BACKGROUND: In studies of occupational health, longitudinal environmental exposure, and biomonitoring data are often subject to right skewing and left censoring, in which measurements fall below the limit of detection (LOD). To address right-skewed data, it is common practice to log-transform the data and model the geometric mean, assuming a log-normal distribution. However, if the transformed data do not follow a known distribution, modeling the mean of exposure may result in bias and reduce efficiency. In addition, when examining longitudinal data, it is possible that certain covariates may vary over time.
OBJECTIVE: To develop predictive quantile regression models to resolve the issues of left censoring and time-dependent covariates and to quantitatively evaluate if previous and current covariates can predict current and/or future exposure levels.
METHODS: To address these gaps, we suggested incorporating different substitution approaches into quantile regression and utilizing a method for selecting a working type of time dependency for covariates.
RESULTS: In a simulation study, we demonstrated that, under different types of time-dependent covariates, the approach of multiple random value imputation outperformed the other approaches. We also applied our methods to a carbon nanotube and nanofiber exposure study. The dependent variables are the left-censored mass of elemental carbon at both the respirable and inhalable aerosol size fractions. In this study, we identified some potential time-dependent covariates with respect to worker-level determinants and job tasks.
CONCLUSIONS: Time dependency for covariates is rarely accounted for when analyzing longitudinal environmental exposure and biomonitoring data with values less than the LOD through predictive modeling. Mistreating the time-dependency as time-independency will lead to an efficiency loss of regression parameter estimation. Therefore, we addressed time-varying covariates in longitudinal exposure and biomonitoring data with left-censored measurements and illustrated an entire conditional distribution through different quantiles.

UNASSIGNED: High blood pressure (BP) is a key contributor to the burden of disease. This study aimed to assess: a) educational differences across the entire BP distribution, and b) educational differences in the trajectories of BP across the adult life course.
UNASSIGNED: Longitudinal data from the Stockholm Diabetes Prevention Program was analysed using quantile regression and linear mixed effects models. Models were adjusted for age, sex, lifestyle, and BP medication.
UNASSIGNED: Lower educational level was associated with higher systolic BP (SBP) at all follow-up periods. Age and sex adjusted mean SBP was 2.49 (95% confidence interval (CI) 1.10, 3.87), 3.95 (95% CI 2.45, 5.45) and 2.61 (95% CI 1.09, 4.13) mmHg higher for people with pre-secondary education compared with post-secondary at baseline, 10 years and 20 years follow-up, respectively. Quantile regressions revealed that the inequalities could be observed across the entire BP continuum. Longitudinally analysed, people with pre-secondary education had 3.01 (95% CI 1.91-4.11) mmHg higher SBP than those with post-secondary education, age and sex adjusted. No significant convergence or divergence of the educational gaps in SBP was observed. Educational differences remained even after adjusting for lifestyle and BP medication.
UNASSIGNED: These results imply that public health interventions should aim to bring about distributional shifts in blood pressure, rather than exclusively focusing on hypertensive people, if they are to effectively minimize the educational disparities in blood pressure and its consequences.

Quantifying how an exposure affects the entire outcome distribution is often important, e.g., for outcomes such as blood pressure which have non-linear effects on long-term morbidity and mortality. Quantile regressions offer a powerful way of estimating an exposure\'s relationship with the outcome distribution but remain underused in epidemiology. We introduce quantile regressions with a focus on distinguishing estimators for quantiles of the conditional and unconditional outcome distributions. We also present an empirical example in which we fit mean and quantile regressions to investigate educational attainment\'s association with later-life systolic blood pressure (SBP). We use data on 8,875 US-born respondents aged 50+ years from the US Health and Retirement Study. More education was negatively associated with mean SBP. Conditional and unconditional quantile regressions both suggested a negative association between education and SBP at all levels of SBP, but the absolute magnitudes of these associations were higher at higher SBP quantiles relative to lower quantiles. In addition to showing that educational attainment shifted the SBP distribution left-wards, quantile regression results revealed that education may have reshaped the SBP distribution through larger protective associations in the right tail, thus benefiting those at highest risk of cardiovascular diseases.

OBJECTIVE: Research on parent-child interaction (PCI) and its impact on children\'s weight status is a thriving study area. However, their potential pathways have not been established. This study investigated the association between PCI and children\'s body-mass index z score (BMIz) examining the role of appetite self-regulation (ASR) as a mediator.
METHODS: Mediation analysis.
METHODS: We included children from 33 kindergartens in Wuhan with parents\' consent, measuring children\'s height and weight, and calculating BMIz. To assess the PCI quality, we utilized the Brigance Parent-Child Interactions Scale. Additionally, children\'s ASR was tested by satiety responsiveness (SR) and food responsiveness (FR) using the Children\'s Eating Behavior Questionnaire. Quantile regression was employed to examine the PCI-BMIz association, while mediation analysis was conducted to explore ASR\'s mediating effect on the relationship between PCI and BMIz.
RESULTS: Of 3973 children (53.88% boys) included in the analysis, the mean BMIz was 0.24 ± 1.13. The results revealed that children with poorer PCI quality have higher BMIz across all selected BMIz percentiles, except for the 5th percentile. Furthermore, these associations were significant across most percentiles, whether for boys or girls. Mediation analysis suggested that these associations were partially mediated by children\'s ASR (indFR = -0.026, PFR < 0.001; indSR = -0.058, PSR < 0.001), with stronger effects observed among boys.
CONCLUSIONS: The variation in how strongly BMIz was linked to PCI across different percentiles suggests that children with poorer PCI have higher BMIz. The link is partially mediated through children\'s ASR. It\'s important to pay attention to the PCI quality in children with higher BMIz levels, especially in boys.

This paper considers estimating functional-coefficient models in panel quantile regression with individual effects, allowing the cross-sectional and temporal dependence for large panel observations. A latent group structure is imposed on the heterogenous quantile regression models so that the number of nonparametric functional coefficients to be estimated can be reduced considerably. With the preliminary local linear quantile estimates of the subject-specific functional coefficients, a classic agglomerative clustering algorithm is used to estimate the unknown group structure and an easy-to-implement ratio criterion is proposed to determine the group number. The estimated group number and structure are shown to be consistent. Furthermore, a post-grouping local linear smoothing method is introduced to estimate the group-specific functional coefficients, and the relevant asymptotic normal distribution theory is derived with a normalisation rate comparable to that in the literature. The developed methodologies and theory are verified through a simulation study and showcased with an application to house price data from UK local authority districts, which reveals different homogeneity structures at different quantile levels.

Species exploiting seasonal environments must alter timings of key life-history events in response to large-scale climatic changes in order to maintain trophic synchrony with required resources. Yet, substantial among-species variation in long-term phenological changes has been observed. Advancing from simply describing such variation towards predicting future phenological responses requires studies that rigorously quantify and explain variation in the direction and magnitude of changing timings across diverse species in relation to key ecological and life-history variables. Accordingly, we fitted multi-quantile regressions to 59 years of multi-species data on spring and autumn bird migration timings through northern Scotland. We demonstrate substantial variation in changes in timings among 72 species, and tested whether such variation can be explained by species ecology, life-history and changes in local abundance. Consistent with predictions, species that advanced their migration timing in one or both seasons had more seasonally restricted diet types, fewer suitable breeding habitat types, shorter generation lengths and capability to produce multiple offspring broods per year. In contrast, species with less seasonally restricted diet types and that produce single annual offspring broods, showed no change. Meanwhile, contrary to prediction, long-distance and short-distance migrants advanced migration timings similarly. Changes in migration timing also varied with changes in local migratory abundance, such that species with increasing seasonal abundance apparently altered their migration timing, whilst species with decreasing abundance did not. Such patterns broadly concur with expectation given adaptive changes in migration timing. However, we demonstrate that similar patterns can be generated by numerical sampling given changing local abundances. Any apparent phenology-abundance relationships should, therefore, be carefully validated and interpreted. Overall, our results show that migrant bird species with differing ecologies and life-histories showed systematically differing phenological changes over six decades contextualised by large-scale environmental changes, potentially facilitating future predictions and altering temporal dynamics of seasonal species co-occurrences.

BACKGROUND: Audiological diagnosis and rehabilitation often involve the assessment of whether the maximum speech identification score (PBmax) is poorer than expected from the pure-tone average (PTA) threshold. This requires the estimation of the lower boundary of the PBmax values expected for a given PTA (one-tailed 95% confidence limit, CL). This study compares the accuracy and consistency of three methods for estimating the 95% CL.
METHODS: The 95% CL values were estimated using a simulation method, the Harrell-Davis (HD) estimator, and non-linear quantile regression (nQR); the latter two are both distribution-free methods. The first two methods require the formation of sub-groups with different PTAs. Accuracy and consistency in the estimation of the 95% CL were assessed by applying each method to many random samples of 50% of the available data and using the fitted parameters to predict the data for the remaining 50%.
METHODS: A total of 642 participants aged 17 to 84 years with sensorineural hearing loss were recruited from audiology clinics. Pure-tone audiograms were obtained and PBmax scores were measured using monosyllables at 40 dB above the speech recognition threshold or at the most comfortable level.
RESULTS: For the simulation method, 6.7 to 8.2% of the PBmax values fell below the 95% CL for both ears, exceeding the target value of 5%. For the HD and nQR methods, the PBmax values fell below the estimated 95% CL for approximately 5% of the ears, indicating good accuracy. Consistency, estimated from the standard deviation of the deviations from the target value of 5%, was similar for all the methods.
CONCLUSIONS: The nQR method is recommended because it has good accuracy and consistency, and it does not require the formation of arbitrary PTA sub-groups.

This research was conducted using many spatial analysis approaches to dissect the spatiotemporal interactive characteristics of carbon emission intensity within the transportation sector from 2002 to 2020. An in-depth exploration of their transition mechanisms was conducted by nesting the obtained timewarp types with the panel quantile model. Finally, the geodetector model aligned with different transition mechanisms was employed to investigate and analyze the interaction effects among various factors influencing carbon intensity in the transportation sector. The results indicated that:① The carbon emission intensity of the transportation sector in 30 provinces and regions of China showed an overall downward trend with fluctuations, and the spatial clustering level was relatively stable. ② The spatiotemporal interactive features of ESTDA revealed that the relationship between the northwest region and its adjacent spatial units was unstable, with significant variations and fluctuations. In contrast, economically developed areas such as coastal cities in the eastern part had established mature transportation networks, resulting in a relatively stable local spatial pattern, though a few areas still exhibited spatiotemporal competitiveness. ③ The spatiotemporal transition of carbon intensity in the transportation sector could be categorized into four driving or constraining modes(the population economy urbanization constraint model, population economy urbanization facility constraint model, technology consumption industry-driven model, and technology industry regulation-driven model). Most provinces were influenced by the low quantile constraint and high quantile drive modes, with only a few affected by the high quantile constraint and low quantile drive modes, the majority of which were located in the northwest or southwest regions. ④ Further, we introduced the geographical detector model based on the identified mechanism of carbon emission intensity transition in the transportation sector, emphasizing the coordinated development of multiple factors and strengthening inter-regional collaborative governance.

It is crucial to provide adequate iodine nutrition to infants and toddlers for proper thyroid function and subsequent brain development. Infants are particularly vulnerable to iodine deficiency during the transition from a milk-based diet (breast milk and/or infant formula) to solid food. This study examines the current iodine levels of children during their first two years of life and investigates the association between these levels and feeding behaviors and the iodine status of their mothers in Shanghai, a city located in eastern China. A hospital-based cohort study was conducted to enroll mother-child pairs, where the child is aged 6-23 months, who visited community health service centers in the 16 districts of Shanghai, China. Data on socio-demographic factors and feeding behavior data were collected from the participants. The urinary iodine concentration (UIC) in both the young children and their mothers were analyzed. A total of 2282 mother-child pairs were included in this analysis. The median (p25-p75) UIC for lactating women, weaning women, and children were 121.3 μg/L (68.1-206.4 μg/L), 123.4 μg/L (58.4-227.2 μg/L), and 152.1 μg/L (75.8-268.3 μg/L), respectively. The UIC in children was found to be higher than that in their mothers (p < 0.001). Children who consumed less than 500 mL per day of formula milk in the last week had lower UICs compared with those who consumed 500 mL per day or more (p = 0.026). Furthermore, the children\'s UIC was positively correlated with the maternal UIC (rs = 0.285, p < 0.001). Multiple quantile regression analysis revealed a statistically significant positive association between maternal UIC and children\'s UIC between the 0.1 and 0.9 quantiles (all p < 0.001). We found that the iodine status of infants and toddlers, as well as of mothers, was sufficient. However, a large minority of children and mothers may be at risk of iodine deficiency. Furthermore, no associations between children\'s UIC and feeding behaviors were observed. Moreover, there was a positive correlation between the UIC of young children and their mothers.

This paper introduces a new family of quantile regression models whose response variable follows a reparameterized Marshall-Olkin distribution indexed by quantile, scale, and asymmetry parameters. The family has arisen by applying the Marshall-Olkin approach to distributions belonging to the location-scale family. Models of higher flexibility and whose structure is similar to generalized linear models were generated by quantile reparameterization. The maximum likelihood (ML) method is presented for the estimation of the model parameters, and simulation studies evaluated the performance of the ML estimators. The advantages of the family are illustrated through an application to a set of nutritional data, whose results indicate it is a good alternative for modeling slightly asymmetric response variables with support on the real line.