Many modern analytical methods are used to analyse samples coming from an experimental design, for example, in medical, biological, or agronomic fields. Those methods generate most of the time highly multivariate data like spectra or images. This is the case of "omics" technologies used to detect genes (genomics), mRNA (transcriptomics), proteins (proteomics), or metabolites (metabolomics) in a specific biological sample. Those technologies produce high-dimensional multivariate databases where the number of variables (descriptors) tends to be much larger than the number of experimental units. Moreover, experiments in omics often follow designs aimed at understanding the effect of several factors on biological systems. Therefore, multivariate statistical tools are needed to highlight variables that are consistently modified by different biological states. It is in this context that 2 recent methods combine analysis of variance (ANOVA) and principal component analysis (PCA), namely, ASCA (ANOVA-simultaneous component analysis) and APCA (ANOVA-PCA). They provide powerful tools to visualize multivariate structures in the space of each effect of the statistical model linked to the experimental design.Their main limitation is that they provide biased estimators of the factor effects when the design of experiment is unbalanced. This paper introduces 2 new methods, ASCA+ and APCA+, that allow, respectively, to extend the use of ASCA and APCA to unbalanced designs using several principles from the theory of general linear models. Both methods are applied on real-life metabolomics data, clearly demonstrating the capacity of ASCA+ and APCA+ methods to highlight correct biomarkers corresponding to effects of interest in unbalanced designs.

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Two main methodologies for assessing equivalence in method-comparison studies are presented separately in the literature. The first one is the well-known and widely applied Bland-Altman approach with its agreement intervals, where two methods are considered interchangeable if their differences are not clinically significant. The second approach is based on errors-in-variables regression in a classical (X,Y) plot and focuses on confidence intervals, whereby two methods are considered equivalent when providing similar measures notwithstanding the random measurement errors. This paper reconciles these two methodologies and shows their similarities and differences using both real data and simulations. A new consistent correlated-errors-in-variables regression is introduced as the errors are shown to be correlated in the Bland-Altman plot. Indeed, the coverage probabilities collapse and the biases soar when this correlation is ignored. Novel tolerance intervals are compared with agreement intervals with or without replicated data, and novel predictive intervals are introduced to predict a single measure in an (X,Y) plot or in a Bland-Atman plot with excellent coverage probabilities. We conclude that the (correlated)-errors-in-variables regressions should not be avoided in method comparison studies, although the Bland-Altman approach is usually applied to avert their complexity. We argue that tolerance or predictive intervals are better alternatives than agreement intervals, and we provide guidelines for practitioners regarding method comparison studies. Copyright © 2016 John Wiley & Sons, Ltd.

The effect of two digestible protein levels (310 and 469 g/kg DM) on the relative lysine (Lys; g Lys/kg DM or g Lys/100 g protein) and the absolute Lys (g Lys intake/kg 0·75 per d) requirements was studied in rainbow trout fry using a dose -response trial. At each protein level, sixteen isoenergetic (22-23 MJ digestible energy/kg DM) diets were tested, involving a full range (2-70 g/kg DM) of sixteen Lys levels. Each diet was given to one group of sixty rainbow trout fry (mean initial body weight 0·78 g) reared at 158C for 31 feeding d. The Lys requirements were estimated based on the relationships between weight, protein, and Lys gains (g/kg 0·75 per d) and Lys concentration (g/kg DM or g/100 g protein) or Lys intake (g/kg 0·75 per d), using the broken-line model (BLM) and the non-linear four-parameter saturation kinetics model (SKM-4). Both the model and the response criterion chosen markedly impacted the relative Lys requirement. The relative Lys requirement for Lys gain of rainbow trout estimated with the BLM (and SKM-4 at 90 % of the maximum response) increased from 16·8 (19·6) g/kg DM at a low protein level to 23·4 (24·5) g/kg DM at a high protein level. However, the dietary protein content affected neither the absolute Lys requirement nor the relative Lys requirement expressed as g Lys/100 g protein nor the Lys requirement for maintenance (21 mg Lys/kg 0·75 per d).