Confidence interval estimation of the difference between paired AUCs based on combined biomarkers

In many diagnostic studies, multiple diagnostic tests are performed on each subject or multiple disease markers are available. Commonly, the information should be combined to improve the diagnostic accuracy. We consider the problem of comparing the discriminatory abilities between two groups of biomarkers. Specifically, this article focuses on confidence interval estimation of the difference between paired AUCs based on optimally combined markers under the assumption of multivariate normality. Simulation studies demonstrate that the proposed generalized variable approach provides confidence intervals with satisfying coverage probabilities at finite sample sizes. The proposed method can also easily provide P-values for hypothesis testing. Application to analysis of a subset of data from a study on coronary heart disease illustrates the utility of the method in practice.     

A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model

In this note we consider the equality of the ordinary least squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of the estimable parametric function in the general Gauss–Markov model. Especially we consider the structures of the covariance matrix V for which the OLSE equals the BLUE. Our results are based on the properties of a particular reparametrized version of the original Gauss–Markov model.      

Efficiency of the generalized-difference-based weighted mixed almost unbiased two-parameter estimator in partially linear model

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in partially linear model when the errors are correlated. A generalized-difference-based almost unbiased two-parameter estimator is defined for the vector parameter β. Under the linear stochastic constraint r = Rβ + e, we introduce a new generalized-difference-based weighted mixed almost unbiased two-parameter estimator. The performance of this new estimator over the generalized-difference-based estimator and generalized- difference-based almost unbiased two-parameter estimator in terms of the MSEM criterion is investigated. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real dataset.     

Bayesian quantile regression for skew-normal linear mixed models

Linear mixed models have been widely used to analyze repeated measures data which arise in many studies. In most applications, it is assumed that both the random effects and the within-subjects errors are normally distributed. This can be extremely restrictive, obscuring important features of within-and among-subject variations. Here, quantile regression in the Bayesian framework for the linear mixed models is described to carry out the robust inferences. We also relax the normality assumption for the random effects by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in the linear mixed models. For posterior inference, we propose a Gibbs sampling algorithm based on a mixture representation of the asymmetric Laplace distribution and multivariate skew-normal distribution. The procedures are demonstrated by both simulated and real data examples.     

Generalized empirical likelihood inference in partially linear model for longitudinal data with missing response variables and error-prone covariates

In this article, we consider statistical inference for longitudinal partial linear models when the response variable is sometimes missing with missingness probability depending on the covariate that is measured with error. A generalized empirical likelihood (GEL) method is proposed by combining correction attenuation and quadratic inference functions. The method that takes into consideration the correlation within groups is used to estimate the regression coefficients. Furthermore, residual-adjusted empirical likelihood (EL) is employed for estimating the baseline function so that undersmoothing is avoided. The empirical log-likelihood ratios are proven to be asymptotically Chi-squared, and the corresponding confidence regions for the parameters of interest are then constructed. Compared with methods based on NAs, the GEL does not require consistent estimators for the asymptotic variance and bias. The numerical study is conducted to compare the performance of the EL and the normal approximation-based method, and a real example is analysed.     

Testing for bioequivalence of highly variable drugs from TR‐RT crossover designs with heterogeneous residual variances

Traditional bioavailability studies assess average bioequivalence (ABE) between the test (T) and reference (R) products under the crossover design with TR and RT sequences. With highly variable (HV) drugs whose intrasubject coefficient of variation in pharmacokinetic measures is 30% or greater, assertion of ABE becomes difficult due to the large sample sizes needed to achieve adequate power. In 2011, the FDA adopted a more relaxed, yet complex, ABE criterion and supplied a procedure to assess this criterion exclusively under TRR‐RTR‐RRT and TRTR‐RTRT designs. However, designs with more than 2 periods are not always feasible. This present work investigates how to evaluate HV drugs under TR‐RT designs. A mixed model with heterogeneous residual variances is used to fit data from TR‐RT designs. Under the assumption of zero subject‐by‐formulation interaction, this basic model is comparable to the FDA‐recommended model for TRR‐RTR‐RRT and TRTR‐RTRT designs, suggesting the conceptual plausibility of our approach. To overcome the distributional dependency among summary statistics of model parameters, we develop statistical tests via the generalized pivotal quantity (GPQ). A real‐world data example is given to illustrate the utility of the resulting procedures. Our simulation study identifies a GPQ‐based testing procedure that evaluates HV drugs under practical TR‐RT designs with desirable type I error rate and reasonable power. In comparison to the FDA's approach, this GPQ‐based procedure gives similar performance when the product's intersubject standard deviation is low (≤0.4) and is most useful when practical considerations restrict the crossover design to 2 periods.     

教育期望中的班级效应分析

班级是中国基础教育领域重要的组织设置。利用“中国教育追踪调查”（CEPS）数据,应用分层线性模型,本研究关注班级设置,包括班级组织结构和班级氛围,对初中生教育期望的影响。研究结果表明,在多个组织结构变量中,班主任的受教育程度和教龄对学生教育期望影响显著,但任课老师的资历影响不显著;在多个班级氛围变量中,学生的教育期望既受到班级客观学业水平的影响,亦受到师生之间互动关系的影响。此外,在控制了班级氛围变量后,师资配置对学生教育期望的影响不再显著。总之,在以往研究重点关注个体、家庭和学校影响的基础上,本研究将对教育期望的研究进一步拓展到学校内部的班级环境,并发现师生之间建立的紧密互动关系及良好的班级氛围对学生的教育期望发挥着最重要的影响。     

Trajectory of problem behaviours of Korean adopted children: using piecewise hierarchical linear growth modelling

This study examined the trajectory of problem behaviours in domestically adopted children in South Korea as they aged. This study used the Panel Study on Korean Adopted Children's longitudinal, three‐wave data (2006, 2008 and 2010). Although data were collected at three time points, our data consisted of six time points, which covered the 5–10 years age range of the adopted children at the time of survey. One hundred sixty‐four children were included in the analysis, 75 of whom contributed to one time point, 74 to two time points and 15 to three time points. The trajectory of the problem behaviours of adopted children was examined using a piecewise hierarchical linear growth model. Because the initial exploration of the data suggested non‐linear changes in behaviour problems over time, we split the growth trajectory into two time periods: Time 1 (5–7 years) and Time 2 (7–10 years). A two‐rate model was used to estimate separate slopes for the two time periods. Results showed that the externalizing and internalizing problems of adopted children have different trajectories. Internalizing problems did not show significant changes after 5 years of age, while externalizing problems increased until 7 years of age and decreased significantly thereafter.