Short panel data quantile regression model with flexible correlated effects

This study applies quantile regression to model the Body Mass Index (BMI) of 152 students from Delta State Polytechnic in Delta State, Nigeria. The BMI serves as the response variable, while skin fold (SK), feeding habit (FH), feeding frequency (FF), and frequency of exercising (FE) are considered as explanatory variables. A comparison is made between the results obtained from the classical linear regression model and quantile regression models at different quantiles (p = 0.1, 0.25, 0.5, 0.75, and 0.9) to examine the impact of the variables on the students' BMI and assess if the relationships differ across quantiles. The findings reveal significant differences between the classical linear regression and quantile regression models, emphasizing the importance of quantile regression in capturing the nuances of the relationship between variables at different points of the BMI distribution. The study highlights the limitations of the classical linear regression model in providing a comprehensive understanding of the data and underscores the value of quantile regression in enhancing our insights into the relationship between BMI and the considered factors. This research contributes to the broader literature on quantile regression and its applications in exploring BMI and related health issues among students

Study on the Influence of Iron Supplementation on Neonatal Birth Weight: A Population-Based Survey in Northwestern China

In this paper, a hybrid method of quantile regression and multivariate wavelet is proposed to deal with the problem of data contamination or the presence of outliers, which uses the median instead of the mean on which the linear regression model and the estimation method for ordinary least squares depend.The paper included a comparison between the proposed (for several wavelets and different threshold) and classical method based on mean absolute error, to get the best fit quantile regression model for the data.The application part dealt with two types of data representing simulation, real data, and analysis using a program designed for this purpose in the MATLAB language, as well as the statistical program SPSS-26 and EasyFit-5.5.The study concluded that the proposed method is more efficient than the classical method in estimating the parameters of a quantile regression model depending on the coefficient of determination and on the mean absolute error and mean squared error criteria.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

Quantile regression analysis of the socioeconomic inequalities in air pollution and birth weight

The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates are allowed to grow as fast as the sample size. We find that all of the usual versions of Eicker-White heteroskedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroskedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroskedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: parametric linear models with many covariates, linear panel models with many fixed effects, and semiparametric semi-linear models with many technical regressors. Simulation evidence consistent with our theoretical results is also provided. The proposed methods are also illustrated with an empirical application.

ABSTRACTThe linear regression model is widely used in empirical work in economics, statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroscedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates is allowed to grow as fast as the sample size. We find that all of the usual versions of Eicker–White heteroscedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroscedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroscedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: parametric linear models with many covariates, linear panel models with many fixed effects, and semiparametric semi-linear models with many technical regressors. Simulation evidence consistent with our theoretical results is provided, and the proposed methods are also illustrated with an empirical application. Supplementary materials for this article are available online.

Prediction of normal values for central apnea-hypopnea index at different ages and altitudes above sea level in healthy children

This study used a quantile regression model and a non-homogeneous regression model to calibrate probabilistic forecasts of wind speed. These techniques were applied to the forecasts of wind speed over Pyeongchang area using 51-member European Centre for Medium-Range Weather Forecast (ECMWF). Reliability analysis was carried out by using rank histogram to identify the statistical consistency of ensemble forecasts and corresponding observations. The performances were evaluated by rank histogram, mean absolute error, root mean square error and continuous ranked probability score. The results showed that the forecasts of quantile regression and non-homogeneous regression models performed better than the raw ensemble forecasts. However, the differences of prediction skills between quantile regression and nonhomogeneous regression models were insignificant.

BackgroundChildren exposed to social adversity carry a greater risk of poor physical and mental health into adulthood. This increased risk is thought to be due, in part, to inflammatory processes associated with early adversity that contribute to the etiology of many adult illnesses. The current study asks whether aspects of the prenatal social environment are associated with levels of inflammation in adulthood, and whether prenatal and childhood adversity both contribute to adult inflammation. MethodsWe examined associations of prenatal and childhood adversity assessed through direct interviews of participants in the Collaborative Perinatal Project between 1959 and 1974 with blood levels of C-reactive protein in 355 offspring interviewed in adulthood (mean age=42.2 years). Linear and quantile regression models were used to estimate the effects of prenatal adversity and childhood adversity on adult inflammation, adjusting for age, sex, and race and other potential confounders. ResultsIn separate linear regression models, high levels of prenatal and childhood adversity were associated with higher CRP in adulthood. When prenatal and childhood adversity were analyzed together, our results support the presence of an effect of prenatal adversity on (log) CRP level in adulthood (β=0.73, 95% CI: 0.26, 1.20) that is independent of childhood adversity and potential confounding factors including maternal health conditions reported during pregnancy. Supplemental analyses revealed similar findings using quantile regression models and logistic regression models that used a clinically-relevant CRP threshold (>3mg/L). In a fully-adjusted model that included childhood adversity, high prenatal adversity was associated with a 3-fold elevated odds (95% CI: 1.15, 8.02) of having a CRP level in adulthood that indicates high risk of cardiovascular disease. ConclusionsSocial adversity during the prenatal period is a risk factor for elevated inflammation in adulthood independent of adversities during childhood. This evidence is consistent with studies demonstrating that adverse exposures in the maternal environment during gestation have lasting effects on development of the immune system. If these results reflect causal associations, they suggest that interventions to improve the social and environmental conditions of pregnancy would promote health over the life course. It remains necessary to identify the mechanisms that link maternal conditions during pregnancy to the development of fetal immune and other systems involved in adaptation to environmental stressors.

Crown width is a critical variable in reflecting the individual tree growth status and in developing forest growth and yield models. With the crown width base model as reference, we developed the crown width quantile regression models for different quantiles (0.50, 0.90, 0.93, 0.95, 0.96, 0.99) based on the data of 2763 Korean pines in 66 permanent plots from the 10-55 years old plantations in Dabiangou forest farm, mountainous areas of eastern Liaoning Province. We used the reparameterization method by introducing the single tree competition index (Rd) and used the dummy variable method by introducing stand density and forest layer variables. We then selected optimal quantile of maximum crown width in the stand by comparing our model developed routine to the traditional methods. The final crown width linear mixed effect quantile regression model was developed based on the optimal quantile at the plot level. The influence of each variable on crown width was analyzed to reflect the difference of crown width among individual trees in the stand. The models with different stand densities and forest layers had significant difference based on F statistical test: the Ra2 of the model increased by 0.0104, the root mean square error decreased by 0.0115 and the mean square error reduction was 7.4%, after the variables of forest layer, forest density, and competition being incorporated into the basic model. The developed quantile regression model performed better than that of the ordinary least square method in simulating the maximum crown width of a single tree in the forest stand. The selected best quantile of the quantile regression model for the upper forest layer and lower forest layer was 0.96 and 0.93, respectively. The linear quantile regression model with the mixed effect was superior to the traditional quantile regression model in Akaike, Bayesion and HQ information criterion and other evaluation para-meters, the standard error for the parameters of estimates was significantly reduced, and the introduced mixed effect well explained differences among different plots. For the upper forest layer and lower forest layer, the maximum crown width decreased with increasing stand density, increased with increasing relative diameters. The influence of stand density on the crown width of the lower forest layer was greater than that of the upper forest layer. The crown width would increase first and then decrease with the increases of DBH when the stand density was large enough. The mixed effect of the quantile regression model developed here could significantly improve the fitting stability of the model. The sustainable development of Korean pine plantation in the mountainous area of eastern Liaoning Pro-vince should be realized by adjusting stand density and moderate tending and thinning in the future.

Article Figures and data Abstract Editor's evaluation Introduction Materials and methods Results Discussion Data availability References Decision letter Author response Article and author information Metrics Abstract Background: The risk of adult onset cardiovascular and metabolic (cardiometabolic) disease accrues from early life. Infection is ubiquitous in infancy and induces inflammation, a key cardiometabolic risk factor, but the relationship between infection, inflammation, and metabolic profiles in early childhood remains unexplored. We investigated relationships between infection and plasma metabolomic and lipidomic profiles at age 6 and 12 months, and mediation of these associations by inflammation. Methods: Matched infection, metabolomics, and lipidomics data were generated from 555 infants in a pre-birth longitudinal cohort. Infection data from birth to 12 months were parent-reported (total infections at age 1, 3, 6, 9, and 12 months), inflammation markers (high-sensitivity C-reactive protein [hsCRP]; glycoprotein acetyls [GlycA]) were quantified at 12 months. Metabolic profiles were 12-month plasma nuclear magnetic resonance metabolomics (228 metabolites) and liquid chromatography/mass spectrometry lipidomics (776 lipids). Associations were evaluated with multivariable linear regression models. In secondary analyses, corresponding inflammation and metabolic data from birth (serum) and 6-month (plasma) time points were used. Results: At 12 months, more frequent infant infections were associated with adverse metabolomic (elevated inflammation markers, triglycerides and phenylalanine, and lower high-density lipoprotein [HDL] cholesterol and apolipoprotein A1) and lipidomic profiles (elevated phosphatidylethanolamines and lower trihexosylceramides, dehydrocholesteryl esters, and plasmalogens). Similar, more marked, profiles were observed with higher GlycA, but not hsCRP. GlycA mediated a substantial proportion of the relationship between infection and metabolome/lipidome, with hsCRP generally mediating a lower proportion. Analogous relationships were observed between infection and 6-month inflammation, HDL cholesterol, and apolipoprotein A1. Conclusions: Infants with a greater infection burden in the first year of life had proinflammatory and proatherogenic plasma metabolomic/lipidomic profiles at 12 months of age that in adults are indicative of heightened risk of cardiovascular disease, obesity, and type 2 diabetes. These findings suggest potentially modifiable pathways linking early life infection and inflammation with subsequent cardiometabolic risk. Funding: The establishment work and infrastructure for the BIS was provided by the Murdoch Children's Research Institute (MCRI), Deakin University, and Barwon Health. Subsequent funding was secured from National Health and Medical Research Council of Australia (NHMRC), The Shepherd Foundation, The Jack Brockhoff Foundation, the Scobie & Claire McKinnon Trust, the Shane O'Brien Memorial Asthma Foundation, the Our Women's Our Children's Fund Raising Committee Barwon Health, the Rotary Club of Geelong, the Minderoo Foundation, the Ilhan Food Allergy Foundation, GMHBA, Vanguard Investments Australia Ltd, and the Percy Baxter Charitable Trust, Perpetual Trustees. In-kind support was provided by the Cotton On Foundation and CreativeForce. The study sponsors were not involved in the collection, analysis, and interpretation of data; writing of the report; or the decision to submit the report for publication. Research at MCRI is supported by the Victorian Government's Operational Infrastructure Support Program. This work was also supported by NHMRC Senior Research Fellowships to ALP (1008396); DB (1064629); and RS (1045161) , NHMRC Investigator Grants to ALP (1110200) and DB (1175744), NHMRC-A*STAR project grant (1149047). TM is supported by an MCRI ECR Fellowship. SB is supported by the Dutch Research Council (452173113). Editor's evaluation This paper provides data from a population-based cohort study on early life infection and proinflammatory, atherogenic metabolomic and lipidomic profiles at 12 months of age. The authors generated matched infection, metabolomics and lipidomics data from 555 infants in a pre-birth longitudinal cohort and they showed that frequent infant infections are associated with adverse metabolomic and lipidomic profiles. They also report that similar profiles are noted with higher glycoprotein acetyls (GlycA), but not hsCRP. The paper is interesting and assesses the role of infection and markers of inflammation on lipid and metabolic profile of patients. It provides a comprehensive analysis of lipids and metabolites in infants in response to infection. https://doi.org/10.7554/eLife.75170.sa0 Decision letter Reviews on Sciety eLife's review process Introduction Infectious diseases are ubiquitous in infancy and childhood, with potential long-term impacts on health across the life course. Infection has been recognised as a potential contributor to atherosclerotic cardiovascular disease (CVD), one of the leading causes of adult morbidity and mortality, since the 19th century (Nieto, 1998). More recent adult studies link previous infection with long-term risks of disease (Bergh et al., 2017; Cowan et al., 2018; Wang et al., 2017). The mechanisms are largely unknown, but likely include immune activation and heightened inflammation (Shah, 2019), which are pathways central to CVD pathogenesis (Donath et al., 2019b; Ferrucci and Fabbri, 2018) and therefore offer potentially druggable targets in high-risk individuals (Donath et al., 2019a; Ridker et al., 2017). High-sensitivity C-reactive protein (hsCRP) has been extensively used as a marker of chronic inflammation in adult studies but is an acute phase reactant in children and may not reflect chronic inflammation in early life. Glycoprotein acetyls (GlycA) is a nuclear magnetic resonance (NMR) composite measure that is suggested to better reflect cumulative, chronic inflammation (Connelly et al., 2017). GlycA is an emerging biomarker for cardiometabolic risk (Connelly et al., 2017) that outperforms hsCRP as a predictor of CVD events and mortality (Akinkuolie et al., 2014; Duprez et al., 2016), and of infection-related morbidity and mortality (Ritchie et al., 2015). For example, in the Multi-Ethnic Study of Atherosclerosis (n = 6523), higher GlycA was associated with increased risk of incidence CVD and death, even after adjustment for hsCRP and other inflammatory markers. Conversely, prediction of these outcomes by hsCRP attenuated to null after mutual adjustment (Duprez et al., 2016). Cardiovascular and metabolic (cardiometabolic) disease pathogenesis begins in early life and accrues across the life course (Nakashima et al., 2008). Infections occur disproportionally in early childhood (Cromer et al., 2014; Grüber et al., 2008; Troeger et al., 2018; Tsagarakis et al., 2018), and there is a dose-response relationship between childhood infections, adverse cardiometabolic phenotypes (Burgner et al., 2015c), and CVD events (Burgner et al., 2015a) in adulthood. Infection is linked to proatherogenic metabolic perturbations in later childhood and adulthood (Feingold and Grunfeld, 2019; Khovidhunkit et al., 2000), including higher triglycerides and oxidised low-density lipoprotein (LDL), and lower high-density lipoprotein (HDL) cholesterol and apolipoprotein A1 (ApoA1) (Liuba et al., 2003; Pesonen et al., 1993), and to acute and chronic inflammation (Burgner et al., 2015b; Ritchie et al., 2015), but little is known about these relationships in early life, when most infections occur. We therefore aimed to characterise metabolomic and lipidomic profiles at 6 and 12 months of age and their relationship to infection burden during the first year of life. We also investigated the extent to which inflammation mediated the relationship between infection burden and metabolomic and lipidomic differences. Materials and methods Study cohort Request a detailed protocol This study used available data from 555 mother-infant dyads in the Barwon Infant Study (BIS), a population-based pre-birth longitudinal cohort (n = 1074 mother-infant dyads). The cohort details and inclusion/exclusion criteria have been detailed elsewhere (Vuillermin et al., 2015); in brief, mothers were eligible if they were residents of the Barwon region in south-east Australia and planned to give birth at the local public or private hospital. Mothers were recruited at approximately 15 weeks' gestation and provided informed consent. They were excluded if they were not a permanent Australian resident, aged <18 years, required an interpreter to complete questionnaires, or had previously participated in BIS. Infants were excluded if they were very preterm (<32 completed weeks gestation) or had a serious illness or major congenital malformation identified during the first few days of life. Ethics approval was granted by the Barwon Health Human Research Ethics Committee (HREC 10/24). Parent-reported infections Request a detailed protocol At the 4-week, 3-month, 6-month, 9-month, and 12-month time points following birth, mothers were asked to report each episode of infant illness or infection since the previous time point using standardised online questionnaires. The number of parent-reported infections from birth to 12 months was defined as the total number of respiratory tract infections, gastroenteritis, conjunctivitis, and acute otitis media episodes. In secondary analyses, numbers of parent-reported infections from birth to 6 months and from 6 to 12 months were considered. It was not possible to identify the proportion of parent-reported infections that lead to health service utilisation (Rowland et al., 2021). Other maternal and infant measures Request a detailed protocol Questionnaires during pregnancy and at birth were used to collect self-reported data on maternal age, household income, maternal education, and prenatal smoking (considered here as a dichotomous any/none exposure). Residential postcode was used to determine neighbourhood disadvantage using the Index of Relative Socio-Economic Disadvantage (IRSD) from the 2011 Socio-Economic Indexes for Areas (SEIFA) (Pink, 2013), with a lower score corresponding to greater socioeconomic disadvantage. Pre-eclampsia (based on International Association of Diabetes and Pregnancy Study Groups criteria; Tranquilli et al., 2014) and gestational diabetes (based on International Society for the Study of Hypertension in Pregnancy criteria; Nankervis et al., 2013) diagnoses were extracted from hospital records. Infant gestational age, birth weight, and mode of delivery (categorised as vaginal, planned caesarean section, or unplanned caesarean section delivery) were collected from birth records, and the age- and sex-standardised birth weight z-score was calculated using the 2009 revised British United Kingdom World Health Organisation (UK-WHO) growth charts (Cole et al., 2011). Postnatal smoking data was collected from questionnaire data, with mothers asked the average number of hours each day someone smoked near or in the same room as the child (Gray et al., 2019). This was dichotomised as any postnatal smoke exposure if >0 hr reported at any time point up to 12 months of age, or no postnatal smoke exposure. Breastfeeding duration up to 12 months of age was collected from maternal questionnaire data. As most evidence for the protective effect of breastfeeding on early life infection is from comparisons between any breastfeeding and no breastfeeding (Victora et al., 2016), and in light of previous evidence in BIS for an association between even a short duration of breastfeeding and lower odds of infection in early infancy (Rowland et al., 2021), we first looked at breastfeeding as a binary (any/none) measure in models (presented in the main text). As most infants (98.2%) were breastfed to some extent, and it is unknown the degree to which breastfeeding, and the timing of breastfeeding, might affect infant metabolomics and lipidomics, we also considered duration of breastfeeding as a continuous variable for sensitivity analyses. Metabolomic and lipidomic profiling Request a detailed protocol Venous peripheral blood was collected from infants at the 6- and 12-month time points in sodium heparin and generally processed within 4 hr, with a minority (197 of 555) of 12-month samples processed after 4 hr (median time for those 197 samples = 19.9 hr, inter-quartile range [IQR] [18.7, 21.4]). The time interval between collection and post-processing storage of samples was included as a covariate in analyses. Due to the bimodal distribution of 12-month sample collection times as samples were either processed same day of collection or the following day, sensitivity analysis excluding participants with a plasma storage time greater than 4 hr (197 out of 555 infants, predominantly processed the following day) was performed, as described in the Statistical analysis section below. Plasma was stored at –80°C, and aliquots were shipped on dry ice to Nightingale Health (Helsinki, Finland) for NMR metabolomic quantification and Baker IDI (Melbourne, Australia) for liquid chromatography/mass spectrometry (LC/MS) lipidomic quantification, as described below. For secondary analyses investigating possible 'reverse causality', that is, whether metabolomic or lipidomic profile at birth was associated with number of parent-reported infections from birth to 6 months of age, metabolomics and lipidomics data using the same platforms from venous cord blood collected at birth, as previously described (Burugupalli et al., 2022; Mansell et al., 2021), was used. The NMR-based metabolomics platform has been described in detail (Kettunen et al., 2016; Soininen et al., 2015), and quantified a broad range of metabolic measures including lipoprotein size subclasses, triglycerides, cholesterols, fatty acids, amino acids, ketone bodies, glycolysis metabolites, and GlycA. In brief, plasma samples were mixed with a sodium phosphate buffer prior to NMR measurements with Bruker AVANCE III 500 MHz and Bruker AVANCE III HD 600 MHz spectrometers (Bruker, Billerica, MA). Samples were kept at 6°C using the SampleJet sample changer (Bruker) to prevent degradation. After initial measurements, samples went through a multiple-step lipid extraction procedure using saturated sodium chloride solution, methanol, dichloromethane, and deuterochloroform. The lipid extracts were then analysed using the 600 MHz instrument (Soininen et al., 2015). The utility of this platform in epidemiological research has been detailed elsewhere (Würtz et al., 2017). Using the Nightingale Health 2016 bioinformatics protocol, 228 metabolomic measures were generated for the 12-month samples. From a subset of participants, replicate samples were quantified, and these showed a low percentage coefficient of variation (<10%). Subsequently, the Nightingale Health 2020 bioinformatics protocol was used to generate 250 metabolomic measures for the 6-month samples, with 224 of these measures also present in the 12-month data. As a large proportion of the NMR metabolomic measures are ratios and are strongly correlated with each other in children and adults (Ellul et al., 2019), an informative subset of 51 measures that captured the majority of variation in the metabolomic dataset, primarily absolute metabolite concentrations, were included in analysis presented in the main text. Analyses for excluded metabolomic measures are presented as supplementary data. To complement GlycA as a measure of inflammation, hsCRP was also quantified in 6- and 12-month plasma using enzyme-linked immunosorbent assay (ELISA) (R&D Systems, Minneapolis, MN, cat. no. DY1707), as per the manufacturer's instruction. The details of the high-performance LC/MS lipidomics platform have been described elsewhere (Beyene et al., 2020). In addition, we used medronic acid to passivate the LC/MS system to avoid peak tailing for acidic phospholipids (Hsiao et al., 2018). In brief, this platform quantified 776 lipid features in 36 lipid classes, including sphingolipids, glycerophospholipids, sterols, glycerolipids, and fatty acyls. Analysis was performed on an Agilent 6490 QQQ mass spectrometer with an Agilent 1290 series high-performance liquid chromatography system and two ZORBAX eclipse plus C18 column (2.1 × 100 mm 1.8 mm) (Agilent, Santa Clara, CA) with the thermostat set at 45°C. Mass spectrometry analysis was performed in both positive and negative ion mode with dynamic scheduled multiple reaction monitoring. Quantification of lipid species was determined by comparison to the relevant internal standard. Lipid class total concentrations were calculated as the sum of individual lipid species concentrations, except in the case of triacylglycerols (TGs) and alkyl-diacylglycerols, where we measured both neutral loss and single ion monitoring (SIM) peaks, and subsequently used the SIM species concentrations for summation purposes. Statistical analysis Request a detailed protocol Analyses were performed in R (version 3.6.3) (R Development Core Team, 2018). All metabolomic and lipidomic measures had their lowest observed non-zero value (considered the lower limit of detection) added to their value before they were natural log-transformed and scaled to a standard distribution (standard deviation units). Pearson's correlations were calculated for number of infections from birth to 12 months with 12-month GlycA and hsCRP. The estimated effect of number of parent-reported infections from birth to 12 months as an exposure on 12-month metabolomic and lipidomic profile was investigated using linear regression models for each metabolomic/lipidomic measure. Standard errors were used to calculate 95% confidence intervals for estimated effects. All models were adjusted for infant sex, exact age at 12-month time point, birth weight z-score, gestational age, maternal household income, exposure to maternal smoking during pregnancy, breastfeeding, and time from collection to storage for the plasma sample. Linear regression models adjusted for the same covariates were used to investigate 12-month GlycA and hsCRP as exposures and each metabolomic/lipidomic measure as an outcome. Two-tailed p-values were adjusted for multiple comparisons within each dataset (NMR metabolomics, LC/MS lipidomic species, and LC/MS lipidomic classes) using the Benjamini-Hochberg method (Benjamini and Hochberg, 1995). To investigate the robustness of the estimates, mean model coefficients and bias-corrected accelerated percentile bootstrap confidence intervals were calculated from nonparametric bootstrap resampling (1000 iterations) using the 'boot' package (Davison and Hinkley, 1997) (version 1.3–25) in R, included in Source Data. The assumption of linearity was investigated post hoc using plots of residual values for the top 10 metabolomic and lipidomic differences (ranked by p-value) for each of number of infections, GlycA, and hsCRP. To further investigate the other sources of potential confounding and variation that could affect findings from the primary models, several sensitivity analyses were performed. These were: (i) additional adjustment of the primary model for postnatal smoking exposure, gestational diabetes, and pre-eclampsia; (ii) analyses excluding twins (five infants); (iii) analyses excluding infants with hsCRP >5 mg/L (24 infants) as a marker of acute infection (Lemiengre et al., 2018; et al., analyses excluding plasma samples with hr from collection to storage (197 and analyses for breastfeeding duration of any Analyses of the primary models adjusted for measures of socioeconomic or maternal of household were also considered. These models are presented as supplementary plots analyses to investigate 6-month of infections were performed. The birth to 6-month models investigated the relationship between infections up to 6 months of age, 6-month inflammation, and 6-month metabolomic/lipidomic The 6- to 12-month models investigated the relationship of infections between 6 and 12 months of age, 12-month inflammation, and 12-month metabolomic/lipidomic with adjustment for the corresponding 6-month For secondary analyses to investigate regression models et al., were either for (i) each metabolomic/lipidomic measure from cord blood at birth as exposure and total number of infections from birth to 6 months of age as or (ii) each 6-month metabolomic/lipidomic measures as exposure and total number of infections from 6 to 12 months of age as the with adjustment for number of infections from birth to 6 months of age. All secondary models were adjusted for the same covariates as the primary models described that is, infant sex, gestational age, exact age 6- or 12-month time birth weight z-score, maternal household income, exposure to maternal smoking during pregnancy, and sample time between collection and post-processing with birth metabolomic/lipidomic measures as the exposure were adjusted for mode of which is associated with differences across NMR metabolomic measures in cord in this cohort et al., 2021). To investigate the potential role of inflammation in mediating associations between infection and metabolic the package et al., 2017) (version in R was then used in a to the natural effect mediated by and natural effect by of infection. 12-month GlycA or hsCRP were considered as for the effect of number of infections from birth to 12 months of age on metabolomic and lipidomic differences at 12 months, for metabolomic and lipidomic measures associated with number of infections with an adjusted from the linear regression models described mediation was calculated as the estimated natural effect by the total effect effect plus natural of the mediation model is in for model investigated in this The natural effect by glycoprotein acetyls or C-reactive protein and natural effect mediated by of parent-reported infections on metabolomic and lipidomic measures were with adjustment for were considered to for associations to exposure to and to As models investigating described suggested that 6-month GlycA or lipidomic measures may number of infections from 6 to 12 months of age, we performed mediation analyses to the percentage mediation of 12-month GlycA and hsCRP for the effect of number of infections from 6 to 12 months of age on 12-month metabolomic and lipidomic with additional adjustment for the corresponding 6-month measures of infections from birth to 6 months of age, 6-month GlycA or and the 6-month metabolomic/lipidomic Results The for the 555 infants included in this study is in and the cohort for these infants are in The number of total parent-reported infections from birth to 12 months of age was = infections from birth to 6 months of age was 2 and infections from 6 to 12 months of age was 12-month hsCRP and GlycA were mg/L and number of parent-reported infections between birth and 12 months of age was more strongly correlated with 12-month GlycA = than hsCRP = The of metabolomic and lipidomic measures at each time point for the cohort are in and (n = age at delivery smoking during pregnancy diabetes (n = (n = household to to to to (n = than year 10 of 10 of or 12 of or of birth caesarean caesarean postnatal smoke exposure to 12 months (n = of duration to weeks age weight weight at 6-month time point at 6 months z-score at 6 at 12-month time point at 12 months z-score at 12 of parent-reported infections from birth to 12 Infections from birth to 6 Infection from 6 to 12 GlycA at 6 months at 6 months at 12 months at 12 months All = 555 infants had complete covariate data for primary models, data of secondary exposures is to the relevant measure. lower value greater socioeconomic disadvantage on 2 of Barwon Infant Study participants included this study participants had complete infection data from time points between birth and 12 months of age, and 12-month plasma nuclear magnetic resonance (NMR) metabolomics data. included participants (n = out of 555) had 12-month plasma liquid chromatography/mass spectrometry (LC/MS) lipidomics data. Infection and inflammation burden and plasma NMR metabolomic profile at 12 months was evidence for higher number of infections with higher inflammatory markers per infection, 95% and hsCRP lower HDL to to and to cholesterols, lower to lower to higher and to a extent with higher triglycerides and lower to In models with GlycA as the marker of inflammation metabolomic differences observed for higher GlycA were largely similar but more those for parent-reported including HDL per in GlycA to higher and lipoprotein to higher apolipoprotein higher total fatty higher total triglycerides and amino and lower to metabolites lower to and lower to were generally similar to standard regression for models. effect were generally similar across most sensitivity analyses excluding samples with time greater than 4 hr the of estimated of parent-reported infections on HDL and hsCRP was associated with lower HDL cholesterol per in to to and to and higher to as observed for GlycA, and with lower of most other amino and to and higher triglycerides with 2 in 12-month plasma nuclear magnetic resonance (NMR) metabolomic measures for each in parent-reported infection to 12 and for each in 12-month glycoprotein acetyls (GlycA) (n = plots of the estimated 12-month metabolomic differences for each additional parent-reported infection from birth to 12 months or 12-month GlycA from adjusted linear regression models, and the

Simultaneous variable selection and parametric estimation for quantile regression

High‐dimensional data analysis emerges in many different areas of scientific research and social practice. Variable selection is an important task in statistical analysis for high‐dimensional data. The traditional all‐subset‐selection method can be ideal for variable selection, but it is computationally intractable in the high‐dimensional setting. In both regression and classification contexts, sparsity penalties are commonly used for the purpose of defining the complexity of the resulting model so as to achieve variable selection. The current article reviews a few important milestones and some recent works in the area of variable selection, especially those methods which useLqnorm and their variants as the penalty term. In particular, we review theLqpenalty, nonconvex penalties, among others. In ultrahigh‐dimensional data analysis, independence learning is often used for the purpose of dimension reduction. Theoretical results, methodological developments and computational innovations in regard to these methods are discussed. These variable selection techniques can be easily extended to problems beyond linear regression, such as classification, quantile regression, etc. Lastly, an interesting and promising research trend is the combination of multiple methods and we review several successful methods which fall into this category.This article is categorized under:Statistical and Graphical Methods of Data Analysis &gt; Modeling Methods and AlgorithmsStatistical Models &gt; Model SelectionStatistical Models &gt; Linear Models

Introduction: Quantile regression is a valuable alternative for survival data analysis, enabling flexible evaluations of covariate effects on survival outcomes with intuitive interpretations. It offers practical computation and reliability. However, challenges arise when applying quantile regression to censored data, particularly for upper quantiles. The minimum distance approach, utilizing dual-kernel estimation and the inverse cumulative distribution function, shows promise in addressing these challenges, especially with higher-dimensional covariates. Methods: This study contrasts two methods within the realm of quantile linear regression for survival analysis: check-based modeling and the minimum distance approach. Effectiveness is assessed across various scenarios through comprehensive simulation. Results: The simulation results showed that using the quantile regression model with the minimum distance approach reduces the percentage of root mean square error in parameter estimation compared to the quantile regression models based on the check loss function. Additionally, a larger sample size and reduced censoring percentage led to decreased root mean square error in parameter estimation. Conclusion: The research highlights the benefits of using the minimum distance approach for quantile regression. It reduces errors, improves model predictions, captures patterns, and optimizes parameters even with complete data. However, this approach has limitations. The accuracy of estimated quantiles can be influenced by the choice of distance metric and weighting scheme. The assumption of independence between censoring mechanism and survival time may not hold in real-world scenarios. Additionally, dealing with large datasets can be computationally complex.