Statistics and Probability Commons^™

On Robust Estimation Of Multivariate Location And Scale With Applications, Soumya Chakraborty

Doctoral Theses

The principal objective of this thesis is, in a nutshell, to provide robust estimators of multivariate location and scale which have reasonable to high model efficiency but avoid high computational complexity so as to be practically useful in real problems. We utilize the minimum density power divergence (DPD) and the related philosophy to invoke robustness. There are some computational issues while minimizing the DPD in different multivariate set-ups. We will work on this problem rigorously and come up with three types of estimation procedures which are explicitly or implicitly related to the minimum DPD methodology, keeping the computational issue in …

Positive Solutions Of Semipositone Singular Three-Points Boundary Value Problems For Nonlinear Fractional Differential Equations, Xueyan Zhang, Zhaocai Hao, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

This study introduces the existence of one positive solution for a specific category of semipositive singular three-point boundary value problems associated with Caputo fractional differential equations. The proof relies on the application of the Guo–Krasnosel'skii fixed point theorem. In the end, we provide an illustrative example.

A Note On Sufficient Dimension Folding For Regression Mean Function With Categorical Predictors, Bilin Zeng, Akim Adekpedjou, Xuerong Meggie Wen

Mathematics and Statistics Faculty Research & Creative Works

Multi-dimensional arrays are referred to as tensors. Tensor-valued predictors are commonly encountered in modern biomedical applications, such as electroencephalogram (EEG), magnetic resonance imaging (MRI), functional MRI (fMRI), diffusion-weighted MRI, and longitudinal health data. In survival analysis, it is both important and challenging to integrate clinically relevant information, such as gender, age, and disease state along with medical imaging tensor data or longitudinal health data to predict disease outcomes. Most existing higher-order sufficient dimension reduction regressions for matrix- or array-valued data focus solely on tensor data, often neglecting established clinical covariates that are readily available and known to have predictive value. …

Typeface: Machine-Viewing Gentrification On Storefront Imagery In Bedford-Stuyvesant, Brooklyn, Alexander Mcquilkin

Dissertations, Theses, and Capstone Projects

Gentrification—broadly, the replacement of a less powerful group by a more powerful one in an urban context—is oft-discussed in the popular press, but its definition is much-debated in the urban planning literature. Furthermore, academic treatments of displacement understandably focus on measurable yet fairly abstract indicators like changes in rent or income, whereas neighborhood change is often registered by residents on the ground using visual, but difficult-to-quantify markers like retail turnover. This project uses image recognition technology on a set of storefront photos to index the visual streetscape of a neighborhood, as well as to track changes to that portrait over …

Derivation Of An Updated Brief Multivariable Prediction Model To Detect Panic-Related Anxiety In Emergency Department Patients With Cardiopulmonary Complaints, Sharon C. Sung, Felicia J. L. Ang, Arul Earnest, Leslie E. C. Lim, Shreshtha Jolly, Gilaine Rui Ng, A. John Rush, Marcus E. H. Ong

Research Collection School of Social Sciences

Background Patients with panic related-anxiety (i.e., panic attacks or panic disorder) frequently present to emergency departments (EDs) with cardiopulmonary complaints but are often undiagnosed, which can lead to recurrent visits and prolonged distress. This study aimed to derive a new symptom-based multivariable diagnostic prediction model to detect panic-related anxiety in ED patients with cardiopulmonary symptoms.Methods We conducted a single-blind prospective derivation study over 15 months in the ED of a major tertiary hospital in Singapore. Patients presenting with symptoms of palpitations, chest pain, dizziness, or difficulty breathing were assessed using the Structured Clinical Interview for DSM Disorders (SCID) to diagnose …

Let's Play Uno! Training Mathematical Thinking With An Inclusive Card Game, Thierry Meyrath, Clara-Ioana Mincu, Antonella Perucca

Journal of Humanistic Mathematics

We explore probability exercises based on the game UNO. Excluding the Wild cards, the deck contains precisely 100 cards, which makes it convenient to express probabilities as percentages. We discuss the mathematical relation between cards that can be played after other cards. We also propose an algebraic exercise that relates several quantities, such as the number of cards left in the losing player’s hand. Finally, we argue that UNO is a very inclusive game: it is logistically easy to play, allows for players of different skill levels, and can be adapted to meet special needs. Beyond being playful exercises, our …

Estimasi Proporsi Pekerja Anak Pulau Maluku & Papua: Pendekatan Small Area Estimation Hierarchical Bayes Distribusi Beta, Apriani Sofiana, Fauzana Afininnas, Fachrol Mochti, Angga Prayoga, Shafira Husna, Nofita Istiana

Jurnal Ekonomi Kependudukan dan Keluarga

Pekerja anak merupakan isu krusial yang memerlukan penanganan segera untuk mendukung pencapaian target pembangunan global. Pengentasan isu ini menuntut ketersediaan data yang akurat hingga wilayah kecil guna mendukung perumusan kebijakan yang tepat sasaran. Penelitian ini bertujuan menduga proporsi pekerja anak usia 5–17 tahun di kabupaten/kota Pulau Maluku dan Papua tahun 2024 menggunakan metode Small Area Estimation (SAE) Hierarchical Bayes (HB) distribusi Beta. Lima variabel penyerta dari PODES dan regsosek dipilih melalui stepwise regression dan dieksplorasi secara spasial. Hasil pemodelan HB Beta Pulau Maluku dan Papua menunjukkan sebagian besar wilayah masih memiliki RSE tinggi. Untuk meningkatkan presisi, dilakukan klasterisasi wilayah sebelum …

Novel R Shiny Tool For Survival Analysis With Time-Varying Covariate In Oncology Studies: Overcoming Biases And Enhancing Collaboration, Yimei Li, Yang Qiao, Fei Gao, Jordan Gauthier, Qiang Ed Zhang, Jenna Voutsinas, Wendy Leisenring, Ted Gooley, Corinne Summers, Alexandre Hirayama, Cameron Turtle, Rebecca Gardner, Jarcy Zee, Qian Vicky Wu

Wills Eye Hospital Papers

PURPOSE: Our study is motivated by evaluating the role of hematopoietic cell transplantation (HCT) after chimeric antigen receptor T-cell (CAR-T) therapy for ALL, a debated topic. Because patients may receive HCT at different times after CAR-T infusion or never, HCT post-CAR-T should be considered as a time-varying covariate (TVC).

METHODS: Standard Cox models and Kaplan-Meier (KM) curves (naïve method) assume that TVC status is known and fixed at baseline, which can yield biased estimates. Landmark analysis is a popular alternative but depends on a chosen landmark time. Time-dependent (TD) Cox model is better suited for TVC although visualizing survival curves …

Handling Missing Data In Copd Research, Chia-Ying Chiu

ETDs from 2020-2029

Chronic Obstructive Pulmonary Disease (COPD) remains a major global health concern and one of the leading causes of death in the United States, affecting approximately 4.6% of adults and reaching a prevalence of 9.4% in Alabama according to 2024 National Health Interview Survey. The disease imposes a substantial burden on quality of life and healthcare costs and contributes to increased disability-adjusted life years and years of life lost, as highlighted by the 2022 Lancet Commission report. Despite its im-pact, COPD is frequently diagnosed only after irreversible lung damage has occurred, largely due to under-recognized symptoms and limited diagnostic tools. Early …

Statistical Analysis Of Log Transformation Effectiveness In Air Traffic Movement Forecasting During Covid-19 In South Africa, John Lehlaka Masekoameng

Journal of Aviation Technology and Engineering

This study evaluates the effectiveness of log transformation in enhancing multiple regression models used to forecast air traffic movements (ATMs) in South Africa during the COVID-19 pandemic. Using 60 monthly observations from October 2016 to September 2021, the analysis incorporates variables such as revenue, lockdown levels, COVID-19 metrics, exchange rates, gross domestic product, and population. Two models are compared: one using raw ATMs and another with log-transformed ATMs as the dependent variable.

While the untransformed model shows stronger explanatory power (R² = 0.904, adjusted R² = 0.891) compared to the log-transformed model (R² = 0.772, adjusted R² = 0.741), the …

Dietary Inflammatory Index And Risk Of Colorectal Cancer In Japanese Men, Ayaka Kotemori, Kumiko Kito, Motoki Iwasaki, Taiki Yamaji, James Hébert Scd, Junko Ishihara, Manami Inoue, Shoichiro Tsugane, Norie Sawada On The Behalf Of Jphc Study Group

Faculty Publications

Background/Objectives: Unhealthy lifestyles lead to chronic low-grade inflammation, increasing the risk of colorectal cancer. Few studies in East Asia have examined the association between the dietary inflammation potential and colorectal cancer incidence. Therefore, we aimed to investigate this association further in the Japanese population. Methods: This study included 38,807 men aged 45–74 years who participated in the Japan Public Health Center-based prospective study (JPHC Study). The energy-adjusted dietary inflammatory index (E-DII) was derived from a food frequency questionnaire. Hazard ratios (HRs) and 95% confidence intervals (CIs) were estimated using Cox proportional hazards regression models. Differences in risk due to a …

Estimation Of Net Premium For Flight Delay Insurance Using The Aggregate Loss Model: A Case Study Of Indonesia Otas, Azka Nurul Husna, Yulial Hikmah, Ira Rosianal Hikmah

Jurnal Vokasi Indonesia

Air transportation, as one of the most chosen transportation modes, is frequently susceptible to delays. Flight Delay Insurance offers a vital solution to mitigate the financial losses associated with this risk. Premium pricing is a key factor influencing the decision to purchase this insurance, particularly on Online Travel Agent (OTA) platforms where product offerings are often highly comparable. The aggregate loss method is employed herein to ascertain the net premium (or pure premium) price. The loss severity component (X) is modeled using an empirical distribution, while the loss frequency component (N) is modeled using a Negative Binomial distribution with parameters …

Determination Of Sample Size In Vaccine Trials, Meghna Bose

Doctoral Theses

Sample size determination is an important as well as delicate problem in clinical trials. Often, prior information available before the beginning of the trial is used to estimate the sample size. Hence, it is of importance to quantify the prior information available in terms of an Effective Sample Size (ESS). The problem of finding Effective Sample Size (ESS) in Phase II clinical trials, where toxicity and efficacy are the two components of the treatment response vector, is considered. In particular, one of the components is assumed to be binary, and the other is assumed to be continuous. Theoretical expressions for …

Protocol For The Development Of The Who Gestational Weight Gain Charts, Thais Rangel Bousquet Carrilho, Olufemi Taiwo Oladapo, Jennifer A. Hutcheon, Giovanna Gatica-Domínquez, Kathleen M. Rasmussen, Monica C. Flores-Urrutia, Richard Kumapley, Ӧzge Tunçalp, Dang Bahya-Batinda, Amel A. Fayed, Annick Bogaerts, Aris T. Papageorghiou, Cinthya Muñoz-Manrique, Dayana Rodrigues Farias, Eric Ohuma, Harshpal Sachdev, Hayfaa A. Wahabi, Helena J. Teede, Molin Wang, Nandita Perumal Phd

Faculty Publications

Introduction Gestational weight gain (GWG) is an important indicator of maternal nutrition to be monitored during pregnancy. However, there is no evidence-based tool that can be used to monitor it across all geographic locations and pre-pregnancy body mass index (BMI) categories. The WHO is undertaking a project to develop GWG charts by pre-pregnancy BMI category, and to identify GWG ranges associated with the lowest risks of adverse maternal and infant outcomes. This protocol describes all the steps that will be used to accomplish the development of these GWG charts.

Methods and analysis This project will involve the analysis of individual …

Statistics For Social Scientists Who Are A Little Afraid Of Them, Kristie L. Campana

MSU Authors Collection

This is a free textbook aimed at helping advanced undergraduate/beginner graduate students navigate statistics in the social sciences. All resources for this book are released under a creative commons license CC BY-SA 4.0. which means you are able to share, copy, and distribute the material in any medium or format, and that you can adapt and transform upon this content for any purpose. However, this can occur only under the following terms:

You must give appropriate attributions to the text, provide a link to the license, and indicate if any alterations to the text have been made. This can be …

Evaluating Lunch Plan Data In The St. Charles School District (Scsd), Maddy Alexander, Guillermo Bilbao Olarreaga, Duncan Krige, Alyssa Schreiber, Nick Wintz, Wojciech Golik

The Confluence

The SCSD is a public school district in St. Charles, with, on average, 4500 students a year. The SCSD is subdivided into an early childhood center, six elementary schools, two intermediate (5-6,7-8) schools, and two high schools. Vocational schools are also within this district but were not included in this report. The SCSD is concerned with the impact of the Covid-19 pandemic on their district’s population and on the number of students that needed assistance with lunch. They have asked Lindenwood’s 2024-25 PIC Math group to analyze their data from the years 2020-25 and identify any trends. Identifying these trends …

Sociodemographic And Hiv-Related Characteristics Associated With Mental Health Diagnoses Among People Living With Hiv, Monique J. Brown Ph.D., Mph, Jiayang Xiao, Xueying Yang Ph.D., Bankole Olatosi Ph.D., Sharon Weissman, Xiaoming Li Ph.D., Jiajia Zhang Ph.D.

Faculty Publications

Mental health diagnoses have been linked to poor HIV treatment outcomes and poorer quality of life among people living with HIV (PLWH). Therefore, this study aimed to investigate the association between sociodemographic and HIV-related characteristics, and common and serious mental health disorders among PLWH in South Carolina (SC). Data were obtained from the integrated system of statewide electronic health record (EHR) data in SC (2006–2019; N = 8,124). Multivariable logistic regression models were used to determine the associations between sociodemographic and HIV-related characteristics, and common mental health disorders and serious mental health disorders. Among the study population, 4% were 60 …

Teaching Numeracy For Social Justice: Educational Equity, Esther Isabelle Wilder, Crystal C. Rodriguez, Caterina Shost, Eduardo Vianna, Frank Wang

Numeracy

The special collection, “Teaching Numeracy for Social Justice: Educational Equity,” focuses on how quantitative reasoning (QR) can function as a vehicle for equity, empowerment, and democratic participation. Building on a longstanding tradition that treats numeracy as inseparable from social justice, these contributions highlight how progressive pedagogies (e.g., active learning, authentic research, and equity-oriented assessment) have the potential to broaden access for students historically excluded from quantitative fields. The studies span a variety of conceptual frameworks, introductory and advanced quantitative instruction, and interdisciplinary applications, showcasing how inclusive QR practices can build confidence, agency, and real-world understanding. These articles demonstrate that when …

Distribution Of New Statistics Of Parking Functions And Their Generalizations, Stephan Wagner, Catherine H. Yan, Mei Yin

Mathematics: Faculty Scholarship

In this paper we present new results on the enumeration of parking functions and labeled forests. We introduce new statistics on parking functions, which are then extended to labeled forests via bijective correspondences. We determine the joint distribution of two statistics on parking functions and their counterparts on labeled forests. Our results on labeled forests also serve to explain the mysterious equidistribution between two seemingly unrelated statistics in parking functions recently identified by Stanley and Yin and give an explicit bijection between the two statistics. Extensions of our techniques are discussed, including joint distribution on further refinement of these new …

Multiple Myeloma Risk Linked To Dna Damage Response Genes, Michael Conry, Irina Ostrovnaya, Yelena Kemel, Saloni Sinha, Linda B. Baughn, Brian Avery, Kylee Maclachlan, Victoria Groner, Lauren Banaszak, Aaron Norman, Nicholas J. Boddicker, Alyssa I. Clay-Gilmour Ph.D., Shaji Kumar, Ellen Kim, Sita Dandiker, Mitul Waghmare, Susan Slager, Douglas Sborov, Judy Garber, Elizabeth E. Brown, Michelle Hildebrandt, Et. Al.

Faculty Publications

Background DNA damage response genes (DDRG), implicated in several cancers as both predisposing risk factors as well as biomarkers for aggressiveness, have not been fully explored in multiple myeloma (MM).

Methods Herein, we analyzed disease associations of pathogenic variations in nine putative candidate genes using 3 446 MM cases and 323 233 cancer-free controls.

Results Increased MM risk was found to be associated with inherited rare pathogenic mutations in TP53, ATM, CHEK2, KDM1A, and ARID1A, with an enrichment of these variants among individuals with early onset or family history of MM. Individuals with TP53 or ATM germline mutations are also …

A Phase 1, First-In-Human, Dose Escalation Study Of Jnj-80038114, A Psmaxcd3 Bispecific Antibody, In Participants With Metastatic Castration-Resistant Prostate Cancer, Andrew Hudson, Anuradha Jayaram, Benjamin Garmezy, Nicholas Zorko, Kevin Zarrabi, Ligi Mathews, Brent Rupnow, Mengjie Li, Debopriya Ghosh, Karen Urtishak, Peter Francis, Sherry Wang, Edward Attiyeh, Johann De Bono

Department of Medical Oncology Faculty Papers

PURPOSE: Prostate-specific membrane antigen (PSMA) has been identified as a therapeutic target for metastatic castration-resistant prostate cancer (mCRPC). The recent success of radioligands targeting PSMA spurred development of new PSMA-targeting agents including immunotherapy. JNJ-80038114 is a bispecific antibody that binds PSMA on tumor cells and CD3 on T cells to induce anti-tumor activity.

METHODS: This was a phase 1, open-label, multicenter study of JNJ-80038114 in participants with mCRPC and ≥ 1 prior systemic therapy. JNJ-80038114 was administered subcutaneously every 3 weeks (Q3W), starting at 0.1 mg. The primary endpoint was safety. Secondary endpoints included pharmacokinetics (PK), immunogenicity, and prostate-specific antigen …

Affect Regulation In The Context Of Sexual And Gender Minority Stress: A Scoping Review Protocol, Daphne Y. Liu, Benjamin A. Swerdlow, Shao Yuan Chong, Nadia Kako, Alex Rubin, Nicholas S. Perry

Psychology: Faculty Scholarship

Objective

To provide a broad, comprehensive picture of affect regulation in the context of sexual and gender minority stress, this scoping review aims to identify and synthesize methods, methodologies, and available evidence pertinent to emotion regulation and coping in the context of minority stress among sexual and gender minority (SGM) people.

Introduction

SGM people face disproportionately high rates of mental health problems due to experiences of minority stress and lack of social safety. Theories and growing evidence suggest that affect regulation plays a critical role in SGM people’s well-being in the face of minority stress. Researchers have largely studied emotion …

A Probabilistic Modeling Analysis Of The Longitudinal Immune Response To Infection And Vaccination Across Demographic Groups And Pulmonary Symptoms, James O'Hanlon, Kaitlyn Sullivan, Lyndsey M. Muehling, Glenda Canderan, Jie Sun, Judith A. Woodfolk, Jeffrey M. Wilson, Rayanne A. Luke

Spora: A Journal of Biomathematics

Antibody and cytokine kinetics describe the dynamic response to immune events such as infection and vaccination. These dynamics are not fully understood, and mathematical characterization may help explain variability across demographic groups and pulmonary symptoms post-acute infection. We fit time-dependent probability models to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) data to obtain distributions of longitudinal antibody response and cytokine values. To assess differences between groups, an overlap metric is applied to the modeled response curves. Our antibody models suggest significant differences between male and female populations and demonstrate deficient antibody responses of less-healthy groups such as smokers. Our cytokine …

Inhomogeneous Branching Random Walks: Incorporating Genealogy And Density Effects, Lauren Ajax, Beatrice Durham, Pratima Hebbar, Cade Johnston, Jiayi Zhang

Spora: A Journal of Biomathematics

We introduce a novel framework using inhomogeneous branching random walks (BRWs) to model biological processes, specifically by introducing genealogy-dependence in branching rates and displacement distributions to model bacterial colony growth. Current stochastic models often either assume independent and identical behavior of individual agents or incorporate only spatiotemporal inhomogeneity, ignoring the effect of genealogy-based inhomogeneity on the long-time behavior of these processes. Such asymptotics are of independent mathematical interest and are crucial in understanding the emergence of patterns. We propose several inhomogeneous BRW models in 2D space where displacement distributions and branching rates vary with time, space, and genealogy. A combined …

Meshless Collocation Methods For Time-Dependent Nonlocal Problems Based On Radial Basis Functions, Qiao Zhuang, Yanzhi Zhang, Zhongqiang Zhang

Mathematics and Statistics Faculty Research & Creative Works

We present radial basis function (RBF) collocation methods for time-dependent space fractional problems on general bounded domains. Building on a recently developed approach for accurately computing the integral fractional Laplacian of any RBF, we design collocation schemes for fractional heat and Stokes equations using extended-domain techniques. In particular, we propose a numerical Leray projection method for fractional Stokes problems, where both the discrete projection operator and the collocation scheme are formulated on extended domains to handle complex domains. Numerical results demonstrate the effectiveness of the proposed methods in solving time-dependent nonlocal problems on complex domains.

Fourier Pseudospectral Methods For The Variable-Order Space Fractional Wave Equations, Yanzhi Zhang, Xiaofei Zhao, Shiping Zhou

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we propose Fourier pseudospectral methods to solve the variable-order space fractional wave equation and develop an accelerated matrix-free approach for its effective implementation. In constant-order cases, fast algorithms can be designed via the fast Fourier transforms (FFTs), and the computational cost at each time step is O(Nlog⁡N) with N the total number of spatial points. In variable-order cases, however, the spatial dependence in the power s(x) leads to the failure of inverse FFTs. While the direct matrix-vector multiplication approach becomes impractical due to excessive memory requirements. Hence, we propose an accelerated matrix-free approach for effective implementation in …

Analyzing Sleep Architecture And Brain State Transitions Via Hidden Markov Models On Fmri Data, Brileigh Jay Cates

Masters Theses

Sleep is associated with systematic changes in brain activity and functional connectivity observable in functional magnetic resonance imagining (fMRI) signals. Because subjects often fall asleep during resting-state experiments, the absence of vigilance monitoring can confound the interpretation of resting-state dynamics. Although electroencephalography (EEG) is the gold standard for sleep staging, simultaneous EEG-fMRI acquisition is not always feasible.

This study investigates whether sleep stages can be inferred directly from fMRI using a probabilistic latent-state framework. Hidden Markov Models (HMMs) are applied to blood-oxygen-level-dependent (BOLD) time series to identify latent brain states and their temporal transitions. Inferred states are aligned with EEG-derived …

Comparative Machine Learning Models For Disease Risk Prediction, Mercy Mawusi Agbley

Theses, Dissertations and Capstones

Accurate prediction of disease outcomes is crucial for improving clinical decision-making and enabling early intervention. This study compares the performance of various statistical and machine learning models for clinical risk prediction using two healthcare datasets: diabetic retinopathy and heart disease. The models assessed include Logistic Regression, LASSO, k-Nearest Neighbors (KNN), Support Vector Machines (SVM), Neural Networks, Random Forests, Gradient Boosting Machines (GBM), and a stacked ensemble model. Prior to modeling, datasets were split into train and test sets. Standardization was applied to numeric features whilst categorical features were one-hot encoded. These transformations were later applied to the test set. Principal …

First-Generation Medical School Applicants: A Quantitative Study Designed To Identify Areas Of Educational Support, Bethsabe Romero, Amanda K. Burbage

EVMS School of Health Professions Faculty Publications

First-generation (First Gen) students are unique medical school applicants. Due to their lived experience, they approach patient care by prioritizing trust, comfort and understanding. They have proven ability to overcome obstacles and were found to be more resilient than their continuing generation (Cont Gen) peers. Despite these notable attributes, they face unique challenges in gaining medical school acceptance. There are very few quantitative studies examining this student subpopulation, and our study identifies characteristics of first-generation medical school applicants while highlighting areas of needed support. This cross-sectional study used deidentified Application and Matriculating Student Questionnaire survey data that was obtained from …

Reply To: S. N. Katkuri Et Al. And H. Liu Et Al. On Early And Sustained Improvements In Sense Of Smell With Tezepelumab Treatment In Patients With Chronic Rhinosinusitis With Nasal Polyps (Waypoint), Joaquim Mullol, Joseph K. Han, Tanya M. Laidlaw, Claire Hopkins, Anju T. Peters, Oliver Pfaar, Martin Desrosiers, Stella E. Lee, Andrew P. Lane, Claudia Chen, Yun Chon, Sandhia S. Ponnarambil, Andrew Foster, Andrew W. Lindsley, Christopher S. Ambrose

Department of Otolaryngology (ENT) Faculty Publications

[Introduction] We thank Dr. S. N. Katkuri, Dr. H. Liu, and their coauthors [1, 2] for their interest in our recent publication describing the improvements in loss of smell symptoms with tezepelumab versus placebo in patients with uncontrolled chronic rhinosinusitis with nasal polyps (CRSwNP) in the WAYPOINT trial (NCT04851964) [3]. We are grateful for the authors' feedback on the clinical significance of the data presented and their appreciation of the consistency observed across a range of baseline clinical characteristic and demographic subgroups.