In order to remove experimental variation from the measurements, normalisation and batch correction were performed on the UPLC glycan data. To make measurements across samples comparable, normalisation by total area was performed. Prior to batch correction, normalised glycan measurements were log-transformed due to right-skewness of their distributions and the multiplicative nature of batch effects. Batch correction was performed on log-transformed measurements using the ComBat method (R package sva) [31], where the technical source of variation (which sample was analysed on which plate) was modelled as batch covariate. To correct measurements for experimental noise, estimated batch effects were subtracted from log-transformed measurements.

Longitudinal analysis of patient samples through their observation period was performed by implementing a linear mixed effects model, where time was modelled as fixed effect, while the individual ID was modelled as random effect, without additional modelling of age. In regards to this, age was not included in the model since the follow-up period for Bariatric cohort was measured in months, therefore the changes in patients’ age are not relevant for glycosylation. Prior to the analyses, glycan variables were all transformed to standard normal distribution by inverse transformation of ranks to Normality (R package “GenABEL”, function rntransform). Using rank transformed variables makes estimated effects of different glycans comparable, as these will have the same standardised variance. False discovery rate (FDR) was controlled by the Benjamini–Hochberg procedure at the specified level of 0.05. Data were analysed and visualised using R programming language (version 3.5.2) [32].

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