Generating a smallest binary tree by proper selection of the longest edges to bisect in a unit simplex refinement

In several areas like global optimization using branch-and-bound methods for mixture design, the unit n-simplex is refined by longest edge bisection (LEB). This process provides a binary search tree. For \(n>2\), simplices appearing during the refinement process can have more than one longest edge (LE). The size of the resulting binary tree depends on the specific sequence of bisected longest edges. The questions are how to calculate the size of one of the smallest binary trees generated by LEB and how to find the corresponding sequence of LEs to bisect, which can be represented by a set of LE indices. Algorithms answering these questions are presented here. We focus on sets of LE indices that are repeated at a level of the binary tree. A set of LEs was presented in Aparicio et al. (Informatica 26(1):17–32, 2015), for \(n=3\). An additional question is whether this set is the best one under the so-called \(m_k\)-valid condition.     

$$D_s$$-optimality in copula models

Optimum experimental design theory has recently been extended for parameter estimation in copula models. The use of these models allows one to gain in flexibility by considering the model parameter set split into marginal and dependence parameters. However, this separation also leads to the natural issue of estimating only a subset of all model parameters. In this work, we treat this problem with the application of the \(D_s\)-optimality to copula models. First, we provide an extension of the corresponding equivalence theory. Then, we analyze a wide range of flexible copula models to highlight the usefulness of \(D_s\)-optimality in many possible scenarios. Finally, we discuss how the usage of the introduced design criterion also relates to the more general issue of copula selection and optimal design for model discrimination.     

Control‐based imputation for sensitivity analyses in informative censoring for recurrent event data

In clinical trials, missing data commonly arise through nonadherence to the randomized treatment or to study procedure. For trials in which recurrent event endpoints are of interests, conventional analyses using the proportional intensity model or the count model assume that the data are missing at random, which cannot be tested using the observed data alone. Thus, sensitivity analyses are recommended. We implement the control‐based multiple imputation as sensitivity analyses for the recurrent event data. We model the recurrent event using a piecewise exponential proportional intensity model with frailty and sample the parameters from the posterior distribution. We impute the number of events after dropped out and correct the variance estimation using a bootstrap procedure. We apply the method to an application of sitagliptin study.     

(Sub) Optimality and (non) optimal satisficing in risky decision experiments

We implement a risky choice experiment based on one-dimensional choice variables and risk neutrality induced via binary lottery incentives. Each participant confronts many parameter constellations with varying optimal payoffs. We assess (sub)optimality, as well as (non)optimal satisficing by eliciting aspirations in addition to choices. Treatments differ in the probability that a binary random event, which are payoff—but not optimal choice—relevant is experimentally induced and whether participants choose portfolios directly or via satisficing, i.e., by forming aspirations and checking for satisficing before making their choice. By incentivizing aspiration formation, we can test satisficing, and in cases of satisficing, determine whether it is optimal.     

Analysis of robust design experiments with time-dependent ordinal response characteristics: a quality improvement study from the horticulture industry

An approach to the analysis of time-dependent ordinal quality score data from robust design experiments is developed and applied to an experiment from commercial horticultural research, using concepts of product robustness and longevity that are familiar to analysts in engineering research. A two-stage analysis is used to develop models describing the effects of a number of experimental treatments on the rate of post-sales product quality decline. The first stage uses a polynomial function on a transformed scale to approximate the quality decline for an individual experimental unit using derived coefficients and the second stage uses a joint mean and dispersion model to investigate the effects of the experimental treatments on these derived coefficients. The approach, developed specifically for an application in horticulture, is exemplified with data from a trial testing ornamental plants that are subjected to a range of treatments during production and home-life. The results of the analysis show how a number of control and noise factors affect the rate of post-production quality decline. Although the model is used to analyse quality data from a trial on ornamental plants, the approach developed is expected to be more generally applicable to a wide range of other complex production systems.