Bayesian optimization design for dose-finding based on toxicity and efficacy outcomes in phase I/II clinical trials

In phase I trials, the main goal is to identify a maximum tolerated dose under an assumption of monotonicity in dose–response relationships. On the other hand, such monotonicity is no longer applied to biologic agents because a different mode of action from that of cytotoxic agents potentially draws unimodal or flat dose–efficacy curves. Therefore, biologic agents require an optimal dose that provides a sufficient efficacy rate under an acceptable toxicity rate instead of a maximum tolerated dose. Many trials incorporate both toxicity and efficacy data, and drugs with a variety of modes of actions are increasingly being developed; thus, optimal dose estimation designs have been receiving increased attention. Although numerous authors have introduced parametric model-based designs, it is not always appropriate to apply strong assumptions in dose–response relationships. We propose a new design based on a Bayesian optimization framework for identifying optimal doses for biologic agents in phase I/II trials. Our proposed design models dose–response relationships via nonparametric models utilizing a Gaussian process prior, and the uncertainty of estimates is considered in the dose selection process. We compared the operating characteristics of our proposed design against those of three other designs through simulation studies. These include an expansion of Bayesian optimal interval design, the parametric model-based EffTox design, and the isotonic design. In simulations, our proposed design performed well and provided results that were more stable than those from the other designs, in terms of the accuracy of optimal dose estimations and the percentage of correct recommendations.     

基于煤矿透水事故应急响应时效性的水泵布局鲁棒优选问题研究

为了提高煤矿透水事故中矿工获救和恢复健康的可能性，本文基于应急响应时效性研究关键资源-水泵布局问题。已有应急资源布局问题的研究多从成本、时间、资源需求满足度等方面进行，煤矿透水事故应急响应时效性是综合考虑被困矿工获救时间以及被困过程中被困位置最低氧气含量和食物缺少量三方面要素的事故应对效果。首先，建立了基于煤矿透水事故发生、发展和应急响应机理的三方面要素计算方法；然后，在供氧和供食物所需资源布局给定的前提下，设计水泵布局的目标函数和约束条件，建立水泵布局鲁棒优选模型，通过机会时间窗概念的引入和分支定界算法的思想，给出水泵布局不可行方案的判别准则，并在此基础上进行优选算法的设计；最后，在实际发生的煤矿透水事故典型案例基础上，构造算例，检验水泵布局鲁棒优选模型的有效性。     

A new search procedure of steepest ascent in response surface exploration

The method of steepest ascent direction has been widely accepted for process optimization in the applications of response surface methodology (RSM). The procedure of steepest ascent direction is performed on experiments run along the gradient of a fitted linear model. Therefore, the RSM practitioner needs to decide a suitable stopping rule such that the optimum point estimate in the search direction can be determined. However, the details of how to deflect and then halt a search in the steepest ascent direction are not thoroughly described in the literature. In common practice, it is convenient to use the simple stopping rules after one to three response deteriorations in a row after a series of fitted linear models used for exploration. In the literature, there are two formal stopping rules proposed, that is, Myers and Khuri's [A new procedure for steepest ascent, Comm. Statist. Theory Methods A 8(14) (1979), pp. 1359–1376] stopping rule and del Castillo's [Stopping rules for steepest ascent in experimental optimization, Comm. Statist. Simul. Comput. 26(4) (1997), pp. 1599–1615] stopping rule. This paper develops a new procedure for determining how to adjust and then when to stop a steepest ascent search in response surface exploration. This proposal wishes to provide the RSM practitioner with a clear-cut and easy-to-implement procedure that can attain the optimum mean response more accurately than the existing procedures. Through the study of simulation optimization, it shows that the average optimum point and response returned by using the new search procedure are considerably improved when compared with two existing stopping rules. The number of experimental trials required for convergence is greatly reduced as well.     

Selection of a stroke risk model based on transcranial Doppler ultrasound velocity

Increased transcranial Doppler ultrasound (TCD) velocity is an indicator of cerebral infarction in children with sickle cell disease (SCD). In this article, the parallel genetic algorithm (PGA) is used to select a stroke risk model with TCD velocity as the response variable. Development of such a stroke risk model leads to the identification of children with SCD who are at a higher risk of stroke and their treatment in the early stages. Using blood velocity data from SCD patients, it is shown that the PGA is an easy-to-use computationally variable selection tool. The results of the PGA are also compared with those obtained from the stochastic search variable selection method, the Dantzig selector and conventional techniques such as stepwise selection and best subset selection.     

先秦黄老学派及其学术理论来源

黄老学派是先秦诸子百家争鸣的产物,它的产生是时代对学术的需求和各学派之间相互借鉴和整合的结果。黄老学派之所以在百家争鸣中脱颖而出并一枝独秀,究其原因是吸收整合了其他学派的学术之长,特别是对道、儒、墨、阴阳等学派有关理论的整合和优化的结果。     

Inter-city bus scheduling under variable market share and uncertain market demands

Bus scheduling is essential to a carrier's profitability, its level of service and its competitiveness in the market. In past research most inter-city bus scheduling models have used only the projected (or average) market share and market demand, meaning that the variations in daily passenger demand that occur in actual operations are neglected. In this research, however, we do not utilize a fixed market share and market demand. Instead, passenger choice behaviors and uncertain market demands are considered. Stochastic and robust optimizations and a passenger choice model are used to develop the models. These models are formulated as a nonlinear integer program that is characterized as NP-hard. We also develop a solution algorithm to efficiently solve the models. They are tested using data from a major Taiwan inter-city bus operation. The results show the good performance of the models and the solution algorithm.     

Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation

The widely used estimator of Berry, Levinsohn, and Pakes (1995) produces estimates of consumer preferences from a discrete‐choice demand model with random coefficients, market‐level demand shocks, and endogenous prices. We derive numerical theory results characterizing the properties of the nested fixed point algorithm used to evaluate the objective function of BLP's estimator. We discuss problems with typical implementations, including cases that can lead to incorrect parameter estimates. As a solution, we recast estimation as a mathematical program with equilibrium constraints, which can be faster and which avoids the numerical issues associated with nested inner loops. The advantages are even more pronounced for forward‐looking demand models where the Bellman equation must also be solved repeatedly. Several Monte Carlo and real‐data experiments support our numerical concerns about the nested fixed point approach and the advantages of constrained optimization. For static BLP, the constrained optimization approach can be as much as ten to forty times faster for large‐dimensional problems with many markets.     

Dynamic Valuation Decomposition Within Stochastic Economies

I explore the equilibrium value implications of economic models that incorporate responses to a stochastic environment with growth. I propose dynamic valuation decompositions (DVD's) designed to distinguish components of an underlying economic model that influence values over long investment horizons from components that impact only the short run. A DVD represents the values of stochastically growing claims to consumption payoffs or cash flows using a stochastic discount process that both discounts the future and adjusts for risk. It is enabled by constructing operators indexed by the elapsed time between the trading date and the date of the future realization of the payoff. Thus formulated, methods from applied mathematics permit me to characterize valuation behavior and the term structure of risk prices in a revealing manner. I apply this approach to investigate how investor beliefs and the associated uncertainty are reflected in current‐period values and risk‐price elasticities.     

Ambiguity in the Small and in the Large

This paper considers local and global multiple‐prior representations of ambiguity for preferences that are (i) monotonic, (ii) Bernoullian, that is, admit an affine utility representation when restricted to constant acts, and (iii) locally Lipschitz continuous. We do not require either certainty independence or uncertainty aversion. We show that the set of priors identified by Ghirardato, Maccheroni, and Marinacci's (2004) “unambiguous preference” relation can be characterized as a union of Clarke differentials. We then introduce a behavioral notion of “locally better deviation” at an act and show that it characterizes the Clarke differential of the preference representation at that act. These results suggest that the priors identified by these preference statements are directly related to (local) optimizing behavior.     

考虑专家判断信息的灰色关联极大熵权重模型

本文提出了一种从关联角度出发将主观先验信息与客观信息纳入约束条件从而求解综合权重的方法。在利用灰关联深度系数对实际决策问题进行客观权重判断研究的基础之上,构建了源于专家判断信息的权重势比的主观约束条件,将主客观因素同时反映在优化模型的约束条件中,并将权重的极大熵作为目标函数,保证权重判断的可信度,从而构建了确定评价指标综合权重的极大熵优化模型。该方法克服了将主客观条件直接通过线性组合作为目标函数时,主客观参数选取导致的权重大小的不确定性,并同其他赋权方法进行案例结果比较,表明了该方法的有效性。