Analysis of contingency tables based on generalised median polish with power transformations and non-additive models

Contingency tables are a very common basis for the investigation of effects of different treatments or influences on a disease or the health state of patients. Many journals put a strong emphasis on p-values to support the validity of results. Therefore, even small contingency tables are analysed by techniques like t-test or ANOVA. Both these concepts are based on normality assumptions for the underlying data. For larger data sets, this assumption is not so critical, since the underlying statistics are based on sums of (independent) random variables which can be assumed to follow approximately a normal distribution, at least for a larger number of summands. But for smaller data sets, the normality assumption can often not be justified. Robust methods like the Wilcoxon-Mann-Whitney-U test or the Kruskal-Wallis test do not lead to statistically significant p-values for small samples. Median polish is a robust alternative to analyse contingency tables providing much more insight than just a p-value. Median polish is a technique that provides more information than just a p-value. It explains the contingency table in terms of an overall effect, row and columns effects and residuals. The underlying model for median polish is an additive model which is sometimes too restrictive. In this paper, we propose two related approach to generalise median polish. A power transformation can be applied to the values in the table, so that better results for median polish can be achieved. We propose a graphical method how to find a suitable power transformation. If the original data should be preserved, one can apply other transformations – based on so-called additive generators – that have an inverse transformation. In this way, median polish can be applied to the original data, but based on a non-additive model. The non-linearity of such a model can also be visualised to better understand the joint effects of rows and columns in a contingency table

CsgD regulatory network in a bacterial trait-altering biofilm formation

In response to the limited nutrients and stressful conditions of their habitats, many microorganisms including Salmonella form a biofilm by secreting a polymeric matrix to interweave individual cells and to build structural communities on an abiotic or living surface. The biofilm formation in Salmonella is tightly regulated by a regulatory network that involves multiple transcriptional regulators. As a master transcriptional regulator in biofilm formation, curli subunit gene D (csgD) functions by activating the biosynthesis of the extracellular polymeric matrix composed of exopolysaccharide cellulose, curli and biofilm-associated proteins (Baps), assisting bacterial cells in transitioning from the planktonic stage to the multicellular state. The expression of CsgD itself is affected by cell growth stage and environmental stimuli through the action of other transcriptional factors, bis-(3′–5′)-cyclic dimeric guanosine monophosphate (c-di-GMP), regulatory small RNAs (sRNAs) and other elements. The formation of biofilm confers new physiological characteristics on the bacteria within, especially resistance against unfavorable environmental conditions. Herein, we summarize the CsgD regulatory network of Salmonella biofilm formation and the new traits acquired by Salmonella when within biofilm