Methodological study of affine transformations of gene expression data with proposed robust non-parametric multi-dimensional normalization method

BACKGROUND: Low-level processing and normalization of microarray data are most important steps in microarray analysis, which have profound impact on downstream analysis. Multiple methods have been suggested to date, but it is not clear which is the best. It is therefore important to further study the different normalization methods in detail and the nature of microarray data in general. RESULTS: A methodological study of affine models for gene expression data is carried out. Focus is on two-channel comparative studies, but the findings generalize also to single- and multi-channel data. The discussion applies to spotted as well as in-situ synthesized microarray data. Existing normalization methods such as curve-fit ("lowess") normalization, parallel and perpendicular translation normalization, and quantile normalization, but also dye-swap normalization are revisited in the light of the affine model and their strengths and weaknesses are investigated in this context. As a direct result from this study, we propose a robust non-parametric multi-dimensional affine normalization method, which can be applied to any number of microarrays with any number of channels either individually or all at once. A high-quality cDNA microarray data set with spike-in controls is used to demonstrate the power of the affine model and the proposed normalization method. CONCLUSION: We find that an affine model can explain non-linear intensity-dependent systematic effects in observed log-ratios. Affine normalization removes such artifacts for non-differentially expressed genes and assures that symmetry between negative and positive log-ratios is obtained, which is fundamental when identifying differentially expressed genes. In addition, affine normalization makes the empirical distributions in different channels more equal, which is the purpose of quantile normalization, and may also explain why dye-swap normalization works or fails. All methods are made available in the aroma package, which is a platform-independent package for R

Assessing, testing and estimating the amount of fine-tuning by means of active information

A general framework is introduced to estimate how much external information has been infused into a search algorithm, the so-called active information. This is rephrased as a test of fine-tuning, where tuning corresponds to the amount of pre-specified knowledge that the algorithm makes use of in order to reach a certain target. A function $f$ quantifies specificity for each possible outcome $x$ of a search, so that the target of the algorithm is a set of highly specified states, whereas fine-tuning occurs if it is much more likely for the algorithm to reach the target than by chance. The distribution of a random outcome $X$ of the algorithm involves a parameter $\theta$ that quantifies how much background information that has been infused. A simple choice of this parameter is to use $\theta f$ in order to exponentially tilt the distribution of the outcome of the search algorithm under the null distribution of no tuning, so that an exponential family of distributions is obtained. Such algorithms are obtained by iterating a Metropolis-Hastings type of Markov chain, and this makes it possible to compute the their active information under equilibrium and non-equilibrium of the Markov chain, with or without stopping when the targeted set of fine-tuned states has been reached. Other choices of tuning parameters $\theta$ are discussed as well. Nonparametric and parametric estimators of active information and tests of fine-tuning are developed when repeated and independent outcomes of the algorithm are available. The theory is illustrated with examples from cosmology, student learning, reinforcement learning, a Moran type model of population genetics, and evolutionary programming.Comment: 28 pages, 3 figure

The relationship between nightmares, depression and suicide

Abstract Objective Previous studies investigating the association between nightmares and suicide have yielded different results. We aimed to investigate whether nightmares, directly or indirectly, influence the incidence of suicide. Methods We used a prospective cohort study, based on 40,902 participants with a mean follow-up duration of 19.0 years. Cox proportional hazards models with attained age as time-scale were fitted to estimate hazard ratios (HR) of suicide with 95% confidence intervals (CI) as a function of the presence or absence of depression and nightmares. Mediation analysis was used to asses to what extent the relationship between nightmares and the incidence rate of suicide could be mediated by depression. Results No association was observed between nightmares and the incidence of suicide among participants without depression. Compared with non-depressed participants without nightmares, the incidence of suicide among participants with a diagnosis of depression was similar among those with and without nightmares (HR 12.3, 95% CI 5.55–27.2 versus HR 13.2, 95% CI 7.25–24.1). The mediation analysis revealed no significant effects of nightmares on suicide incidence. However, the incidence of depression during follow-up was higher among those who suffered from nightmares than among those who did not (p Conclusions Our findings indicate that nightmares have no influence on the incidence rate of suicide, but may reflect pre-existing depression. This is supported by a recent discovery of a strong genetic correlation of nightmares with depressive disorders, with no evidence that nightmares would predispose to psychiatric illness or psychological problems. Interventions targeting both depression and nightmares, when these conditions co-occur, may provide additional therapeutic benefit