Bootstrap Estimation of Benchmark Doses and Confidence Limits with Clustered Quantal Data

The benchmark dose (BMD) is an exposure level that would induce a small risk increase (BMR level) above the background. The BMD approach to deriving a reference dose for risk assessment of noncancer effects is advantageous in that the estimate of BMD is not restricted to experimental doses and utilizes most available dose-response information. To quantify statistical uncertainty of a BMD estimate, we often calculate and report its lower confidence limit (i.e., BMDL), and may even consider it as a more conservative alternative to BMD itself. Computation of BMDL may involve normal confidence limits to BMD in conjunction with the delta method. Therefore, factors, such as small sample size and nonlinearity in model parameters, can affect the performance of the delta method BMDL, and alternative methods are useful. In this article, we propose a bootstrap method to estimate BMDL utilizing a scheme that consists of a resampling of residuals after model fitting and a one-step formula for parameter estimation. We illustrate the method with clustered binary data from developmental toxicity experiments. Our analysis shows that with moderately elevated dose-response data, the distribution of BMD estimator tends to be left-skewed and bootstrap BMDL s are smaller than the delta method BMDL s on average, hence quantifying risk more conservatively. Statistically, the bootstrap BMDL quantifies the uncertainty of the true BMD more honestly than the delta method BMDL as its coverage probability is closer to the nominal level than that of delta method BMDL. We find that BMD and BMDL estimates are generally insensitive to model choices provided that the models fit the data comparably well near the region of BMD. Our analysis also suggests that, in the presence of a significant and moderately strong dose-response relationship, the developmental toxicity experiments under the standard protocol support dose-response assessment at 5% BMR for BMD and 95% confidence level for BMDL.     

二元序列优化的二种快速算法

基于二相编码雷达对大压缩比信号的要求,提出了一种比直接算法平均提高效率0.5P(P 为序列长度)的快速数字优化方法。作为这种快速算法的实际应用,还对 P=255的二相编码脉冲压缩信号进行了优化。     

从收支项目看秦汉二元财政的源流

汉代财政分为国家财政和帝室财政,由大司农和少府分掌,为大家所熟知。但对二元财政的来源却少有辨析,一般承袭郑玄关于大司农是太府继承的说法。实际上少府和太府在收支项目上都比较接近,有着明显的继承关系,而大司农则是由负责主持策命诸侯及保管爵禄文书的内史演变而来。在国家职能转轨过程中,内史发展成为管理国家财政及畿内地区事务的机构,最后进一步分离出专门管理国家财政的治粟内史。二元财政体制的设计来源于收支对应的原始财政平衡思想。     

A fast splitting procedure for classification trees

This paper provides a faster method to find the best split at each node when using the CART methodology. The predictability index is proposed as a splitting rule for growing the same classification tree as CART does when using the Gini index of heterogeneity as an impurity measure. A theorem is introduced to show a new property of the index : the for a given predictor has a value not lower than the for any split generated by the predictor. This property is used to make a substantial saving in the time required to generate a classification tree. Three simulation studies are presented in order to show the computational gain in terms of both the number of splits analysed at each node and the CPU time. The proposed splitting algorithm can prove computational efficiency in real data sets as shown in an example.     

基于二元关系的产业关联分析方法研究

本文运用二元关系理论和Warshall算法计算产业系统中各产业之间的连通关联关系,为认识产业结构和产业关联状况提供了简便的量化分析方法。结合安徽产业系统的实例,分析了安徽产业结构的特点及产业关联状况。     

Assessment of modeling longitudinal binary data based on graphical methods

Longitudinal categorical data are commonly applied in a variety of fields and are frequently analyzed by generalized estimating equation (GEE) method. Prior to making further inference based on the GEE model, the assessment of model fit is crucial. Graphical techniques have long been in widespread use for assessing the model adequacy. We develop alternative graphical approaches utilizing plots of marginal model-checking condition and local mean deviance to assess the GEE model with logit link for longitudinal binary responses. The applications of the proposed procedures are illustrated through two longitudinal binary datasets.     

Treatment Choice With Trial Data: Statistical Decision Theory Should Supplant Hypothesis Testing

Abstract

A central objective of empirical research on treatment response is to inform treatment choice. Unfortunately, researchers commonly use concepts of statistical inference whose foundations are distant from the problem of treatment choice. It has been particularly common to use hypothesis tests to compare treatments. Wald’s development of statistical decision theory provides a coherent frequentist framework for use of sample data on treatment response to make treatment decisions. A body of recent research applies statistical decision theory to characterize uniformly satisfactory treatment choices, in the sense of maximum loss relative to optimal decisions (also known as maximum regret). This article describes the basic ideas and findings, which provide an appealing practical alternative to use of hypothesis tests. For simplicity, the article focuses on medical treatment with evidence from classical randomized clinical trials. The ideas apply generally, encompassing use of observational data and treatment choice in nonmedical contexts.     

The precision of regression-type estimator for incremental cost–effectiveness ratio

The estimation of incremental cost–effectiveness ratio (ICER) has received increasing attention recently. It is expressed in terms of the ratio of the change in costs of a therapeutic intervention to the change in the effects of the intervention. Despite the intuitive interpretation of ICER as an additional cost per additional benefit unit, it is a challenge to estimate the distribution of a ratio of two stochastically dependent distributions. A vast literature regarding the statistical methods of ICER has developed in the past two decades, but none of these methods provide an unbiased estimator. Here, to obtain the unbiased estimator of the cost–effectiveness ratio (CER), the zero intercept of the bivariate normal regression is assumed. In equal sample sizes, the Iman–Conover algorithm is applied to construct the desired variance–covariance matrix of two random bivariate samples, and the estimation then follows the same approach as CER to obtain the unbiased estimator of ICER. The bootstrapping method with the Iman–Conover algorithm is employed for unequal sample sizes. Simulation experiments are conducted to evaluate the proposed method. The regression-type estimator performs overwhelmingly better than the sample mean estimator in terms of mean squared error in all cases.     

Comparing diagnostic tests: test of hypothesis for likelihood ratios

Likelihood ratios (LRs) are used to characterize the efficiency of diagnostic tests. In this paper, we use the classical weighted least squares (CWLS) test procedure, which was originally used for testing the homogeneity of relative risks, for comparing the LRs of two or more binary diagnostic tests. We compare the performance of this method with the relative diagnostic likelihood ratio (rDLR) method and the diagnostic likelihood ratio regression (DLRReg) approach in terms of size and power, and we observe that the performances of CWLS and rDLR are the same when used to compare two diagnostic tests, while DLRReg method has higher type I error rates and powers. We also examine the performances of the CWLS and DLRReg methods for comparing three diagnostic tests in various sample size and prevalence combinations. On the basis of Monte Carlo simulations, we conclude that all of the tests are generally conservative and have low power, especially in settings of small sample size and low prevalence.     

Utilizing Bayesian predictive power in clinical trial design

The Bayesian paradigm provides an ideal platform to update uncertainties and carry them over into the future in the presence of data. Bayesian predictive power (BPP) reflects our belief in the eventual success of a clinical trial to meet its goals. In this paper we derive mathematical expressions for the most common types of outcomes, to make the BPP accessible to practitioners, facilitate fast computations in adaptive trial design simulations that use interim futility monitoring, and propose an organized BPP-based phase II-to-phase III design framework.