Biostatistics

Eigenanalysis is common practice in biostatistics, and the largest eigenvalue of a data set contains valuable information about the data. However, to make inferences about the size of the largest eigenvalue, its distribution must be known.

Partial Least Squares-Discriminant Analysis (PLS-DA) is a PLS regression method with a special binary 'dummy' y-variable and it is commonly used for classification purposes and biomarker selection in metabolomics studies. Several statistical approaches are currently in use to validate outcomes of PLS-DA analyses e.g. double cross validation procedures or permutation testing.

Not only the levels of individual metabolites, but also the relations between the levels of different metabolites may indicate (experimentally induced) changes in a biological system. Component analysis methods in current ‘standard’ use for metabolomics, such as Principal Component Analysis (PCA), do not focus on changes in these relations. We therefore propose the concept of ‘Between Metabolite Relationships’ (BMRs): common changes in the covariance (or correlation) between all metabolites in an organism.

Data sets resulting from metabolomics, proteomics, or metabolic profiling experiments are usually complex. This type of data contains underlying factors, such as time, doses, or combinations thereof. Classical biostatistics methods do not take into account the structure of such complex data sets.

The combination of the different data sources for classification purposes, also called data fusion, can be done at different levels: low-level, i.e. concatenating data matrices, medium-level, i.e. concatenating data matrices after feature selection and high-level, i.e. combining model outputs. In this paper the predictive performance of high-level data fusion is investigated. Partial least squares is used on each of the data sets and dummy variables representing the classes are used as response variables.

One of the new expanding areas in functional genomics is metabolomics: measuring the metabolome of an organism. Data being generated in metabolomics studies are very diverse in nature depending on the design underlying the experiment. Traditionally, variation in measurements is conceptually broken down in systematic variation and noise where the latter contains, e.g. technical variation. There is increasing evidence that this distinction does not hold (or is too simple) for metabolomics data.

In this paper we introduce discriminant Q² (DQ²) as an improvement for the Q² value used in the validation of PLSDA models. DQ² does not penalize class predictions beyond the class label value. With rigorous Monte Carlo simulations we show that when DQ² is used, a smaller effect can be found statistically significant than when the standard Q² is used.

For analyzing designed high-dimensional data, no standard methods are currently available. A method that is becoming more and more popular for analyzing such data is ASCA. The mathematics of ASCA are already described elsewhere but a geometrical interpretation is still lacking. The geometry can help practitioners to understand what ASCA does and the more advanced user can get insight into the properties of the method. This paper shows the geometry of ASCA in both the row- and column-space of the matrices involved.