Properties of the weighted log‐rank test in the design of confirmatory studies with delayed effects

Proportional hazards are a common assumption when designing confirmatory clinical trials in oncology. This assumption not only affects the analysis part but also the sample size calculation. The presence of delayed effects causes a change in the hazard ratio while the trial is ongoing since at the beginning we do not observe any difference between treatment arms, and after some unknown time point, the differences between treatment arms will start to appear. Hence, the proportional hazards assumption no longer holds, and both sample size calculation and analysis methods to be used should be reconsidered. The weighted log‐rank test allows a weighting for early, middle, and late differences through the Fleming and Harrington class of weights and is proven to be more efficient when the proportional hazards assumption does not hold. The Fleming and Harrington class of weights, along with the estimated delay, can be incorporated into the sample size calculation in order to maintain the desired power once the treatment arm differences start to appear. In this article, we explore the impact of delayed effects in group sequential and adaptive group sequential designs and make an empirical evaluation in terms of power and type‐I error rate of the of the weighted log‐rank test in a simulated scenario with fixed values of the Fleming and Harrington class of weights. We also give some practical recommendations regarding which methodology should be used in the presence of delayed effects depending on certain characteristics of the trial.     

Comparison of Four New General Classes of Search Designs

A factor screening experiment identifies a few important factors from a large list of factors that potentially influence the response. If a list consists of m factors each at three levels, a design is a subset of all possible 3 ^m runs. This paper considers the problem of finding designs with small numbers of runs, using the search linear model introduced in Srivastava (1975). The paper presents four new general classes of these 'search designs', each with 2 m −1 runs, which permit, at most, two important factors out of m factors to be searched for and identified. The paper compares the designs for 4 ≤ m ≤ 10, using arithmetic and geometric means of the determinants, traces and maximum characteristic roots of particular matrices. Two of the designs are found to be superior in all six criteria studied. The four designs are identical for m = 3 and this design is an optimal design in the class of all search designs under the six criteria. The four designs are also identical for m = 4 under some row and column permutations.     

试析布哈林国民经济综合平衡发展理论

列宁逝世以后，布哈林继续坚持和捍卫列宁的新经济政策思想，并结合俄国的实际，针对当时苏联国民经济发展中出现的一系列问题，总结过去经济建设中的经验教训，系统地阐发自己的观点，从而形成了关于国民经济综合平衡发展的比较全面系统的理论。他认为，要使国民经济持续健康发展，必须尊重客观经济规律，重视市场调节的作用，使工业和农业、重工业和轻工业、农业内部、积累和消费之间保持综合平衡。在建设有中国特色社会主义的今天，重温布哈林的国民经济综合平衡发展理论，无疑会给我们以很好的教益和启迪。     

具有带误差逼近的赋值伪压缩映像的公共不动点迭代序列

在实一致光滑Banach空间中引入了一类新的逼近三个极值强伪压缩映象唯一公共不动点的带误差迭代序列,以及通过Petryshyn不等式讨论了该带误差迭代序列的收敛性.     

Examples of the use of an equivalence theorem in constructing optimum experimental designs for random-effects nonlinear regression models

The problem considered is that of finding an optimum measurement schedule to estimate population parameters in a nonlinear model when the patient effects are random. The paper presents examples of the use of sensitivity functions, derived from the General Equivalence Theorem for D-optimality, in the construction of optimum population designs for such schedules. With independent observations, the theorem applies to the potential inclusion of a single observation. However, in population designs the observations are correlated and the theorem applies to the inclusion of an additional measurement schedule. In one example, three groups of patients of differing size are subject to distinct schedules. Numerical, as opposed to analytical, calculation of the sensitivity function is advocated. The required covariances of the observations are found by simulation.     

Efficient designs based on orthogonal arrays of type I and type II for experiments using units ordered over time or space

For a wide variety of applications, experiments are based on units ordered over time or space. Models for these experiments generally may include one or more of: correlations, systematic trends, carryover effects and interference effects. Since the standard optimal block designs may not be efficient in these situations, orthogonal arrays of type I and type II, which were introduced in 1961 by C.R. Rao [Combinatorial arrangements analogous to orthogonal arrays, Sankhya A 23 (1961) 283–286], have been recently used to construct optimal and efficient designs for many of these experiments. Results in this area are unified and the salient features are outlined.     

Robustness of a Class of Partial Diallel Cross Designs to the Unavailability of a Complete Block of Observations

Complete and partial diallel cross designs are examined as to their construction and robustness against the loss of a block of observations. A simple generalized inverse is found for the information matrix of the line effects, which allows evaluation of expressions for the variances of the line-effect differences with and without the missing block. A-efficiencies, based on average variances of the elementary contrasts of the line-effects, suggest that these designs are fairly robust. The loss of efficiency is generally less than 10%, but it is shown that specific comparisons might suffer a loss of efficiency of as much as 40%.     

The repeated public goods game: A solution using Tit-for-Tat and the Lindahl point

This paper demonstrates how a repeated public goods problem may be solved by using Tit-for-Tat (TFT) on the Lindahl point. The general solution is developed; geometric and numerical examples are offered.I wish to thank an anonymous reviewer for very helpful comments on earlier drafts of this paper.     

数控机床功能的扩展

本文主要分析了HEIDENHAIN TNC 310数控铣床系统中圆弧铣削指令及螺纹铣削指令,对螺纹铣削功能进行延伸,扩展到圆弧三轴联动,并对螺纹铣削指令格式进行了修改,从而具有圆弧三轴联动铣削功能。     

多功能开放型企业供需网成员企业合作关系的经济模型

多功能开放型企业供需网(SDN)合作伙伴关系的稳定性，将直接决定SDN创新管理理念的生命力和未来发展前景，传统企业间的一次性静态博弈和供应链(SC)盟员间的有限次重复博弈，都是低效的合作关系，因而其稳定性较差，无限次重复博弈以及由此而引发的触发策略，能够实现帕累托最优的纳什均衡，是SDN合作伙伴关系稳定发展的深层经济学原因，通过建立SDN成员企业合作关系的经济模型，论证了SDN的稳定性。