Estimation of multi-state models with missing covariate values based on observed data likelihood

Abstract

Continuous-time multi-state models are commonly used to study diseases with multiple stages. Potential risk factors associated with the disease are added to the transition intensities of the model as covariates, but missing covariate measurements arise frequently in practice. We propose a likelihood-based method that deals efficiently with a missing covariate in these models. Our simulation study showed that the method performs well for both “missing completely at random” and “missing at random” mechanisms. We also applied our method to a real dataset, the Einstein Aging Study.     

Auxiliary covariate in additive hazards regression for survival data

We consider the additive hazards regression analysis by utilising auxiliary covariate information to improve the efficiency of the statistical inference when the primary covariate is ascertained only for a randomly selected subsample. We construct a martingale-based estimating equation for the regression parameter and establish the asymptotic consistency and normality of the resultant estimator. Simulation study shows that our proposed method can improve the efficiency compared with the estimator which discards the auxiliary covariate information. A real example is also analysed as an illustration.     

国际油气价格与汇率动态相依关系研究:基于一种新的时变最优Copula模型

本文提出一个新的时变最优Copula模型,可以准确识别二元时间序列任意时点最优的相依结构。该模型构造了半旋转copula以刻画非对称的反向相依关系,并引入独立性的无分布检验证实相依关系的存在性。同时,我们对能源商品市场（原油、天然气）、外汇市场间动态相依关系进行了实证分析,实证结果表明跨市场相依结构类型确实是时变的,突发事件往往是相依结构突变的主因。另外,时变最优Copula模型的主要优势在于不仅能够捕捉相依方向和相依强度的动态性,还能有效捕捉相依结构类型的动态性。     

3PL参与的时变需求变质品三级供应链模型

随着现代物流业的发展,企业将一些业务如运输等外包已经成为参与当今市场竞争的一种手段和趋势,因此考虑包含第三方物流服务提供商（3PL）的供应链更具有现实和理论意义。但是现有文献很少考虑3PL对包含时间因素的变质品供应链模型的影响。基于此,本文建立了一个包含3PL的时变需求变质品三级供应链模型,并运用动态博弈理论求解了该模型的分散式下的均衡解。研究表明与制造商单独承担运输费用相比,由3PL承担运输费用使得产品的订货周期缩短,订货量减少。通过对比分散式决策和集中式决策下的最优解,研究发现考虑系统总体利润情况下,集中式决策的方式不能使该供应链达到协调。最后给出算例验证结论的正确性。     

Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates

This article investigates the asymptotic properties of the Gaussian quasi-maximum-likelihood estimators (QMLE’s) of the GARCH model augmented by including an additional explanatory variable—the so-called GARCH-X model. The additional covariate is allowed to exhibit any degree of persistence as captured by its long-memory parameter d_x; in particular, we allow for both stationary and nonstationary covariates. We show that the QMLE’s of the parameters entering the volatility equation are consistent and mixed-normally distributed in large samples. The convergence rates and limiting distributions of the QMLE’s depend on whether the regressor is stationary or not. However, standard inferential tools for the parameters are robust to the level of persistence of the regressor with t-statistics following standard Normal distributions in large sample irrespective of whether the regressor is stationary or not. Supplementary materials for this article are available online.     

预测精度和成本双时变的短生命周期产品供应链优化与协调

对于提前期可压缩的短生命周期产品供应链,压缩提前期可以提高销售商的需求预测精度,但增加了制造商的生产成本,因而供应链面临何时订货、订多少,以及如何实现Pareto改进的挑战。通过建立数学模型并求解,分析了分散系统和集中系统的最优决策,进一步开发了一个激励方案以实现供应链成员之间的协调。研究结果表明:具有订货回馈与惩罚的动态批发价契约能够有效协调双时变参数供应链,契约参数α在一定范围内取值可实现供需双方共赢。     

Instrumental variable-based empirical likelihood inferences for varying-coefficient models with error-prone covariates

This paper presents the empirical likelihood inferences for a class of varying-coefficient models with error-prone covariates. We focus on the case that the covariance matrix of the measurement errors is unknown and neither repeated measurements nor validation data are available. We propose an instrumental variable-based empirical likelihood inference method and show that the proposed empirical log-likelihood ratio is asymptotically chi-squared. Then, the confidence intervals for the varying-coefficient functions are constructed. Some simulation studies and a real data application are used to assess the finite sample performance of the proposed empirical likelihood procedure.     

A note on the multivariate miser for balancing experiments

The MISER criterion for pre-experiment balancing of experiments that will be analyzed by the analysis of covariance was proposed by Press (1987). The idea was to minimize, over all designs, the inflation produced by design imbalance (inequality of cell covariate vectors) , of the average standard errors of contrasts. In this note we consider the balancing problem in the case of multiple response experiments, and we show that under certain reasonable assumptions, the multivariate result is analogous to that in the univariate case.     

Asymptotic efficiency of a competing risks model: A two-sample case

A generalized Cox regression model is studied for the covariance analysis of competing risks data subject to independent random censoring. The information of the maximum partial likelihood estimates is compared with that of maximum likelihood estimates assuming a log linear hazard function.The method of generalized variance is used to define the efficiency of estimation between the two models. This is then applied to two-sample problems with two exponentially censoring rates. Numerical results are summarized ane presented graphically.The detailed results indicate that the semi-parametric model wrks well for a higher rate of censoring. A method of generalizing the result to type 1 censoring and the efficiency of estimating the coefficient of the covariate are discussecd. A brief account of using the results to help design experiments is also given.     

Multicovariate-adjusted regression models

We introduce multicovariate-adjusted regression (MCAR), an adjustment method for regression analysis, where both the response (Y) and predictors (X ₁, …, X _p ) are not directly observed. The available data have been contaminated by unknown functions of a set of observable distorting covariates, Z ₁, …, Z _s , in a multiplicative fashion. The proposed method substantially extends the current contaminated regression modelling capability, by allowing for multiple distorting covariate effects. MCAR is a flexible generalisation of the recently proposed covariate-adjusted regression method, an effective adjustment method in the presence of a single covariate, Z. For MCAR estimation, we establish a connection between the MCAR models and adaptive varying coefficient models. This connection leads to an adaptation of a hybrid backfitting estimation algorithm. Extensive simulations are used to study the performance and limitations of the proposed iterative estimation algorithm. In particular, the bias and mean square error of the proposed MCAR estimators are examined, relative to a baseline and a consistent benchmark estimator. The method is also illustrated with a Pima Indian diabetes data set, where the response and predictors are potentially contaminated by body mass index and triceps skin fold thickness. Both distorting covariates measure aspects of obesity, an important risk factor in type 2 diabetes.