Regression Estimation Using Multivariate Failure Time Data and a Common Baseline Hazard Function Model

Recent ‘marginal’ methods for the regression analysis of multivariate failure time data have mostly assumed Cox (1972)model hazard functions in which the members of the cluster have distinct baseline hazard functions. In some important applications, including sibling family studies in genetic epidemiology and group randomized intervention trials, a common baseline hazard assumption is more natural. Here we consider a weighted partial likelihood score equation for the estimation of regression parameters under a common baseline hazard model, and provide corresponding asymptotic distribution theory. An extensive series of simulation studies is used to examine the adequacy of the asymptotic distributional approximations, and especially the efficiency gain due to weighting, as a function of strength of dependency within cluster, and cluster size. This revised version was published online in July 2006 with corrections to the Cover Date.     

核子中价夸克极化分布函数的OCD标度破坏

本文通过对A-P方程作Mellin变换和对演化函数的Mellin变换结果作展开近似,求得了核子中价夸克极化分布函数随Q~2变化的解析表达式,并利用所得结果给出了核子中夸克自旋不对称量的一些理论预言     

Estimating stellar-oscillation-related parameters and their uncertainties with the moment method

Summary.  The moment method is a well-known astronomical mode identification technique in asteroseismology which uses a time series of the first three moments of a spectral line to estimate the discrete oscillation mode parameters l and m . The method, in contrast with many other mode identification techniques, also provides estimates of other important continuous parameters such as the inclination angle α and the rotational velocity v _e. We developed a statistical formalism for the moment method based on so-called generalized estimating equations. This formalism allows an estimation of the uncertainty of the continuous parameters, taking into account that the different moments of a line profile are correlated and that the uncertainty of the observed moments also depends on the model parameters. Furthermore, we set up a procedure to take into account the mode uncertainty, i.e. the fact that often several modes ( l ,  m ) can adequately describe the data. We also introduce a new lack-of-fit function which works at least as well as a previous discriminant function, and which in addition allows us to identify the sign of the azimuthal order m . We applied our method to star HD181558 by using several numerical methods, from which we learned that numerically solving the estimating equations is an intensive task. We report on the numerical results, from which we gain insight in the statistical uncertainties of the physical parameters that are involved in the moment method.     

Multiple imputation compared with restricted pseudo‐likelihood and generalized estimating equations for analysis of binary repeated measures in clinical studies

Non‐likelihood‐based methods for repeated measures analysis of binary data in clinical trials can result in biased estimates of treatment effects and associated standard errors when the dropout process is not completely at random. We tested the utility of a multiple imputation approach in reducing these biases. Simulations were used to compare performance of multiple imputation with generalized estimating equations and restricted pseudo‐likelihood in five representative clinical trial profiles for estimating (a) overall treatment effects and (b) treatment differences at the last scheduled visit. In clinical trials with moderate to high (40–60%) dropout rates with dropouts missing at random, multiple imputation led to less biased and more precise estimates of treatment differences for binary outcomes based on underlying continuous scores. Copyright © 2005 John Wiley & Sons, Ltd.     

广义集压缩映射原理及其对积分方程组的应用

本文对Banach空间中映射组证明了一个不动点定理.利用这个定理,我们给出了Banach空间中非线性Fredholm和Volterra积分方程组解的存在性定理,也获得了非线性Volterra积分方程组极值解的存在定理和比较定理.这些定理推广了文[1]中的相应结果.     

一类非线性退缩抛物方程解的唯一性

本文研究下述Cauchy问题（其中）广义解的唯一性问题，在一定条件下，得到了唯一性结论，并给出严格证明．     

代数微分方程组的可允许解

应用亚纯函数的Nevanlinna理论 ,讨论了代数微分方程组的可允许解 ,得到了不同于单个方程的结果     

The assessment of tumour response to treatment

Summary.  A parsimonious model for treated tumours is developed as a continuation of our previous work on regrowth curve theory. The statistical model belongs to the family of marginal non-linear models since the only linear parameters of the model are tumour specific and random facilitating parameter estimation. An important feature of the model is that it enables the estimation of the fraction of cancer cells surviving the treatment in vivo having easy-to-obtain longitudinal measurements of tumour volume. We compare several methods of estimation, including Lindstrom–Bates, iterated reweighted least squares and maximum likelihood. The last two methods are computed via the total estimating equations approach and variance least squares. The theory is illustrated with a photodynamic tumour therapy example.     

Bifurcation for a Type of Quasilinear Elliptic Equations On R" under the Natural Growth Conditions

The article proved the existence of H~1 (R) ∩ L~∞ (R~n) at the bifurcation λ= 0 by discussing the following nonlinear eigenvalue:—D-(ij)(a_(ij)(x,u)D_ju) +1/2a_(iju)(x,u)D_iuD_ju — q(x)|u|~σu = λu0≠u∈H~1(R~n) ,0<σ< 4/n,n≥3,x∈ R~nMeanwhile the article studied the conditions of q(x) under which λ=0 was a bifurcation point for the nonlinear eigenvalue . Here a_(ij) are not required to be bounded as u varies.     

Parameter estimation in a verhulst stochastic model

Summary Maximum likelihood estimation is a well-known statistical tool. When applied to the study of dynamical continuous-time phenomena, it requires some specific assumptions. In this paper we discuss some properties of the maximum likelihood estimator for a stochastic Verhulst model and we show some simulation results on the behaviour of the corresponding discrete estimator.