Smoothed rank-based procedure for censored data

A smoothed rank-based procedure is developed for the accelerated failure time model to overcome computational issues. The proposed estimator is based on an EM-type procedure coupled with the induced smoothing. "The proposed iterative approach converges provided the initial value is based on a consistent estimator, and the limiting covariance matrix can be obtained from a sandwich-type formula. The consistency and asymptotic normality of the proposed estimator are also established. Extensive simulations show that the new estimator is not only computationally less demanding but also more reliable than the other existing estimators.

Efficient estimation for rank-based regression with clustered data

Rank-based inference is widely used because of its robustness. This article provides optimal rank-based estimating functions in analysis of clustered data with random cluster effects. The extensive simulation studies carried out to evaluate the performance of the proposed method demonstrate that it is robust to outliers and is highly efficient given the existence of strong cluster correlations. The performance of the proposed method is satisfactory even when the correlation structure is misspecified, or when heteroscedasticity in variance is present. Finally, a real dataset is analyzed for illustration.

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.

Rank regression for accelerated failure time model with clustered and censored data

For clustered survival data, the traditional Gehan-type estimator is asymptotically equivalent to using only the between-cluster ranks, and the within-cluster ranks are ignored. The contribution of this paper is two fold: - (i) incorporating within-cluster ranks in censored data analysis, and; - (ii) applying the induced smoothing of Brown and Wang (2005, Biometrika) for computational convenience. Asymptotic properties of the resulting estimating functions are given. We also carry out numerical studies to assess the performance of the proposed approach and conclude that the proposed approach can lead to much improved estimators when strong clustering effects exist. A dataset from a litter-matched tumorigenesis experiment is used for illustration.

Rank regression analysis of correlated water quality data from South East Queensland

With growing population and fast urbanization in Australia, it is a challenging task to maintain our water quality. It is essential to develop an appropriate statistical methodology in analyzing water quality data in order to draw valid conclusions and hence provide useful advices in water management. This paper is to develop robust rank-based procedures for analyzing nonnormally distributed data collected over time at different sites. To take account of temporal correlations of the observations within sites, we consider the optimally combined estimating functions proposed by Wang and Zhu (Biometrika, 93:459-464, 2006) which leads to more efficient parameter estimation. Furthermore, we apply the induced smoothing method to reduce the computational burden. Smoothing leads to easy calculation of the parameter estimates and their variance-covariance matrix. Analysis of water quality data from Total Iron and Total Cyanophytes shows the differences between the traditional generalized linear mixed models and rank regression models. Our analysis also demonstrates the advantages of the rank regression models for analyzing nonnormal data.

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.

Rank regression for analysis of clustered data: A natural induced smoothing approach

We consider rank regression for clustered data analysis and investigate the induced smoothing method for obtaining the asymptotic covariance matrices of the parameter estimators. We prove that the induced estimating functions are asymptotically unbiased and the resulting estimators are strongly consistent and asymptotically normal. The induced smoothing approach provides an effective way for obtaining asymptotic covariance matrices for between- and within-cluster estimators and for a combined estimator to take account of within-cluster correlations. We also carry out extensive simulation studies to assess the performance of different estimators. The proposed methodology is substantially Much faster in computation and more stable in numerical results than the existing methods. We apply the proposed methodology to a dataset from a randomized clinical trial.

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.

Weighted rank regression for clustered data analysis

We consider ranked-based regression models for clustered data analysis. A weighted Wilcoxon rank method is proposed to take account of within-cluster correlations and varying cluster sizes. The asymptotic normality of the resulting estimators is established. A method to estimate covariance of the estimators is also given, which can bypass estimation of the density function. Simulation studies are carried out to compare different estimators for a number of scenarios on the correlation structure, presence/absence of outliers and different correlation values. The proposed methods appear to perform well, in particular, the one incorporating the correlation in the weighting achieves the highest efficiency and robustness against misspecification of correlation structure and outliers. A real example is provided for illustration.

Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

Rank-based regression for analysis of repeated measures

We consider rank-based regression models for repeated measures. To account for possible withinsubject correlations, we decompose the total ranks into between- and within-subject ranks and obtain two different estimators based on between- and within-subject ranks. A simple perturbation method is then introduced to generate bootstrap replicates of the estimating functions and the parameter estimates. This provides a convenient way for combining the corresponding two types of estimating function for more efficient estimation.

A modified pseudolikelihood approach for analysis of longitudinal data

We consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters. In general, inconsistent estimators of the covariance (variance/correlation) parameters will be produced when the "working" correlation matrix is misspecified, which may result in great loss of efficiency of the mean parameter estimators (albeit the consistency is preserved). We consider using different "Working" correlation models for the variance and the mean parameters. In particular, we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified. The designated "working" correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters. Simulation studies indicate that the proposed algorithm performs very well. We also applied different estimation procedures to a data set from a clinical trial for illustration.

Robust estimating functions and bias correction for longitudinal data analysis

Robust methods are useful in making reliable statistical inferences when there are small deviations from the model assumptions. The widely used method of the generalized estimating equations can be "robustified" by replacing the standardized residuals with the M-residuals. If the Pearson residuals are assumed to be unbiased from zero, parameter estimators from the robust approach are asymptotically biased when error distributions are not symmetric. We propose a distribution-free method for correcting this bias. Our extensive numerical studies show that the proposed method can reduce the bias substantially. Examples are given for illustration.

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.

Assignment of fundamental vibrations of. ,N'-dimethylthiourea,

The infrared spectra of symmetric N,N′-dimethylthiourea (s-DMTU) and its N-deuterated (s-DMTU-d2) species have been measured. The fundamental frequencies have been assigned by comparison with the assignments in structurally related molecules and the infrared band shifts on N-deuteration, S-methylation, available Raman data and with the aid of theoretical band assignments from normal coordinate treatments for s-DMTU-d0 and -d2. A force field is derived for s-DMTU by transferring the force constants chiefly from N-methylthiourea and the subsequent refinement of the force constants by a least squares procedure.