A Metaheuristic Adaptive Cubature Based Algorithm to Find Bayesian Optimal Designs for Nonlinear Models

Finding Bayesian optimal designs for nonlinear models is a difficult task because the optimality criteriontypically requires us to evaluate complex integrals before we perform a constrained optimization. Wepropose a hybridized method where we combine an adaptive multidimensional integration algorithm anda metaheuristic algorithm called imperialist competitive algorithm to find Bayesian optimal designs. Weapply our numerical method to a few challenging design problems to demonstrate its efficiency. Theyinclude finding D-optimal designs for an item response model commonly used in education, Bayesianoptimal designs for survivalmodels, and Bayesian optimal designs for a four-parameter sigmoid Emax doseresponse model. Supplementary materials for this article are available online and they contain an R packagefor implementing the proposed algorithm and codes for reproducing all the results in this paper

Personalisierung von EUS für Entscheidungsprozesse von Experten – Gestaltungspotenziale des Recognition-Primed Decision-Modells

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Comparison of random‐effects meta‐analysis models for the relative risk in the case of rare events - a simulation study

Pooling the relative risk (RR) across studies investigating rare events, for example, adverse events, via meta‐analytical methods still presents a challenge to researchers. The main reason for this is the high probability of observing no events in treatment or control group or both, resulting in an undefined log RR (the basis of standard meta‐analysis). Other technical challenges ensue, for example, the violation of normality assumptions, or bias due to exclusion of studies and application of continuity corrections, leading to poor performance of standard approaches. In the present simulation study, we compared three recently proposed alternative models (random‐effects [RE] Poisson regression, RE zero‐inflated Poisson [ZIP] regression, binomial regression) to the standard methods in conjunction with different continuity corrections and to different versions of beta‐binomial regression. Based on our investigation of the models' performance in 162 different simulation settings informed by meta‐analyses from the Cochrane database and distinguished by different underlying true effects, degrees of between‐study heterogeneity, numbers of primary studies, group size ratios, and baseline risks, we recommend the use of the RE Poisson regression model. The beta‐binomial model recommended by Kuss (2015) also performed well. Decent performance was also exhibited by the ZIP models, but they also had considerable convergence issues. We stress that these recommendations are only valid for meta‐analyses with larger numbers of primary studies. All models are applied to data from two Cochrane reviews to illustrate differences between and issues of the models. Limitations as well as practical implications and recommendations are discussed; a flowchart summarizing recommendations is provided

Evaluation der multimedialen Lehre in der Leistungs- und Kostenrechnung

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Optimal design of the Wilcoxon-Mann-Whitney-test

In scientific research, many hypotheses relate to the comparison of two independent groups. Usually, it is of interest to use a design (i.e., the allocation of sample sizes $m$ and $n$ for fixed $N = m + n$) that maximizes the power of the applied statistical test. It is known that the two-sample t-tests for homogeneous and heterogeneous variances may lose substantial power when variances are unequal but equally large samples are used. We demonstrate that this is not the case for the non-parametric Wilcoxon-Mann-Whitney-test, whose application in biometrical research fields is motivated by two examples from cancer research. We prove the optimality of the design $m = n$ in case of symmetric and identically shaped distributions using normal approximations and show that this design generally offers power only negligibly lower than the optimal design for a wide range of distributions. Please cite this paper as published in the Biometrical Journal (https://doi.org/10.1002/bimj.201600022)

A flexible ratio regression approach for zero-truncated capture–recapture counts

Capture–recapture methods are used to estimate the size of a population of interest which is only partially observed. In such studies, each member of the population carries a count of the number of times it has been identified during the observational period. In real-life applications, only positive counts are recorded, and we get a truncated at zero-observed distribution. We need to use the truncated count distribution to estimate the number of unobserved units. We consider ratios of neighboring count probabilities, estimated by ratios of observed frequencies, regardless of whether we have a zero-truncated or an untruncated distribution. Rocchetti et al. (2011) have shown that, for densities in the Katz family, these ratios can be modeled by a regression approach, and Rocchetti et al. (2014) have specialized the approach to the beta-binomial distribution. Once the regression model has been estimated, the unobserved frequency of zero counts can be simply derived. The guiding principle is that it is often easier to find an appropriate regression model than a proper model for the count distribution. However, a full analysis of the connection between the regression model and the associated count distribution has been missing. In this manuscript, we fill the gap and show that the regression model approach leads, under general conditions, to a valid count distribution; we also consider a wider class of regression models, based on fractional polynomials. The proposed approach is illustrated by analyzing various empirical applications, and by means of a simulation study

Estimating the size of undetected cases of the COVID-19 outbreak in Europe: An upper bound estimator

Under embargo until: 2021-12-23Background While the number of detected COVID-19 infections are widely available, an understanding of the extent of undetected cases is urgently needed for an effective tackling of the pandemic. The aim of this work is to estimate the true number of COVID-19 (detected and undetected) infections in several European countries. The question being asked is: How many cases have actually occurred? Methods We propose an upper bound estimator under cumulative data distributions, in an open population, based on a day-wise estimator that allows for heterogeneity. The estimator is data-driven and can be easily computed from the distributions of daily cases and deaths. Uncertainty surrounding the estimates is obtained using bootstrap methods. Results We focus on the ratio of the total estimated cases to the observed cases at April 17th. Differences arise at the country level, and we get estimates ranging from the 3.93 times of Norway to the 7.94 times of France. Accurate estimates are obtained, as bootstrap-based intervals are rather narrow. Conclusions Many parametric or semi-parametric models have been developed to estimate the population size from aggregated counts leading to an approximation of the missed population and/or to the estimate of the threshold under which the number of missed people cannot fall (i.e. a lower bound). Here, we provide a methodological contribution introducing an upper bound estimator and provide reliable estimates on the dark number, i.e. how many undetected cases are going around for several European countries, where the epidemic spreads differently.publishedVersio