The objective of this research focuses on whether the variation in the amount of sulfur amino acids (SAA) intake affects the metabolic process. Traditional approaches, which evaluate specific biomarkers after a series of preprocessing procedures, have been criticized as not being fully informative as well as inappropriate for the translation of methodology. Rather than focusing on particular biomarkers, our proposed methodology involving multifractal analysis measures inhomogeneity of regularity of proton nuclear magnetic resonance (1H-NMR) spectrum by wavelet-based multifractal spectrum. With two different statistical models (Day model (Model I) and Hour model (Model-II)), three different geometric features of the multifractal spectrum of each 1H-NMR spectrum (spectral mode, left slope, and broadness) are employed to evaluate the effect of SAA and discriminate 1H-NMR spectra associated with different treatments. The investigated effects of SAA include group effect (high and low dose of SAA), depletion/repletion effect, and time over data effect. The 1H-NMR spectra analysis outcomes show that the group effect is significant for all features of both models. The hourly variation in time and depletion/repletion effects do not show noticeable differences for the three features in Model-I. However, these two effects are significant only for the spectral mode feature in Model-II. The 1H-NMR spectra of the SAA low groups exhibit highly regular patterns with more variability than that of the SAA high group for both models. Moreover, the discriminatory analysis conducted using the support vector machine and the principal components analysis shows that 1H-NMR spectra of the SAA high and low group can be easily discriminatory for both models, while the spectra of depletion and repletion within these groups are discriminatory for Model-I and Model-II. Therefore, the study outcomes imply that the amount of SAA is important and that the SAA intake affects mostly the hourly variation of the metabolic process and the difference between depletion and repletion each day. In conclusion, multifractal analysis of 1H-NMR spectra can provide novel tools to investigate metabolic processes.

In observational studies where the compared groups may be imbalanced in  terms of significant prognostic factors related to time-to-event  outcomes, traditional methods like the Kaplan-Meier (KM) function might  not align with multivariable regression models. To address this, we  introduce a new R package, “AdjKMCIF”, and a corresponding R shiny  application. This tool allows for the estimation of covariate-adjusted  KM functions and CIFs using the Cox and Fine-Gray regression models. The  package also integrates the Gail and Byar method, the Storer method for  stratified models, and the bootstrap method for confidence interval  estimation.