Optimal matching with minimal deviation from fine balance in a study of obesity and surgical outcomes

In multivariate matching, fine balance constrains the marginal distributions of a nominal variable in treated and matched control groups to be identical without constraining who is matched to whom. In this way, a fine balance constraint can balance a nominal variable with many levels while focusing efforts on other more important variables when pairing individuals to minimize the total covariate distance within pairs. Fine balance is not always possible; that is, it is a constraint on an optimization problem, but the constraint is not always feasible. We propose a new algorithm that returns a minimum distance finely balanced match when one is feasible, and otherwise minimizes the total distance among all matched samples that minimize the deviation from fine balance. Perhaps we can come very close to fine balance when fine balance is not attainable; moreover, in any event, because our algorithm is guaranteed to come as close as possible to fine balance, the investigator may perform one match, and on that basis judge whether the best attainable balance is adequate or not. We also show how to incorporate an additional constraint. The algorithm is implemented in two similar ways, first as an optimal assignment problem with an augmented distance matrix, second as a minimum cost flow problem in a network. The case of knee surgery in the Obesity and Surgical Outcomes Study motivated the development of this algorithm and is used as an illustration. In that example, 2 of 47 hospitals had too few nonobese patients to permit fine balance for the nominal variable with 47 levels representing the hospital, but our new algorithm came very close to fine balance. Moreover, in that example, there was a shortage of nonobese diabetic patients, and incorporation of an additional constraint forced the match to include all of these nonobese diabetic patients, thereby coming as close as possible to balance for this important but recalcitrant covariate.     

Sequential monitoring of randomization tests: stratified randomization

In many clinical trials, it is desirable to establish a sequential monitoring plan, whereby the test statistic is computed at an interim point or points in the trial and a decision is made whether to stop early due to evidence of treatment efficacy. In this article, we will set up a sequential monitoring plan for randomization-based inference under the permuted block design, stratified block design, and stratified urn design. We will also propose a definition of information fraction in these settings and discuss its calculation under these different designs.     

Design of multivariate selection experiments to estimate genetic parameters

Summary The precision of estimates of genetic variances and covariances obtained from multivariate selection experiments of various designs are discussed. The efficiencies of experimental designs are compared using criteria based on a confidence region of the estimated genetic parameters, with estimation using both responses and selection differentials and offspring-parent regression. A good selection criterion is shown to be to select individuals as parents using an index of the sums of squares and crossproducts of the phenotypic measurements. Formulae are given for the optimum selection proportion when the relative numbers of individuals in the parent and progeny generations are fixed or variable. Although the optimum depends on a priori knowledge of the genetic parameters to be estimated, the designs are very robust to poor estimates. For bivariate uncorrelated data, the variance of the estimated genetic parameters can be reduced by approximately 0.4 relative to designs of a more conventional nature when half of the individuals are selected on one trait and half on the other trait. There are larger reductions in variances if the traits are correlated.     

Virtual parameter-estimation experiments in Bioprocess-Engineering education

Cell growth kinetics and reactor concepts constitute essential knowledge for Bioprocess-Engineering students. Traditional learning of these concepts is supported by lectures, tutorials, and practicals: ICT offers opportunities for improvement. A virtual-experiment environment was developed that supports both model-related and experimenting-related learning objectives. Students have to design experiments to estimate model parameters: they choose initial conditions and ‘measure’ output variables. The results contain experimental error, which is an important constraint for experimental design. Students learn from these results and use the new knowledge to re-design their experiment. Within a couple of hours, students design and run many experiments that would take weeks in reality. Usage was evaluated in two courses with questionnaires and in the final exam. The faculties involved in the two courses are convinced that the experiment environment supports essential learning objectives well.     

Optimal adaptive randomized designs for clinical trials

Optimal decision-analytic designs are deterministic. Such designsare appropriately criticized in the context of clinical trialsbecause they are subject to assignment bias. On the other hand,balanced randomized designs may assign an excessive number ofpatients to a treatment arm that is performing relatively poorly.We propose a compromise between these two extremes, one thatachieves some of the good characteristics of both. We introducea constrained optimal adaptive design for a fully sequentialrandomized clinical trial with k arms and n patients. An r-designis one for which, at each allocation, each arm has probabilityat least r of being chosen, 0 r 1/k. An optimal design amongall r-designs is called r-optimal. An r₁-design is also an r₂-designif r₁ r₂. A design without constraint is the special case r = 0and a balanced randomized design is the special case r = 1/k.The optimization criterion is to maximize the expected overallutility in a Bayesian decision-analytic approach, where utilityis the sum over the utilities for individual patients over a‘patient horizon’ N. We prove analytically thatthere exists an r-optimal design such that each patient is assignedto a particular one of the arms with probability 1 – (k – 1)r,and to the remaining arms with probability r. We also show thatthe balanced design is asymptotically r-optimal for any givenr, 0 r < 1/k, as N/n  . This implies that everyr-optimal design is asymptotically optimal without constraint.Numerical computations using backward induction for k = 2arms show that, in general, this asymptotic optimality featurefor r-optimal designs can be accomplished with moderate trialsize n if the patient horizon N is large relative to n. We alsoshow that, in a trial with an r-optimal design, r < 1/2,fewer patients are assigned to an inferior arm than when followinga balanced design, even for r-optimal designs having the samestatistical power as a balanced design. We discuss extensionsto various clinical trial settings.     

Optimal adaptive designs for binary response trials

Summary. We derive the optimal allocation between two treatments in a clinical trial based on the following optimality criterion: for fixed variance of the test statistic, what allocation minimizes the expected number of treatment failures? A sequential design is described that leads asymptotically to the optimal allocation and is compared with the randomized play‐the‐winner rule, sequential Neyman allocation, and equal allocation at similar power levels. We find that the sequential procedure generally results in fewer treatment failures than the other procedures, particularly when the success probabilities of treatments are smaller.     

海藻希瓦氏菌(Shewanella alga)发酵培养基条件优化的研究

目的:优化海藻希瓦氏菌生产河豚毒素的发酵培养基。方法:通过测定菌体密度(用OD600表示)和菌体收获量,研究了部分初始条件及添加不同营养物质对海藻希瓦氏菌生长的影响,采用单因素试验和正交试验对发酵条件进行了优化。结果:最适发酵初始pH为7.5,最适摇瓶装液量为150mL。通过正交试验找出最大影响因素为葡萄糖供应,优化后的培养基最佳配方为:在2216E培养基中添加1.0%葡萄糖、2.5%酵母粉、1.0%磷酸高铁。结论:优化后的培养基培养供试菌,菌体收获量比在2216E培养基中培养增加了2.012g.L-1。     

Genetic algorithm for multi-objective experimental optimization

A new software tool making use of a genetic algorithm for multi-objective experimental optimization (GAME.opt) was developed based on a strength Pareto evolutionary algorithm. The software deals with high dimensional variable spaces and unknown interactions of design variables. This approach was evaluated by means of multi-objective test problems replacing the experimental results. A default parameter setting is proposed enabling users without expert knowledge to minimize the experimental effort (small population sizes and few generations).     

Optimal promising zone designs

Clinical trials with adaptive sample size reassessment based on an unblinded analysis of interim results are perhaps the most popular class of adaptive designs (see Elsäßer et al., 2007). Such trials are typically designed by prespecifying a zone for the interim test statistic, termed the promising zone, along with a decision rule for increasing the sample size within that zone. Mehta and Pocock (2011) provided some examples of promising zone designs and discussed several procedures for controlling their type‐1 error. They did not, however, address how to choose the promising zone or the corresponding sample size reassessment rule, and proposed instead that the operating characteristics of alternative promising zone designs could be compared by simulation. Jennison and Turnbull (2015) developed an approach based on maximizing expected utility whereby one could evaluate alternative promising zone designs relative to a gold‐standard optimal design. In this paper, we show how, by eliciting a few preferences from the trial sponsor, one can construct promising zone designs that are both intuitive and achieve the Jennison and Turnbull (2015) gold‐standard for optimality.     

适用于获取最优化配方的一种算法

本文应用印楝种仁提取物（F3）与敌敌畏混配为例,以斜纹夜蛾（Spodopteralitura）为目标害虫,介绍一种适用于获取最优化配方的算法,在二次通用回归旋转组合设计的基础上,经参数辨识,获取二次回归方程,经失拟性、回归显著性检验,本方程基本能够反映杀虫剂用量与斜纹夜蛾幼虫死亡机率值之间的关系．在害虫防治实践中,要求在防治费用最小的基础上,目标害虫有最大的死亡率.因此,以防治目标害虫的费用作为优化算法的目标函数,以害虫死亡机率值最大作为约束条件,有如下的一组优化算式为目标函数约束条件式中a1,a2分别为参试杀虫剂1,2最低用量,b1,b2则为相应的最高用量．C1,C2分别为杀虫剂1,2的单价,N1,N2为杀虫剂l,2的用量．Y为目标害虫死亡机率值回归方程．本文所依据的试验设计中,以对数函数关系变换编码值与使用浓度之间的关系,所以应用拉格朗日求极值原理求取最优化配方．由计算所得的混配比例与其他方法所获结果一致．     

A new approach to define optimized range of medium composition for enhancement of hairy root production in fed-batch process

This work proposes a new methodology to identify the best medium concentrations for fed-batch production of hairy root using Datura innoxia as a model. Firstly, the role of each component on the growth rate is investigated separately. Then, an experimental design allows refining the optimization studying the interactions between the major species. The result analysis let to define concentration range optimized for fed-batch process. The work novelties lie in two aspects. Firstly, concentrations have been kept constant during each run. Thus, biomass uptakes do not affect the optimization and the growth rate is maintained constant during the exponential phase. Secondly, the effects of salts are generally studied. In this work, the influences of each ion are investigated in order to avoid bias due to the counter-ion effects. Compared to the classical B₅ medium, the optimized medium shows a significant improvement leading to more than 80% increase of final biomass production.     

Response-adaptive randomization for clinical trials with continuous outcomes

We provide an explicit asymptotic method to evaluate the performance of different response-adaptive randomization procedures in clinical trials with continuous outcomes. We use this method to investigate four different response-adaptive randomization procedures. Their performance, especially in power and treatment assignment skewing to the better treatment, is thoroughly evaluated theoretically. These results are then verified by simulation. Our analysis concludes that the doubly adaptive biased coin design procedure targeting optimal allocation is the best one for practical use. We also consider the effect of delay in responses and nonstandard responses, for example, Cauchy distributed response. We illustrate our procedure by redesigning a real clinical trial.     

Optimal surveillance strategy for invasive species management when surveys stop after detection

Invasive species are a cause for concern in natural and economic systems and require both monitoring and management. There is a trade‐off between the amount of resources spent on surveying for the species and conducting early management of occupied sites, and the resources that are ultimately spent in delayed management at sites where the species was present but undetected. Previous work addressed this optimal resource allocation problem assuming that surveys continue despite detection until the initially planned survey effort is consumed. However, a more realistic scenario is often that surveys stop after detection (i.e., follow a “removal” sampling design) and then management begins. Such an approach will indicate a different optimal survey design and can be expected to be more efficient. We analyze this case and compare the expected efficiency of invasive species management programs under both survey methods. We also evaluate the impact of mis‐specifying the type of sampling approach during the program design phase. We derive analytical expressions that optimize resource allocation between monitoring and management in surveillance programs when surveys stop after detection. We do this under a scenario of unconstrained resources and scenarios where survey budget is constrained. The efficiency of surveillance programs is greater if a “removal survey” design is used, with larger gains obtained when savings from early detection are high, occupancy is high, and survey costs are not much lower than early management costs at a site. Designing a surveillance program disregarding that surveys stop after detection can result in an efficiency loss. Our results help guide the design of future surveillance programs for invasive species. Addressing program design within a decision‐theoretic framework can lead to a better use of available resources. We show how species prevalence, its detectability, and the benefits derived from early detection can be considered.