Principal components analysis (PCA) is a standard tool in multivariate data analysis to reduce the number of dimensions, while retaining as much as possible of the data's variation. Instead of investigating thousands of original variables, the first few components containing the majority of the data's variation are explored. The visualization and statistical analysis of these new variables, the principal components, can help to find similarities and differences between samples. Important original variables that are the major contributors to the first few components can be discovered as well.This chapter seeks to deliver a conceptual understanding of PCA as well as a mathematical description. We describe how PCA can be used to analyze different datasets, and we include practical code examples. Possible shortcomings of the methodology and ways to overcome these problems are also discussed.

(1) Background: We present a new statistical approach labeled as “St. Nicolas House Analysis” (SNHA) for detecting and visualizing extensive interactions among variables. (2) Method: We rank absolute bivariate correlation coefficients in descending order according to magnitude and create hierarchic “association chains” defined by sequences where reversing start and end point does not alter the ordering of elements. Association chains are used to characterize dependence structures of interacting variables by a graph. (3) Results: SNHA depicts association chains in highly, but also in weakly correlated data, and is robust towards spurious accidental associations. Overlapping association chains can be visualized as network graphs. Between independent variables significantly fewer associations are detected compared to standard correlation or linear model-based approaches. (4) Conclusion: We propose reversible association chains as a principle to detect dependencies among variables. The proposed method can be conceptualized as a non-parametric statistical method. It is especially suited for secondary data analysis as only aggregate information such as correlations matrices are required. The analysis provides an initial approach for clarifying potential associations that may be subject to subsequent hypothesis testing.

Dysregulated cytokine expression by T cells plays a pivotal role in the pathogenesis of autoimmune diseases. However, the identification of the corresponding pathogenic subpopulations is a challenge, since a distinction between physiological variation and a new quality in the expression of protein markers requires combinatorial evaluation. Here, we were able to identify a super-functional follicular helper T cell (Tfh)-like subpopulation in lupus-prone NZBxW mice with our binning approach "pattern recognition of immune cells (PRI)". PRI uncovered a subpopulation of IL-21+ IFN-γhigh PD-1low CD40Lhigh CXCR5- Bcl-6- T cells specifically expanded in diseased mice. In addition, these cells express high levels of TNF-α and IL-2, and provide B cell help for IgG production in an IL-21 and CD40L dependent manner. This super-functional T cell subset might be a superior driver of autoimmune processes due to a polyfunctional and high cytokine expression combined with Tfh-like properties.

Aim: Influence of nutrition in human growth failure, especially stunting, is a well-accepted idea. The present study assesses the influence of nutrition and non-nutritional factors on height growth in a short stature population. Material and methods: The present study was conducted among the children and adolescents of Sikkim, India. The sample size was 538 (boys and girls) of age 2-18 years. The anthropometric indices mid upper arm circumference-forage Z-scores (MUACZ) and BMI-forage Z-scores (BAZ) were utilised as proxy of nutritional status and growth was assessed using height-forage Z-scores (HAZ). Associations were assessed using correlation, St. Nicolas house analysis (SNHA), principal component analysis (PCA) and regression. Results: Nutritional status of the participating children and adolescents as assessed by MUACZ and BAZ were largely normal. Despite variation in HAZ from-4 to +2 there was no influence of the nutritional indices on height. Further, there was clear lack of association between HAZ and socioeconomic variables in the present study. Conclusion: The findings of the present study suggest nutrition is not the primary regulator of human growth. The possible influence of community effects on height is discussed.

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