Aalen's Linear Model for Sampled Risk Set Data: A Large Sample Study

Borgan and Langholz (1997) describe a method for estimating the parameter functions in Aalen's linear hazard regression model from sampled risk set data. Using a counting process formulation and the martingale central limit theorem, we provide a study of the asymptotic distributional properties of the estimator. The results are applied to study the efficiencies of the nested case-control and counter-matched designs relative to a full cohort analysis.     

Shrinkage and Orthogonal Decomposition

ABSTRACT. The problem of estimating the mean of a multivariate normal distribution when the parameter space allows an orthogonal decomposition is discussed. Risk functions and lower bounds for a class of shrinkage estimators that includes Stein's estimator are derived, and an improvement on Stein's estimator that takes advantage of the orthogonal decomposition is introduced. Uniform asymptotics related to Pinsker's minimax risk is derived and we give conditions for attaining the lower risk bound. Special cases including regression and analysis of variance are discussed.     

Predicting infectious disease outbreak risk via migratory waterfowl vectors

The spread of an emerging infectious disease is a major public health threat. Given the uncertainties associated with vector-borne diseases, in terms of vector dynamics and disease transmission, it is critical to develop statistical models that address how and when such an infectious disease could spread throughout a region such as the USA. This paper considers a spatio-temporal statistical model for how an infectious disease could be carried into the USA by migratory waterfowl vectors during their seasonal migration and, ultimately, the risk of transmission of such a disease to domestic fowl. Modeling spatio-temporal data of this type is inherently difficult given the uncertainty associated with observations, complexity of the dynamics, high dimensionality of the underlying process, and the presence of excessive zeros. In particular, the spatio-temporal dynamics of the waterfowl migration are developed by way of a two-tiered functional temporal and spatial dimension reduction procedure that captures spatial and seasonal trends, as well as regional dynamics. Furthermore, the model relates the migration to a population of poultry farms that are known to be susceptible to such diseases, and is one of the possible avenues toward transmission to domestic poultry and humans. The result is a predictive distribution of those counties containing poultry farms that are at the greatest risk of having the infectious disease infiltrate their flocks assuming that the migratory population was infected. The model naturally fits into the hierarchical Bayesian framework.     

知识共享对供应链信用风险传染的影响研究

将企业间知识共享这一因素引入供应链上下游企业博弈过程,在完全信息条件下研究三级供应链中零售商分别与分销商、制造商进行知识共享时知识共享量与企业信用风险水平和供应链信用风险传染强度之间的关系,并结合算例进行了数值分析.基于Stackelberg博弈模型的研究结果表明,供应链上的知识共享有助于降低供应链成员企业的信用风险;进行知识共享的企业间信用风险传染强度随着知识共享量的增加而增大;企业进行知识共享比不进行知识共享时受到其它企业信用风险传染的影响大.     

The asymptotic distribution of the partial attributable risk in cross-sectional studies

The partial attributable risk (PAR) has been introduced as a tool for partitioning the responsibility for causing an adverse event between various risk factors. It has arisen from epidemiology, but it is also a valid general risk allocation concept, which can, for example, be applied to data from customer satisfaction surveys. So far, a variance formula for the PAR has been missing so that the confidence intervals were not directly available. This paper provides the asymptotic normal distribution for the PAR determined from a cross-sectional study.     

Sample Size Calculation and Blinded Sample Size Recalculation in Clinical Trials Where the Treatment Effect is Measured by the Relative Risk

In clinical trials with binary endpoints, the required sample size does not depend only on the specified type I error rate, the desired power and the treatment effect but also on the overall event rate which, however, is usually uncertain. The internal pilot study design has been proposed to overcome this difficulty. Here, nuisance parameters required for sample size calculation are re-estimated during the ongoing trial and the sample size is recalculated accordingly. We performed extensive simulation studies to investigate the characteristics of the internal pilot study design for two-group superiority trials where the treatment effect is captured by the relative risk. As the performance of the sample size recalculation procedure crucially depends on the accuracy of the applied sample size formula, we firstly explored the precision of three approximate sample size formulae proposed in the literature for this situation. It turned out that the unequal variance asymptotic normal formula outperforms the other two, especially in case of unbalanced sample size allocation. Using this formula for sample size recalculation in the internal pilot study design assures that the desired power is achieved even if the overall rate is mis-specified in the planning phase. The maximum inflation of the type I error rate observed for the internal pilot study design is small and lies below the maximum excess that occurred for the fixed sample size design.     

Minimum average risk estimators for coefficients in linear models

We consider the problem of estimating the coefficient vector β of a linear regression model with quadratic loss function. Some biased estimators which utilize the prior information about β are considered. Also studied is the problem of estimating the parameters of an over-identified structural equation from undersized samples.     

The Econometrics of Piecewise-Linear Budget Constraints

In this article maximum likelihood techniques for estimating consumer demand functions when budget constraints are piecewise linear are exposited and surveyed. Consumer demand functions are formally derived under such constraints, and it is shown that the functions are themselves nonlinear as a result. The econometric problems in estimating such functions are exposited, and the importance of the stochastic specification is stressed, in particular the specification of both unobserved heterogeneity of preferences and measurement error. Econometric issues in estimation and testing are discussed, and the results of the studies that have been conducted to date are surveyed.     

Approximate Bayes estimation of the parameters and reliability function of a mixture of two inverse Weibull distributions under Type-2 censoring

The main goal of this paper is to develop the approximate Bayes estimation of the five-dimensional vector of the parameters and reliability function of a mixture of two inverse Weibull distributions (MTIWD) under Type-2 censoring. Usually, the posterior distribution is complicated under the scheme of Type-2 censoring and the integrals that are involved cannot be obtained in a simple explicit form. In this study, we use Lindley's [Approximate Bayesian method, Trabajos Estadist. 31 (1980), pp. 223–237] approximate form of Bayes estimation in the case of an MTIWD under Type-2 censoring. Later, we calculate the estimated risks (ERs) of the Bayes estimates and compare them with the corresponding ERs of the maximum-likelihood estimates through Monte Carlo simulation. Finally, we analyse a real data set using the findings.     

Comparing the relative efficiency of three sequential procedures

We consider the sequential procedures developed by Robbins and Siegmund (1974), Louis (1975) and Zoubeidi (1992) for comparing the means of two treatments. We let the procedures have equal power functions and compare their Bayes and minimax risks using the invariance property of their power functions. For each of several formulations of the problem we determine the most relatively efficient procedure and compute its expected total sample size.