Robust testing with generalized partial linear models for longitudinal data

By approximating the nonparametric component using a regression spline in generalized partial linear models (GPLM), robust generalized estimating equations (GEE), involving bounded score function and leverage-based weighting function, can be used to estimate the regression parameters in GPLM robustly for longitudinal data or clustered data. In this paper, score test statistics are proposed for testing the regression parameters with robustness, and their asymptotic distributions under the null hypothesis and a class of local alternative hypotheses are studied. The proposed score tests reply on the estimation of a smaller model without the testing parameters involved, and perform well in the simulation studies and real data analysis conducted in this paper.     

农村居民看病难、看病贵原因实证分析

利用扩展的线性支出系统模型(ELES),采用最小二乘法估计计算了我国农村居民的短期医疗服务需求价格弹性。研究结果表明:农村居民的短期医疗服务需求价格缺乏弹性。由于农村居民的短期医疗服务需求价格缺乏弹性,加上我国目前医疗体制存在的以药养医和医疗机构的逐利行为以及医疗市场缺乏有效的监管等问题,导致农村居民看病难、看病贵。解决这个问题,需要国家增加对卫生领域的投入,降低农民看病时自费的比例,增强卫生市场的竞争性,适当使医疗卫生资源向农村地区倾斜,并逐渐把医疗机构办成非盈利机构。     

Backfitting Random Varying-Coefficient Models with Time-Dependent Smoothing Covariates

Abstract.  In this paper, we propose a random varying-coefficient model for longitudinal data. This model is different from the standard varying-coefficient model in the sense that the time-varying coefficients are assumed to be subject-specific, and can be considered as realizations of stochastic processes. This modelling strategy allows us to employ powerful mixed-effects modelling techniques to efficiently incorporate the within-subject and between-subject variations in the estimators of time-varying coefficients. Thus, the subject-specific feature of longitudinal data is effectively considered in the proposed model. A backfitting algorithm is proposed to estimate the coefficient functions. Simulation studies show that the proposed estimation methods are more efficient in finite-sample performance compared with the standard local least squares method. An application to an AIDS clinical study is presented to illustrate the proposed methodologies.     

对基础研究投入问题的思考

文章首先从公共财政的角度对基础研究的投入进行分析,其次从布什和斯托克斯的科研模式角度对基础研究的投入进行分析。在此基础上对加大我国基础研究的投入提出了相关建议。     

Local influence in multilevel models

The authors study the local influence of observations in multilevel regression models. To this end, they perturb simultaneously the variances, responses and design matrix. To measure the local change caused by these perturbations, they use generalized Cook statistics for the fixed and random parameter estimates. Closed form local influence measures also allow them to assess the joint influence of various observations. They suggest a simple computation method and illustrate their results using two examples.     

Quantifying uncertainty in the biospheric carbon flux for England and Wales

Summary.  A crucial issue in the current global warming debate is the effect of vegetation and soils on carbon dioxide (CO₂) concentrations in the atmosphere. Vegetation can extract CO₂ through photosynthesis, but respiration, decay of soil organic matter and disturbance effects such as fire return it to the atmosphere. The balance of these processes is the net carbon flux. To estimate the biospheric carbon flux for England and Wales, we address the statistical problem of inference for the sum of multiple outputs from a complex deterministic computer code whose input parameters are uncertain. The code is a process model which simulates the carbon dynamics of vegetation and soils, including the amount of carbon that is stored as a result of photosynthesis and the amount that is returned to the atmosphere through respiration. The aggregation of outputs corresponding to multiple sites and types of vegetation in a region gives an estimate of the total carbon flux for that region over a period of time. Expert prior opinions are elicited for marginal uncertainty about the relevant input parameters and for correlations of inputs between sites. A Gaussian process model is used to build emulators of the multiple code outputs and Bayesian uncertainty analysis is then used to propagate uncertainty in the input parameters through to uncertainty on the aggregated output. Numerical results are presented for England and Wales in the year 2000. It is estimated that vegetation and soils in England and Wales constituted a net sink of 7.55 Mt C (1 Mt C = 10¹² g of carbon) in 2000, with standard deviation 0.56 Mt C resulting from the sources of uncertainty that are considered.     

Adaptive tests of regression functions via multiscale generalized likelihood ratios

Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. She derives the asymptotic joint distribution of the component tests and that of the proposed test under the null hypothesis. She also develops a simple method of selecting the smoothing parameters for the proposed test and presents two approximate methods for obtaining its P‐value. Finally, she evaluates the proposed test through simulations and illustrates its application to a set of real data.     

Choice of the primary analysis in longitudinal clinical trials

Missing data, and the bias they can cause, are an almost ever‐present concern in clinical trials. The last observation carried forward (LOCF) approach has been frequently utilized to handle missing data in clinical trials, and is often specified in conjunction with analysis of variance (LOCF ANOVA) for the primary analysis. Considerable advances in statistical methodology, and in our ability to implement these methods, have been made in recent years. Likelihood‐based, mixed‐effects model approaches implemented under the missing at random (MAR) framework are now easy to implement, and are commonly used to analyse clinical trial data. Furthermore, such approaches are more robust to the biases from missing data, and provide better control of Type I and Type II errors than LOCF ANOVA. Empirical research and analytic proof have demonstrated that the behaviour of LOCF is uncertain, and in many situations it has not been conservative. Using LOCF as a composite measure of safety, tolerability and efficacy can lead to erroneous conclusions regarding the effectiveness of a drug. This approach also violates the fundamental basis of statistics as it involves testing an outcome that is not a physical parameter of the population, but rather a quantity that can be influenced by investigator behaviour, trial design, etc. Practice should shift away from using LOCF ANOVA as the primary analysis and focus on likelihood‐based, mixed‐effects model approaches developed under the MAR framework, with missing not at random methods used to assess robustness of the primary analysis. Copyright © 2004 John Wiley & Sons, Ltd.     

BURR CRITICAL VALUE APPROXIMATIONS FOR TESTS OF AUTOCORRELATION AND HETEROSCEDASTICITY

The paper evaluates the accuracy of Burr approximations of critical values and p-values for test a of autocorrelation and heteroscedasticity in the linear regression model.     

关于线性互补问题的迭代算法

建立了一类求解线性互补问题的迭代算法。在一定条件下,研究了保证原问题的解存在唯一的充分条件,并且证明了新算法的收敛性。