Quantile regression for longitudinal data with a working correlation model

This paper proposes a linear quantile regression analysis method for longitudinal data that combines the between- and within-subject estimating functions, which incorporates the correlations between repeated measurements. Therefore, the proposed method results in more efficient parameter estimation relative to the estimating functions based on an independence working model. To reduce computational burdens, the induced smoothing method is introduced to obtain parameter estimates and their variances. Under some regularity conditions, the estimators derived by the induced smoothing method are consistent and have asymptotically normal distributions. A number of simulation studies are carried out to evaluate the performance of the proposed method. The results indicate that the efficiency gain for the proposed method is substantial especially when strong within correlations exist. Finally, a dataset from the audiology growth research is used to illustrate the proposed methodology.

Modeling strategies in longitudinal data analysis: Covariate, variance function and correlation structure selection

A modeling paradigm is proposed for covariate, variance and working correlation structure selection for longitudinal data analysis. Appropriate selection of covariates is pertinent to correct variance modeling and selecting the appropriate covariates and variance function is vital to correlation structure selection. This leads to a stepwise model selection procedure that deploys a combination of different model selection criteria. Although these criteria find a common theoretical root based on approximating the Kullback-Leibler distance, they are designed to address different aspects of model selection and have different merits and limitations. For example, the extended quasi-likelihood information criterion (EQIC) with a covariance penalty performs well for covariate selection even when the working variance function is misspecified, but EQIC contains little information on correlation structures. The proposed model selection strategies are outlined and a Monte Carlo assessment of their finite sample properties is reported. Two longitudinal studies are used for illustration.

Discussion of “Generalized estimating equations: Notes on the choice of the working correlation matrix”

Objective To discuss generalized estimating equations as an extension of generalized linear models by commenting on the paper of Ziegler and Vens "Generalized Estimating Equations. Notes on the Choice of the Working Correlation Matrix". Methods Inviting an international group of experts to comment on this paper. Results Several perspectives have been taken by the discussants. Econometricians have established parallels to the generalized method of moments (GMM). Statisticians discussed model assumptions and the aspect of missing data Applied statisticians; commented on practical aspects in data analysis. Conclusions In general, careful modeling correlation is encouraged when considering estimation efficiency and other implications, and a comparison of choosing instruments in GMM and generalized estimating equations, (GEE) would be worthwhile. Some theoretical drawbacks of GEE need to be further addressed and require careful analysis of data This particularly applies to the situation when data are missing at random.

Working-correlation-structure identification in generalized estimating equations

Selecting an appropriate working correlation structure is pertinent to clustered data analysis using generalized estimating equations (GEE) because an inappropriate choice will lead to inefficient parameter estimation. We investigate the well-known criterion of QIC for selecting a working correlation Structure. and have found that performance of the QIC is deteriorated by a term that is theoretically independent of the correlation structures but has to be estimated with an error. This leads LIS to propose a correlation information criterion (CIC) that substantially improves the QIC performance. Extensive simulation studies indicate that the CIC has remarkable improvement in selecting the correct correlation structures. We also illustrate our findings using a data set from the Madras Longitudinal Schizophrenia Study.

Criteria for working-correlation-structure selection in GEE: Assessment via simulation

Efficiency of analysis using generalized estimation equations is enhanced when intracluster correlation structure is accurately modeled. We compare two existing criteria (a quasi-likelihood information criterion, and the Rotnitzky-Jewell criterion) to identify the true correlation structure via simulations with Gaussian or binomial response, covariates varying at cluster or observation level, and exchangeable or AR(l) intracluster correlation structure. Rotnitzky and Jewell's approach performs better when the true intracluster correlation structure is exchangeable, while the quasi-likelihood criteria performs better for an AR(l) structure.

Unbiased estimating equations from working correlation models for irregularly timed repeated measures

The method of generalized estimating equation-, (GEEs) has been criticized recently for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. However, the feasibility and efficiency of GEE methods can be enhanced considerably by using flexible families of working correlation models. We propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance GEE. The supplementary estimating equations are obtained by differentiation of the Cholesky decomposition of the working correlation, or as score equations for decoupled Gaussian pseudolikelihood. The estimating equations are solved with computational effort equivalent to that required for a first-order GEE. Full details and analytic expressions are developed for a generalized Markovian model that was evaluated through simulation. Large-sample ".sandwich" standard errors for working correlation parameter estimates are derived and shown to have good performance. The proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children.

Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance

The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three-features of the analysis, namely (i) the discrepancy between the working correlation structure and the unobservable true correlation structure, (ii) the method by which the correlation parameters are estimated and (iii) the 'design', by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes. Analytical and numerical studies of realistic data-analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency. Protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a 'Gaussian estimation' pseudolikelihood procedure is used with an AR(1) structure.

Inverse Correlation between Vitamin D and C-Reactive Protein in Newborns

Some studies suggested that adequate vitamin D might reduce inflammation in adults. However, little is known about this association in early life. We aimed to determine the relationship between cord blood 25-hydroxyvitamin D (25(OH)D) and C-reactive protein (CRP) in neonates. Cord blood levels of 25(OH)D and CRP were measured in 1491 neonates in Hefei, China. Potential confounders including maternal sociodemographic characteristics, perinatal health status, lifestyle, and birth outcomes were prospectively collected. The average values of cord blood 25(OH)D and CRP were 39.43 nmol/L (SD = 20.35) and 6.71 mg/L (SD = 3.07), respectively. Stratified by 25(OH)D levels, per 10 nmol/L increase in 25(OH)D, CRP decreased by 1.42 mg/L (95% CI: 0.90, 1.95) among neonates with 25(OH)D <25.0 nmol/L, and decreased by 0.49 mg/L (95% CI: 0.17, 0.80) among neonates with 25(OH)D between 25.0 nmol/L and 49.9 nmol/L, after adjusting for potential confounders. However, no significant association between 25(OH)D and CRP was observed among neonates with 25(OH)D ≥50 nmol/L. Cord blood 25(OH)D and CRP levels showed a significant seasonal trend with lower 25(OH)D and higher CRP during winter-spring than summer-autumn. Stratified by season, a significant linear association of 25(OH)D with CRP was observed in neonates born in winter-spring (adjusted β = −0.11, 95% CI: −0.13, −0.10), but not summer-autumn. Among neonates born in winter-spring, neonates with 25(OH)D <25 nmol/L had higher risk of CRP ≥10 mg/L (adjusted OR = 3.06, 95% CI: 2.00, 4.69), compared to neonates with 25(OH)D ≥25 nmol/L. Neonates with vitamin D deficiency had higher risk of exposure to elevated inflammation at birth.

Single layer bismuth iodide: Computational exploration of structural, electrical, mechanical and optical properties

Layered graphitic materials exhibit new intriguing electronic structure and the search for new types of two-dimensional (2D) monolayer is of importance for the fabrication of next generation miniature electronic and optoelectronic devices. By means of density functional theory (DFT) computations, we investigated in detail the structural, electronic, mechanical and optical properties of the single-layer bismuth iodide (BiI3) nanosheet. Monolayer BiI3 is dynamically stable as confirmed by the computed phonon spectrum. The cleavage energy (Ecl) and interlayer coupling strength of bulk BiI3 are comparable to the experimental values of graphite, which indicates that the exfoliation of BiI3 is highly feasible. The obtained stress-strain curve shows that the BiI3 nanosheet is a brittle material with a breaking strain of 13%. The BiI3 monolayer has an indirect band gap of 1.57 eV with spin orbit coupling (SOC), indicating its potential application for solar cells. Furthermore, the band gap of BiI3 monolayer can be modulated by biaxial strain. Most interestingly, interfacing electrically active graphene with monolayer BiI3 nanosheet leads to enhanced light absorption compared to that in pure monolayer BiI3 nanosheet, highlighting its great potential applications in photonics and photovoltaic solar cells.

Spectral analysis of pair-correlation bandwidth: Application to cell biology images

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.

DFT study of electronic and optical properties of anatase titanium dioxide tuned by nitrogen and lithium co-doping

The electronic and optical properties of anatase titanium dioxide (TiO2), co-doped by nitrogen (N) and lithium (Li), have been investigated by density functional theory plus Hubbard correction term U, namely DFT+U. It is found that Li-dopants can effectively balance the net charges brought by N-dopants and shift the local state to the top of valence band. Depending on the distribution of dopants, the adsorption edges of TiO2 may be red- or blue-shifted, being consistent with recent experimental observations.

Ion irradiation as a tool for modifying the surface and optical properties of plasma polymerised thin films

Radio frequency (R.F.) glow discharge polyterpenol thin films were prepared on silicon wafers and irradiated with I10+ ions to fluences of 1 × 1010 and 1 × 1012 ions/cm2. Post-irradiation characterisation of these films indicated the development of well-defined nano-scale ion entry tracks, highlighting prospective applications for ion irradiated polyterpenol thin films in a variety of membrane and nanotube-fabrication functions. Optical characterisation showed the films to be optically transparent within the visible spectrum and revealed an ability to selectively control the thin film refractive index as a function of fluence. This indicates that ion irradiation processing may be employed to produce plasma-polymer waveguides to accommodate a variety of wavelengths. XRR probing of the substrate-thin film interface revealed interfacial roughness values comparable to those obtained for the uncoated substrate's surface (i.e., both on the order of 5 Å), indicating minimal substrate etching during the plasma deposition process.

Optical and surface characterization of radio frequency plasma polymerized 1-isopropyl-4-methyl-1,4-cyclohexadiene thin films

Low pressure radio frequency plasma-assisted deposition of 1-isopropyl-4-methyl-1,4-cyclohexadiene thin films was investigated for different polymerization conditions. Transparent, environmentally stable and flexible, these organic films are promising candidates for organic photovoltaics (OPV) and flexible electronics applications, where they can be used as encapsulating coatings and insulating interlayers. The effect of deposition RF power on optical properties of the films was limited, with all films being optically transparent, with refractive indices in a range of 1.57–1.58 at 500 nm. The optical band gap (Eg) of ~3 eV fell into the insulating Eg region, decreasing for films fabricated at higher RF power. Independent of deposition conditions, the surfaces were smooth and defect-free, with uniformly distributed morphological features and average roughness between 0.30 nm (at 10 W) and 0.21 nm (at 75 W). Films fabricated at higher deposition power displayed enhanced resistance to delamination and wear, and improved hardness, from 0.40 GPa for 10 W to 0.58 GPa for 75 W at a load of 700 μN. From an application perspective, it is therefore possible to tune the mechanical and morphological properties of these films without compromising their optical transparency or insulating property.

Analyzing hysteresis behavior of capacitance-voltage characteristics of IZO/C₆₀/pentacene/Au diodes with a hole-transport electron-blocking polyterpenol layer by electric-field-induced optical second-harmonic generation measurement

By using electric-field-induced optical second-harmonic generation (EFISHG) measurement, we analyzed hysteresis behavior of capacitance-voltage (C-V) characteristics of IZO/polyterpenol (PT)/C₆₀/pentacene/Au diodes, where PT layer is actively working as a hole-transport electron-blocking layer. The EFISHG measurement verified the presence of interface accumulated charges in the diodes, and showed that a space charge electric field from accumulated excess electrons (holes) that remain at the PT/C₆₀ (C₆₀/pentacene) interface is responsible for the hysteresis loop observed in the C-V characteristics.

Optical and chemical properties of polyterpenol thin films deposited via plasma-enhanced chemical vapor deposition

The development of novel organic polymer thin films is essential for the advancement of many emerging fields including organic electronics and biomedical coatings. In this study, the effect of synthesis conditions, namely radio frequency (rf) deposition power, on the material properties of polyterpenol thin films derived from nonsynthetic environmentally friendly monomer was investigated. At lower deposition powers, the polyterpenol films preserved more of the original monomer constituents, such as hydroxy functional groups; however, they were also softer and more hydrophilic compared to polymers fabricated at higher power. Enhanced monomer fragmentation and consequent reduction in the presence of the polar groups in the structure of the high-power samples reduced their optical band gap value from 2.95 eV for 10 W to 2.64 eV for 100 W. Regardless of deposition power, all samples were found to be optically transparent with smooth, defect-free, and homogenous surfaces.