Effective forecasting of energy consumption structure is vital for China to reach its \"dual carbon\" objective. However, little attention has been paid to existing studies on the holistic nature and internal properties of energy consumption structure. Therefore, this paper incorporates the theory of compositional data into the study of energy consumption structure, which not only takes into account the specificity of the internal features of the structure, but also digs deeper into the relative information. Meanwhile, based on the minimization theory of squares of the Aitchison distance in the compositional data, a combined model based on the three single models, namely the metabolism grey model (MGM), back-propagation neural network (BPNN) model, and autoregressive integrated moving average (ARIMA) model, is structured in this paper. The forecast results of the energy consumption structure in 2023-2040 indicate that the future energy consumption structure of China will evolve towards a more diversified pattern, but the proportion of natural gas and non-fossil energy has yet to meet the policy goals set by the government. This paper not only suggests that compositional data from joint prediction models have a high applicability value in the energy sector, but also has some theoretical significance for adapting and improving the energy consumption structure in China.

OBJECTIVE: This study aimed to explore the association between arm elevation and neck/shoulder pain, and trunk forwarding bending and low back pain among home care workers.
METHODS: Home care workers (N = 116) from 11 home care units in Trondheim, Norway, filled in pain assessment and working hours questionnaire, and wore 3 accelerometers for up to 7 consecutive days. Work time was partitioned into upright awkward posture, nonawkward posture, and nonupright time, i.e. sitting. Within a compositional approach framework, posture time compositions were expressed in terms of log-ratio coordinates for statistical analysis and modeling. Poisson generalized linear mixed models were used to analyze the relationship between arm elevation in upright postures and neck/shoulder pain, and between trunk forward bending in upright postures and low back pain, respectively. Isotemporal substitution analysis was used to investigate the association of pain assessment with the reallocation of time spent in the different postures.
RESULTS: Time spent in awkward postures was modest, especially for the more extreme angles (60° and 90°). Adjusting for age, gender, and body mass index, our study suggested that the compositions of time spent by home care workers in awkward postures were significantly associated with pain assessment (P < 0.01). Isotemporal substitution analysis showed that reallocating 5 min from upright posture with arms elevated below to above 60° and 90° was associated with a 6.8% and 19.9% increase in the neck/shoulder pain score, respectively. Reallocating 5 min from a forward bending posture while upright below to above 30°, 60°, and 90° was associated with 1.8%, 3.5%, and 4.0% increase in low back pain, respectively.
CONCLUSIONS: Although the exposure to awkward postures was modest, our results showed an association between increased time spent in awkward postures and an increase in neck/shoulder pain and low back pain in home care workers. As musculoskeletal pain is the leading cause of sickness absence, these findings suggest that home care units could benefit from re-organizing work to avoid excessive arm elevation and trunk forward bending in workers.

Traditional process monitoring control charts (CCs) focused on sampling methods using fixed sampling intervals (FSIs). The variable sampling intervals (VSIs) scheme is receiving increasing attention, in which the sampling interval (SI) length varies according to the process monitoring statistics. A shorter SI is considered when the process quality indicates the possibility of an out-of-control (OOC) situation; otherwise, a longer SI is preferred. The VSI multivariate exponentially moving average for compositional data (VSI-MEWMACoDa) CC based on a coordinate representation using isometric log-ratio (ilr) transformation is proposed in this study. A methodology is proposed to obtain the optimal parameters by considering the zero-state (ZS) average time to signal (ZATS) and the steady-state (SS) average time to signal (SATS). The statistical performance of the proposed CC is evaluated based on a continuous-time Markov chain (CTMC) method for both cases, the ZS and the SS using a fixed value of in-control (IC) ATS0. Simulation results demonstrate that the VSI-MEWMACoDa CC has significantly decreased the OOC average time to signal (ATS) than the FSIMEWMACoDa CC. Moreover, it is found that the number of variables (d) has a negative impact on the ATS of the VSI-MEWMACoDa CC, and the subgroup size (n) has a mildly positive impact on the ATS of the VSI-MEWMACoDa CC. At the same time, the SATS of the VSI-MEWMACoDa CC is less than the ZATS of the VSI-MEWMACoDa CC for all the values of n and d. The proposed VSI-MEWMACoDa CC under steady-State performs effectively compared to its competitors, such as the FSI-MEWMACoDa CC, the VSI-T2CoDa CC and the FSI-T2CoDa CC. An example of an industrial problem from a plant in Europe is also given to study the statistical significance of the VSI-MEWMACoDa CC.

BACKGROUND: A compositional mediation model of survival outcomes was established to explore whether 24-h time-use behaviors mediate the relationship between depression and mortality.
METHODS: 4137 adults from the National Health and Nutrition Examination Survey (NHANES 2005-2006) were followed up to 2019. Cox proportional hazards regression model was used to estimate the total effect of depression on mortality. Compositional data analysis was used to examine the relationship between 24-h time-use compositions and mortality. Furthermore, we constructed a compositional mediation model for survival outcomes to investigate the mediating effect of 24-h time-use behaviors on depression and mortality.
RESULTS: Compared with participants without depression, depressive patients had a significantly higher risk of overall mortality (HR = 1.49, 95 % CI: 1.25,1.79), cardiovascular disease -specific mortality (HR =1.89, 95 % CI: (1.37,2.63)) and mortality from causes other than cardiovascular disease or cancer (HR = 1.62, 95 % CI: (1.25,2.08)). Physical activity, especially moderate-to-vigorous physical activity, significantly mediated the relationship between depression and all-cause and CVD-specific mortality.
CONCLUSIONS: Despite being a cohort study, the exposure and mediatiors were measured at the baseline. Further research is necessary to require a temporal order between the exposure and mediating variables.
CONCLUSIONS: Our findings indicate that 24-h time-use behaviors link depression to mortality. In particular, increasing the time spent on physical activity can reduce the risk of death in patients with depression. This finding provides potential interventions for reducing the risk of death in patients with depression.

Rivers can be sinks for potential toxic elements (PTEs) inputted in their systems by both natural and anthropic processes. Many indices have been proposed to assess the contamination degree of sediments and the environmental conditions of surficial water bodies. Above all, enrichment factor (EF) is the most used tool, but also it is the most debated for its limitations. The need for a reference element and for a background/baseline composition makes the EF method dependent on the researcher\'s expertise, implying that its repeatability may not be granted. Starting from the awareness that geochemical processes, bringing to compositional changes in the environmental matrices, involve multiple elements rather than individual variables, we developed a modified EF (mEF) based on the use of elemental associations. Different multivariate statistical methods (i.e. Robust Principal Component Analysis and Fuzzy Clustering), in a compositional data analysis (CoDA) perspective, were used to set all the terms of the mEF. The mEF was applied to 101 sediment samples collected from a 2 m-long core, covering a sedimentation period of about 150 years (1850-2007), located in the lower Changjiang River (China). The method resulted effective in recognizing most of the signals proceeding from the main natural and anthropogenic events which affected the lower river basin in the considered timespan. The largest geochemical variations recorded fit well the flooding events occurred; besides, the effects produced on the system by the recent socio-economic development (following the end of the civil war in 1949 and the beginning of economic reforms in 1978) and the start-up of the Three Gorges Dam (the world\'s largest power station since 2012) were also intercepted. The proposed method represents a step forward to enhance the effectiveness of the EF in discriminating geochemical anomalies that may be significant to assess the human historical impact on the environment.

The common approach for regression analysis with compositional variables is to express compositions in log-ratio coordinates (coefficients) and then perform standard statistical processing in real space. Similar to working in real space, the problem is that the standard least squares regression fails when the number of parts of all compositional covariates is higher than the number of observations. The aim of this study is to analyze in detail the partial least squares (PLS) regression which can deal with this problem. In this paper, we focus on the PLS regression between more than one compositional response variable and more than one compositional covariate. First, we give the PLS regression model with log-ratio coordinates of compositional variables, then we express the PLS model directly in the simplex. We also prove that the PLS model is invariant under the change of coordinate system, such as the ilr coordinates with a different contrast matrix or the clr coefficients. Moreover, we give the estimation and inference for parameters in PLS model. Finally, the PLS model with clr coefficients is used to analyze the relationship between the chemical metabolites of Astragali Radix and the plasma metabolites of rat after giving Astragali Radix.

In the field of nutritional epidemiology, principal component analysis (PCA) has been used extensively in identifying dietary patterns. Recently, compositional data analysis (CoDA) has emerged as an alternative approach for obtaining dietary patterns. We aimed to directly compare and evaluate the ability of PCA and principal balances analysis (PBA), a data-driven method in CoDA, in identifying dietary patterns and their associations with the risk of hypertension.
Cohort study. A 24-h dietary recall questionnaire was used to collect dietary data. Multivariate logistic regression analysis was used to analyse the association between dietary patterns and hypertension.
2004 and 2009 China Health and Nutrition Survey.
A total of 3892 study participants aged 18-60 years were included as the subjects.
PCA and PBA identified five patterns each. PCA patterns comprised a linear combination of all food groups, whereas PBA patterns included several food groups with zero loadings. The coarse cereals pattern identified by PBA was inversely associated with hypertension risk (highest quintile: OR = 0·74 (95 % CI 0·57, 0·95); Pfor trend = 0·037). None of the five PCA patterns was associated with hypertension. Compared with the PCA patterns, the PBA patterns were clearly interpretable and accounted for a higher percentage of variance in food intake.
Findings showed that PBA might be an appropriate and promising approach in dietary pattern analysis. Higher adherence to the coarse cereals dietary pattern was associated with a lower risk of hypertension. Nevertheless, the advantages of PBA over PCA should be confirmed in future studies.

Zeros in compositional data are very common and can be classified into rounded and essential zeros. The rounded zero refers to a small proportion or below detection limit value, while the essential zero refers to the complete absence of the component in the composition. In this article, we propose a new framework for analyzing compositional data with zero entries by introducing a stochastic representation. In particular, a new distribution, namely the Dirichlet composition distribution, is developed to accommodate the possible essential-zero feature in compositional data. We derive its distributional properties (e.g., its moments). The calculation of maximum likelihood estimates via the Expectation-Maximization (EM) algorithm will be proposed. The regression model based on the new Dirichlet composition distribution will be considered. Simulation studies are conducted to evaluate the performance of the proposed methodologies. Finally, our method is employed to analyze a dataset of fluorescence in situ hybridization (FISH) for chromosome detection.

Dyslipidemia is associated with lifestyle behaviors, while several lifestyle behaviors exist collectively among some populaitons. This study aims to identify lifestyle behavior clusters and their relations to dyslipidemia. This cross-sectional study was conducted in Wuhai City, China. Cluster analysis combined with compositional data analysis was conducted, with 24-h time-use on daily activities and dietary patterns as input variables. Multiple logistic regression was conducted to compare dyslipidemia among clusters. A total of 4306 participants were included. A higher prevalence of newly diagnosed dyslipidemia was found among participants in cluster 1 (long sedentary behavior (SB) and the shortest sleep, high-salt and oil diet) /cluster 5 (the longest SB and short sleep), relative to the other clusters in both age groups (<50 years and ≥50 years). In conclusion, unhealthy lifestyle behaviors may exist together among some of the population, suggesting that these people are potential subjects of health education and behavior interventions. Future research should be conducted to investigate the relative significance of specific lifestyle behaviors in relation to dyslipidemia.

Microbial communities analysis is drawing growing attention due to the rapid development fire of high-throughput sequencing techniques nowadays. The observed data has the following typical characteristics: it is high-dimensional, compositional (lying in a simplex) and even would be leptokurtic and highly skewed due to the existence of overly abundant taxa, which makes the conventional correlation analysis infeasible to study the co-occurrence and co-exclusion relationship between microbial taxa. In this article, we address the challenges of covariance estimation for this kind of data. Assuming the basis covariance matrix lying in a well-recognized class of sparse covariance matrices, we adopt a proxy matrix known as centered log-ratio covariance matrix in the literature. We construct a Median-of-Means estimator for the centered log-ratio covariance matrix and propose a thresholding procedure that is adaptive to the variability of individual entries. By imposing a much weaker finite fourth moment condition compared with the sub-Gaussianity condition in the literature, we derive the optimal rate of convergence under the spectral norm. In addition, we also provide theoretical guarantee on support recovery. The adaptive thresholding procedure of the MOM estimator is easy to implement and gains robustness when outliers or heavy-tailedness exist. Thorough simulation studies are conducted to show the advantages of the proposed procedure over some state-of-the-arts methods. At last, we apply the proposed method to analyze a microbiome dataset in human gut.