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Cohen's and Fleiss' kappa are well-known measures for inter-rater reliability. However, they only allow a rater to select exactly one category for each subject. This is a severe limitation in some research contexts: for example, measuring the inter-rater reliability of a group of psychiatrists diagnosing patients into multiple disorders is impossible with these measures. This paper proposes a generalisation of the Fleiss' kappa coefficient that lifts this limitation. Specifically, the proposed $\kappa$ statistic measures inter-rater reliability between multiple raters classifying subjects into one-or-more nominal categories. These categories can be weighted according to their importance, and the measure can take into account the category hierarchy (e.g., categories consisting of subcategories that are only available when choosing the main category like a primary psychiatric disorder and sub-disorders; but much more complex dependencies between categories are possible as well). The proposed $\kappa$ statistic can handle missing data and a varying number of raters for subjects or categories. The paper briefly overviews existing methods allowing raters to classify subjects into multiple categories. Next, we derive our proposed measure step-by-step and prove that the proposed measure equals Fleiss' kappa when a fixed number of raters chose one category for each subject. The measure was developed to investigate the reliability of a new mathematics assessment method, of which an example is elaborated. The paper concludes with the worked-out example of psychiatrists diagnosing patients into multiple disorders., Comment: 19 pages, 2 figures

This paper reviews the growing field of Bayesian prediction. Bayes point and interval prediction are defined and exemplified and situated in statistical prediction more generally. Then, four general approaches to Bayes prediction are defined and we turn to predictor selection. This can be done predictively or non-predictively and predictors can be based on single models or multiple models. We call these latter cases unitary predictors and model average predictors, respectively. Then we turn to the most recent aspect of prediction to emerge, namely prediction in the context of large observational data sets and discuss three further classes of techniques. We conclude with a summary and statement of several current open problems., Comment: 33 pages

Response-Adaptive Randomization (RAR) is part of a wider class of data-dependent sampling algorithms, for which clinical trials are typically used as a motivating application. In that context, patient allocation to treatments is determined by randomization probabilities that change based on the accrued response data in order to achieve experimental goals. RAR has received abundant theoretical attention from the biostatistical literature since the 1930's and has been the subject of numerous debates. In the last decade, it has received renewed consideration from the applied and methodological communities, driven by well-known practical examples and its widespread use in machine learning. Papers on the subject present different views on its usefulness, and these are not easy to reconcile. This work aims to address this gap by providing a unified, broad and fresh review of methodological and practical issues to consider when debating the use of RAR in clinical trials., Comment: Update in response to editor comments

Modern data analysis frequently involves large-scale hypothesis testing, which naturally gives rise to the problem of maintaining control of a suitable type I error rate, such as the false discovery rate (FDR). In many biomedical and technological applications, an additional complexity is that hypotheses are tested in an online manner, one-by-one over time. However, traditional procedures that control the FDR, such as the Benjamini-Hochberg procedure, assume that all p-values are available to be tested at a single time point. To address these challenges, a new field of methodology has developed over the past 15 years showing how to control error rates for online multiple hypothesis testing. In this framework, hypotheses arrive in a stream, and at each time point the analyst decides whether to reject the current hypothesis based both on the evidence against it, and on the previous rejection decisions. In this paper, we present a comprehensive exposition of the literature on online error rate control, with a review of key theory as well as a focus on applied examples. We also provide simulation results comparing different online testing algorithms and an up-to-date overview of the many methodological extensions that have been proposed., Comment: Updated in response to reviewer comments

Modern data analysis frequently involves large-scale hypothesis testing, which naturally gives rise to the problem of maintaining control of a suitable type I error rate, such as the false discovery rate (FDR). In many biomedical and technological applications, an additional complexity is that hypotheses are tested in an online manner, one-by-one over time. However, traditional procedures that control the FDR, such as the Benjamini-Hochberg procedure, assume that all p-values are available to be tested at a single time point. To address these challenges, a new field of methodology has developed over the past 15 years showing how to control error rates for online multiple hypothesis testing. In this framework, hypotheses arrive in a stream, and at each time point the analyst decides whether to reject the current hypothesis based both on the evidence against it, and on the previous rejection decisions. In this paper, we present a comprehensive exposition of the literature on online error rate control, with a review of key theory as well as a focus on applied examples. We also provide simulation results comparing different online testing algorithms and an up-to-date overview of the many methodological extensions that have been proposed., Updated in response to reviewer comments

Objectives To present a comprehensive real-world micro-costing analysis of bariatric surgery. Methods Patients were included if they underwent primary bariatric surgery (gastric banding [GB], gastric bypass [GBP] and sleeve gastrectomy [SG]) between 2013 and 2019. Costs were disaggregated into cost items and average-per-patient costs from the Australian healthcare systems perspective were expressed in constant 2019 Australian dollars for the entire cohort and subgroup analysis. Annual population-based costs were calculated to capture longitudinal trends. A generalized linear model (GLM) predicted the overall bariatric-related costs. Results N = 240 publicly funded patients were included, with the waitlist times of ≤ 10.7 years. The mean direct costs were $11,269. The operating theatre constituted the largest component of bariatric-related costs, followed by medical supplies, salaries, critical care use, and labour on-costs. Average cost for SG ($12,632) and GBP ($15,041) was higher than that for GB ($10,049). Operating theatre accounted for the largest component for SG/GBP costs, whilst medical supplies were the largest for GB. We observed an increase in SG and a decrease in GB procedures over time. Correspondingly, the main cost driver changed from medical supplies in 2014–2015 for GB procedures to operating theatre for SG thereafter. GLM model estimates of bariatric average cost ranged from $7,580 to $36,633. Conclusions We presented the first detailed characterization of the scale, disaggregated profile and determinants of bariatric-related costs, and examined the evolution of resource utilization patterns and costs, reflecting the shift in the Australian bariatric landscape over time. Understanding these patterns and forecasting of future changes are critical for efficient resource allocation. Supplementary Information The online version contains supplementary material available at 10.1007/s10198-021-01405-x.

Unobserved spatial confounding variables are prevalent in environmental and ecological applications where the system under study is complex and the data are often observational. Instrumental variables (IVs) are a common way to address unobserved confounding; however, the efficacy of using IVs on spatial confounding is largely unknown. This paper explores the effectiveness of IVs in this situation -- with particular attention paid to the spatial scale of the instrument. We show that, in case of spatially-dependent treatments, IVs are most effective when they vary at a finer spatial resolution than the treatment. We investigate IV performance in extensive simulations and apply the model in the example of long term trends in the air pollution and cardiovascular mortality in the United States over 1990-2010. Finally, the IV approach is also extended to the spatial interference setting, in which treatments can affect nearby responses., 27 pages, 5 figures, 9 tables

When assessing causal effects, determining the target population to which the results are intended to generalize is a critical decision. Randomized and observational studies each have strengths and limitations for estimating causal effects in a target population. Estimates from randomized data may have internal validity but are often not representative of the target population. Observational data may better reflect the target population, and hence be more likely to have external validity, but are subject to potential bias due to unmeasured confounding. While much of the causal inference literature has focused on addressing internal validity bias, both internal and external validity are necessary for unbiased estimates in a target population. This paper presents a framework for addressing external validity bias, including a synthesis of approaches for generalizability and transportability, the assumptions they require, as well as tests for the heterogeneity of treatment effects and differences between study and target populations., Comment: 30 pages, 3 figures

As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale and complex data by assuming that data are continuous functions, e.g., a realization of a continuous process (curves) or continuous random fields (surfaces), and that each curve or surface is considered as a single observation. Here, we provide an overview of functional data analysis when data are complex and spatially correlated. We provide definitions and estimators of the first and second moments of the corresponding functional random variable. We present two main approaches: The first assumes that data are realizations of a functional random field, i.e., each observation is a curve with a spatial component. We call them 'spatial functional data'. The second approach assumes that data are continuous deterministic fields observed over time. In this case, one observation is a surface or manifold, and we call them 'surface time series'. For the two approaches, we describe software available for the statistical analysis. We also present a data illustration, using a high-resolution wind speed simulated dataset, as an example of the two approaches. The functional data approach offers a new paradigm of data analysis, where the continuous processes or random fields are considered as a single entity. We consider this approach to be very valuable in the context of big data., Some typos fixed and new references added

In this paper, we address the problem of identification of maximum safe dose, where the maximum safe is defined as the highest dose that is non-inferior to the reference treatment (negative control) dose such that any other lower dose is also non-inferior to the reference dose. Statistical methodology for non-inferiority trial for several multiple treatments in establishing efficacy of new treatment readily available for multiplicity adjustment. We extend this methodology to identification of maximum safe dose in a toxicological experiment by incorporating the confidence set-based stepwise procedure using Fieller's confidence interval method under heteroscedasticity without multiplicity adjustment. Our simulation studies indicate that the familywise error rate (FWER) is properly controlled in a strong sense, and the power of our procedure depicts that power increases with increasing in sample size and the ratio of mean difference. Results from our studies support the theoretical findings.

In this paper we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring" on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide range of interference functions encountered in applications, we show both by theory and simulations that the classical Neymanian estimator for the direct effect has desirable properties for our designs. This further extends to settings where homophily is present in addition to interference.

We propose a modified unrelated question randomized response technique (RRT) model which allows respondents the option of answering a sensitive question directly without using the randomization device if they find the question nonsensitive. This situation has been handled before by Gupta, Tuck, Spears Gill, and Crowe using the split sample approach. In this work we avoid the split sample approach, which requires larger total sample size. Instead, we estimate the prevalence of the sensitive characteristic by using an optional unrelated question RRT model, but the corresponding sensitivity level is estimated from the same sample by using the traditional binary unrelated question RRT model of Greenberg, Abul-Ela, Simmons, and Horvitz. We compare the simulation results of this new model with those of the split-sample based optional unrelated question RRT model of Gupta et al. and the simple unrelated question RRT model of Greenberg et al. Computer simulations show that the new binary response and quantitative response models have the smallest variance among the three models when they have the same sample size.

Researchers are sometimes interested in predicting a distal or external outcome (such as smoking cessation at follow-up) from the trajectory of an intensively recorded longitudinal variable (such as urge to smoke). This can be done in a semiparametric way via scalar-on-function regression. However, the resulting fitted coefficient regression function requires special care for correct interpretation, as it represents the joint relationship of time points to the outcome, rather than a marginal or cross-sectional relationship. We provide practical guidelines, based on experience with scientific applications, for helping practitioners interpret their results and illustrate these ideas using data from a smoking cessation study.

Les soins prenatals chez les femmes enceintes sont l'un des facteurs les plus importants de la reduire la morbidite maternelle, la mortalite, les traumatismes a la naissance et d'autres problemes de la puerperale. Dans le present article, les facteurs affectant l'utilisation des services de soins prenatals, la disponibilite de ces services, la perception des femmes a son egard, le niveau de sensibilisation, le taux de participation, les sources et types d'informations sur les services de soins prenatals chez les femmes des âge de procreer sont ete etudies. Les outls d'analyse descriptive tels que les tableaux, lees diagrammes a secteurs et a barres sont utilises pour la presentation des variables sociodemographiques et de recherche. Des tests d'hypotheses sous forme de tests d'association entre l'utilisation par les femmes des services de sante des soins prenatals et certaines variables demographiques telles que l'âge, l'education, la formation du conjoint, la religion, etc, sont abordes a un seuil de signification de 5%.

We provide a review of prior distributions for objective Bayesian analysis. We start by examining some foundational issues and then organize our exposition into priors for: i) estimation or prediction; ii) model selection; iii) high-dimensional models. With regard to i), we present some basic notions, and then move to more recent contributions on discrete parameter space, hierarchical models, nonparametric models, and penalizing complexity priors. Point ii) is the focus of this paper: it discusses principles for objective Bayesian model comparison, and singles out some major concepts for building priors, which are subsequently illustrated in some detail for the classic problem of variable selection in normal linear models. We also present some recent contributions in the area of objective priors on model space. With regard to point iii) we only provide a short summary of some default priors for high-dimensional models, a rapidly growing area of research.

We present a selective review of statistical modeling of dynamic networks. We focus on models with latent variables, specifically, the latent space models and the latent class models (or stochastic blockmodels), which investigate both the observed features and the unobserved structure of networks. We begin with an overview of the static models, and then we introduce the dynamic extensions. For each dynamic model, we also discuss its applications that have been studied in the literature, with the data source listed in Appendix. Based on the review, we summarize a list of open problems and challenges in dynamic network modeling with latent variables.

We survey some aspects of the classical prediction theory for stationary processes, in discrete time in Section 1, turning in Section 2 to continuous time, with particular reference to reproducing-kernel Hilbert spaces and the sampling theorem. We discuss the discrete-continuous theories of ARMA-CARMA, GARCH-COGARCH, and OPUC-COPUC in Section 3. We compare the various models treated in Section 4 by how well they model volatility, in particular volatility clustering. We discuss the infinite-dimensional case in Section 5, and turn briefly to applications in Section 6.

Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in: phylogenetic analysis, network tomography, computer vision, causal modeling, and data clustering. They also contain other well-known classes of models like hidden Markov models, Brownian motion tree model, the Ising model on a tree, and many popular models used in phylogenetics. This article offers a concise introduction to the theory of latent tree models. We emphasise the role of tree metrics in the structural description of this model class, in designing learning algorithms, and in understanding fundamental limits of what and when can be learned.

Extracting information from large graphs has become an important statistical problem since network data is now common in various fields. In this minicourse we will investigate the most natural statistical questions for three canonical probabilistic models of networks: (i) community detection in the stochastic block model, (ii) finding the embedding of a random geometric graph, and (iii) finding the original vertex in a preferential attachment tree. Along the way we will cover many interesting topics in probability theory such as P\'olya urns, large deviation theory, concentration of measure in high dimension, entropic central limit theorems, and more., Comment: 38 pages, 10 figures. Lecture notes for a graduate minicourse presented at University of Washington and the XX Brazilian School of Probability in June/July 2016

Errata for “A survey of Bayesian predictive methods for model assessment, selection and comparison” by A. Vehtari and J. Ojanen, Statistics Surveys, 6 (2012), 142–228. doi:10.1214/12-SS102.