected by selecting the genes with P-values (derived using an appropriate hypothesis test) below a certain rejection level. This selection, however, is not possible without accepting some false positives and negatives since the two sets of P-values, associated with the genes whose expression is and is not affected by the distinction between the different malignancies, overlap. We describe a procedure for the study of differential expression in microarray data based on receiver-operating characteristic curves. This approach can be useful to select a rejection level that balances the number of false positives and negatives and to assess the degree of overlap between the two sets of P-values. Since this degree of overlap characterises the balance that can be reached between the number of false positives and negatives, this quantity can be seen as a quality measure of microarray data with respect to the detection of differential expression. As an example, we apply our method to data sets studying acute leukaemia.

Joint mapping of genes and conditions via multidimensional unfolding analysis

BackgroundMicroarray compendia profile the expression of genes in a number of experimental conditions. Such data compendia are useful not only to group genes and conditions based on their similarity in overall expression over profiles but also to gain information on more subtle relations between genes and conditions. Getting a clear visual overview of all these patterns in a single easy-to-grasp representation is a useful preliminary analysis step: We propose to use for this purpose an advanced exploratory method, called multidimensional unfolding.ResultsWe present a novel algorithm for multidimensional unfolding that overcomes both general problems and problems that are specific for the analysis of gene expression data sets. Applying the algorithm to two publicly available microarray compendia illustrates its power as a tool for exploratory data analysis: The unfolding analysis of a first data set resulted in a two-dimensional representation which clearly reveals temporal regulation patterns for the genes and a meaningful structure for the time points, while the analysis of a second data set showed the algorithms ability to go beyond a mere identification of those genes that discriminate between different patient or tissue types.ConclusionMultidimensional unfolding offers a useful tool for preliminary explorations of microarray data: By relying on an easy-to-grasp low-dimensional geometric framework, relations among genes, among conditions and between genes and conditions are simultaneously represented in an accessible way which may reveal interesting patterns in the data. An additional advantage of the method is that it can be applied to the raw data without necessitating the choice of suitable genewise transformations of the data.

A Nonlinear Mixed-Effects Model for Estimating Calibration Intervals for Unknown Concentrations in Two-Color Microarray Data with Spike-Ins

In this study, we propose a calibration method for preprocessing spiked-in microarray experiments based on nonlinear mixed-effects models. This method uses a spike-in calibration curve to estimate normalized absolute expression values. Moreover, using the asymptotic properties of the calibration estimate, 100(1-α)% confidence intervals for the estimated expression values can be constructed. Simulations are used to show that the approximations on which the construction of the confidence intervals are based are sufficiently accurate to reach the desired coverage probabilities. We illustrate applicability of our method, by estimating the normalized absolute expression values together with the corresponding confidence intervals for two publicly available cDNA microarray experiments (Hilson et al., 2004; Smets et al., 2008). This method can easily be adapted to preprocess one-color oligonucleotide microarray data with a slight adjustment to the mixed model.