Search

Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological summaries, most noticeably the Persistence Diagram, are typically defined in complex spaces, we adopt a kernel approach to translate them into more familiar vector spaces. We define a topological exponential kernel, we characterize it, and we show that, despite not being positive semi-definite, it can be successfully used in regression and classification tasks.

This paper explores the mobility of the highly educated young Greek scholars. This is made possible through a bibliometric analysis of the affiliation countries of scholars who have published in peer reviewed journals indexed in Scopus. Approximately half of the researchers are identified from publications covered in Scopus for the period 2000–2019. A general taxonomy model is followed for analysing scientific mobility using affiliation changes. The greatest share of researchers (78.3%) appear to be static (74.6% in Greece and 3.7% abroad), whereas the mobile researcher category (21.7%) is divided into migrants (8.9%)—researchers who have left their country of origin—and travellers (12.8%)—researchers who gain additional affiliations while maintaining affiliation with their country of origin. According to the findings, the majority and especially the researcher elite (90.5%) did not sever ties with their country of origin, Greece, but instead built a chain of affiliations that linked nations together. Such chains are represented as groups of countries (clusters), in which the scientific connections between different countries can be visualised. It can be reasoned that the majority of researchers (70.3%) have a tendency to publish to a group of countries with ‘traditionally’ significant scientific impact.

Objectives The purpose of this study was to establish reference charts for fetal corpus callosum length in a convenience sample. Methods A prospective cross-sectional study was conducted at the Artemisia Fetal–Maternal Medical Center between December 2008 and January 2012. Among 16,975 fetal biometric measurements between 19 weeks and 37 weeks 6 days’ gestation, 3438 measurements of the corpus callosum (20.3%) were available. After excluding 488 measurements (14.2%), a total of 2950 fetuses (85.8%) were considered and analyzed only once. Parametric and nonparametric quantile regression models were used for the statistical analysis. To evaluate the robustness of the proposed reference charts with respect to various distributional assumptions on the sonographic measurements at hand, we compared the gestational age (GA)-specific reference curves produced by the statistical methods used. Results The mean corpus callosum length was 26.18 mm (SD, 4.5 mm; 95% confidence interval, 26.01–26.34 mm). The linear regression equation expressing the length of the corpus callosum as a function of GA was length (mm) = −11.17 + 1.62 × GA. The correlation between the dimension and gestation was expressed by the coefficient r = 0.83. Normal mean lengths according the parametric and nonparametric methods were defined for each week of gestation. Conclusions This work provides new quantile-based reference charts for corpus callosum length measurements that may be useful for diagnosis of congenital corpus callosum anomalies in fetal life.

Experimental design represents the typical context in which the interplay between Bayesian and frequentist methodology is natural and useful. Before the data are observed, it is licit and unavoidable even for a Bayesian statistician to take into account sample variability for the evaluation of statistical procedures and for decision making. At the same time, design planning fatally involves a number of pre-experimental choices that even a frequentist statistician is forced to make, preferably by exploiting external sources of knowledge. In this paper we discuss this mutual exchange between Bayesian and frequentist methodology, with specific focus on the primary crucial aspect of experimental designs, that is sample size determination (SSD). We review this topic by highlighting how the interplay between two prior distributions helps in managing the close relationship between the two approaches. Although the distinction between decisional and performance-based methods for Bayesian SSD is discussed, the main interest of this article is on the latter. We propose a general framework that includes several performance-based methods as special cases and thus makes the comparison of their characteristics easier. Finally, we extend the overview to robust methods for Bayesian SSD that allow to deal with the critical issue of sensitivity to prior elicitation. Illustrative examples are provided for normal models.

In sequential experiments the sample size is not planned in advance. Data are progressively collected and a stopping rule based on the observed results is defined in order to terminate the study. In a Bayesian framework, it is straightforward to monitor an ongoing experiment looking at the posterior probability that a parameter of interest $$\theta $$ , belongs to a given set. Specifically, in this paper we focus on the context of phase II clinical trials, where $$\theta $$ represents treatment efficacy. The Bayesian stopping rule we adopt involves the posterior probability that $$\theta $$ exceeds a clinically relevant threshold. Moreover, we introduce a robust version of this criterion by replacing the single prior distribution with a class of prior distributions. A simulation study is performed to compare the average sample sizes of the robust sequential approach both with the sample sizes of the non robust approach and of the non sequential approach. An interesting result is that, when the class of prior distributions is sufficiently narrow, the average sample sizes of the robust sequential approach can be smaller than the non sequential sample sizes.

In this paper we propose a predictive Bayesian approach to sample size determination (SSD) and re-estimation in clinical trials, in the presence of multiple sources of prior information. The method we suggest is based on the use of mixtures of prior distributions for the unknown quantity of interest, typically a treatment effect or an effects-difference. Methodologies are developed using normal models with mixtures of conjugate priors. In particular we extend the SSD analysis of Gajewski and Mayo (Statist. Med. 2006; 25:2554-2566) and the sample size re-estimation technique of Wang (Biometrical J. 2006; 48(5):1-13).

This article considers sample size determination methods based on Bayesian credible intervals for θ , an unknown real-valued parameter of interest. We consider clinical trials and assume that θ represents the difference in the effects of a new and a standard therapy. In this context, it is typical to identify an interval of parameter values that imply equivalence of the two treatments (range of equivalence). Then, an experiment designed to show superiority of the new treatment is successful if it yields evidence that θ is sufficiently large, i.e. if an interval estimate of θ lies entirely above the superior limit of the range of equivalence. Following a robust Bayesian approach, we model uncertainty on prior specification with a class Γ of distributions for θ and we assume that the data yield robust evidence if, as the prior varies in Γ , the lower bound of the credible set inferior limit is sufficiently large. Sample size criteria in the article consist in selecting the minimal number of observations such that the experiment is likely to yield robust evidence. These criteria are based on summaries of the predictive distributions of lower bounds of the random inferior limits of credible intervals. The method is developed for the conjugate normal model and applied to a trial for surgery of gastric cancer.

Objective To establish reference charts for fetal cerebellar vermis height in an unselected population. Methods A prospective cross-sectional study between September 2009 and December 2014 was carried out at ALTAMEDICA Fetal–Maternal Medical Centre, Rome, Italy. Of 25203 fetal biometric measurements, 12167 (48%) measurements of the cerebellar vermis were available. After excluding 1562 (12.8%) measurements, a total of 10605 (87.2%) fetuses were considered and analyzed once only. Parametric and nonparametric quantile regression models were used for the statistical analysis. In order to evaluate the robustness of the proposed reference charts regarding various distributional assumptions on the ultrasound measurements at hand, we compared the gestational age-specific reference curves we produced through the statistical methods used. Normal mean height based on parametric and nonparametric methods were defined for each week of gestation and the regression equation expressing the height of the cerebellar vermis as a function of gestational age was calculated. Finally the correlation between dimension/gestation was measured. Results The mean height of the cerebellar vermis was 12.7mm (SD, 1.6mm; 95% confidence interval, 12.7–12.8mm). The regression equation expressing the height of the CV as a function of the gestational age was: height (mm) = -4.85+0.78 x gestational age. The correlation between dimension/gestation was expressed by the coefficient r = 0.87. Conclusion This is the first prospective cross-sectional study on fetal cerebellar vermis biometry with such a large sample size reported in literature. It is a detailed statistical survey and contains new centile-based reference charts for fetal height of cerebellar vermis measurements.

Introduction: Since the introduction of the European Society of Human Reproduction and Embryology/European Society for Gynaecological Endoscopy (ESHRE/ESGE) classification of Mullerian anomalies, various authors have raised major concern about its clinical implications, as specific diagnostic criteria that clearly correlate to pregnancy have not yet been validated in clinical practice by any prospective or retrospectives studies. In this study, we aimed to correlate the ESHRE/ESGE classification with the occurrence of pregnancy, consideringthetwo different definitions of myometrial thickness. Methods: A retrospective study, including an ultra-selected cohort of 79 patients, from January 2010 to March 2014. All women with fertilityproblems, who had an isolated andsuspected uterine malformation, t ultrasound and hysteroscopy, were retrospectively included in this study. Myometrial thickness was defined as the entire myometrial layer, as suggested by the ESHRE/ESGE criteria, or the free myometrial layer, as suggested by Gubbini. Results: We failed to evidence an association between the occurrence of pregnancy in the two most representative classes (U0 and U2), considering the free myometrial layer, and the entire myometrial layer. When we considered the effect of hysteroscopic surgery on the occurrence of pregnancy, we also failed to obtain a statistically significant difference. Discussion: The ESHRE/ESGE classification may be useful in classifying Mullerian anomalies, but it needs to be applied in larger series. However, we think that new parameters and algorithms are needed for a better prediction of pregnancy. We recommendto associate the fundal uterine vascularization to the ESHRE/ESGE criteria to be analysed in further studies.

In the presence of prior information on an unknown parameter of a statistical model, Bayesian and frequentist estimates based on the same observed data do not coincide. However, in many standard parametric problems, this difference tends to decrease for growing sample size. In this paper we consider as a measure of discrepancy (Dn) the squared difference between Bayesian and frequentist point estimators of the parameter of a model. We derive the predictive distribution of Dn for finite sample sizes in the case of a one-dimensional exponential family and we study its behavior for increasing sample size. Numerical examples are illustrated for normal models.

Tan and Machin (biStat. Med. 2002; 21:1991-2012) introduce a Bayesian two-stage design for phase II clinical trials where the binary endpoint of interest is treatment efficacy. In this paper we propose an extension of their design to incorporate safety considerations. At each stage we define the treatment successful and deserving of further study if the total number of adverse events is sufficiently small and the number of responders who simultaneously do not experience any toxicity is sufficiently large. Therefore, our criterion is based on the joint posterior probability that the true overall toxicity rate and the true efficacy-and-safety rate are, respectively, smaller and larger than conveniently pre-specified target values. The optimal two-stage sample sizes are determined specifying a minimum threshold for the above-mentioned posterior probability, computed under the assumption that favorable outcomes have occurred. Besides describing the proposed design, we suggest how to construct informative prior scenarios and we also apply the reference algorithm to derive a non-informative prior distribution. Finally, some numerical results are provided and a real data application is illustrated.

This article deals with determination of a sample size that guarantees the success of a trial. We follow a Bayesian approach and we say an experiment is successful if it yields a large posterior probability that an unknown parameter of interest (an unknown treatment effect or an effects-difference) is greater than a chosen threshold. In this context, a straightforward sample size criterion is to select the minimal number of observations so that the predictive probability of a successful trial is sufficiently large. In the paper we address the most typical criticism to Bayesian methods-their sensitivity to prior assumptions-by proposing a robust version of this sample size criterion. Specifically, instead of a single distribution, we consider a class of plausible priors for the parameter of interest. Robust sample sizes are then selected by looking at the predictive distribution of the lower bound of the posterior probability that the unknown parameter is greater than a chosen threshold. For their flexibility and mathematical tractability, we consider classes of epsilon-contamination priors. As specific applications we consider sample size determination for a Phase III trial.

Functional data are usually assumed to be observed on a common domain. However, it is often the case that some portion of the functional data is missing for some statistical unit, invalidating most of the existing techniques for functional data analysis. The development of methods able to handle partially observed or incomplete functional data is currently attracting increasing interest. We here briefly review this literature. We then focus on discrimination based on principal component analysis and illustrate a few possible methods via simulation studies and an application to the AneuRisk65 data set. We show that carrying out the analysis over the full domain, where at least one of the functional data is observed, may not be the optimal choice for classification purposes.