Small Sample Bias Research Articles

Geessbin: an R package for analyzing small-sample binary data using modified generalized estimating equations with bias-adjusted covariance estimators.

The generalized estimating equation (GEE) method is widely used for analyzing longitudinal and clustered data. Although the GEE estimate for regression coefficients and sandwich covariance estimate are consistent regardless of the choice of covariance structure, they are generally biased for small sample sizes. Various researchers have proposed modified GEE methods and covariance estimators to handle small-sample bias. We briefly present bias-corrected and penalized GEE methods, along with 11 bias-adjusted covariance estimators. In addition, we focus on analyzing longitudinal or clustered data with binary outcomes using the logit link function and introduce package geessbin in R to implement conventional and modified GEE methods with bias-adjusted covariance estimators. Finally, we illustrate the implementation and detail a usage example of the package. The package is available from the Comprehensive R Archive Network (CRAN) at https://cran.r-project.org/web/packages/geessbin/index.html . The geessbin package provides three GEE estimates with numerous covariance estimates. It is useful for analyzing correlated data such as longitudinal and clustered data. Additionally, the geessbin is designed to be user-friendly, making it accessible to non-statisticians.

An evaluation of the impact of the Lambeth PCN pharmacist anticoagulation skills development project

Abstract Background Atrial Fibrillation (AF) is a prevalent heart condition linked to significant morbidity and mortality due to its association with stroke.1 Despite the clear benefits of anticoagulation in reducing stroke risk, its underuse and suboptimal monitoring remain a concern.2 Aim This study aims to evaluate the impact of a pharmacist-led training programme in Lambeth, London, focusing on improving pharmacists' competency and confidence in managing Direct Oral Anticoagulants (DOACs). It assesses if the training met pharmacists' needs, evaluates current monitoring patterns to determine if training was warranted, and identified areas for further training improvement. Methods The study involved 41 GP practices across 9 Primary Care Networks (PCNs) in Lambeth. Practices were eligible based on their involvement in the management of AF patients prescribed DOACs. All pharmacists at these practices who were actively engaged in anticoagulation management and willing to participate in pre- and post-training assessments were invited to take part. Recruitment involved direct communication through practice managers and emails detailing the study’s objectives and benefits. DOAC monitoring data was extracted from patient medication records and subsequently compared to the South East London anticoagulation guidelines3 to establish compliance percentages. A competency assessment was conducted on pharmacists using a pre- and post-training checklist framework devised by the Consultant Anticoagulant Team at Guy’s and St Thomas’ NHS Foundation Trust (GSTT). The Wilcoxon signed-rank test analysed this paired data, with a p < 0.05 set for statistical significance. Additionally, semi-structured interviews were conducted to gather insights on their training experience and perceptions. Transcripts were coded using NVIVO software to identify themes. Ethical approval was obtained from Kingston University London. Results Of the 2,987 AF patients across the 41 GP practices, 87.6% were on DOACs. Prescribing and monitoring trends were consistent across all GPs, with scope to improve compliance across all parameters, such as CHA₂DS₂-VASc score assessment prior to DOAC initiation. The competency assessment, completed by ten pharmacists, showed a significant improvement post-training, with mean scores rising from 3.3 to 4.1 (p< 0.00001). Improvements were seen across all domains, particularly in explaining the rationale for anticoagulation, showing CHA₂DS₂-VASc and HASBLED scores, and discussing modifiable HASBLED factors. Competency in patient communication remained highest, while managing particular cases like reversal procedures and patients with cancer showed lower competency, indicating areas for training improvement. The interviews, conducted with ten pharmacists, revealed three main themes: (1) Confidence and competence in anticoagulant prescribing and optimisation, (2) Evaluation of the training programme's effectiveness, and (3) Professional growth and career development. Pharmacists reported greater confidence in managing DOACs post-training, though challenges remained in patient engagement and collaboration with GPs lacking DOAC knowledge. Discussion / Conclusion The evaluation proved a positive impact on pharmacists' competency and confidence in DOAC management. Suboptimal monitoring practices in Lambeth highlighted the need for this training programme and its crucial role in improving patient outcomes. Limitations include a small interview sample and potential biases in self-reported evaluations. A longitudinal study is recommended to assess long-term impacts. Ongoing training and systematic data collection are essential, and similar training should be extended to other healthcare professionals.

Small sample adjustment for inference without assuming orthogonality in a mixed model for repeated measures analysis

ABSTRACT The mixed model for repeated measures (MMRM) analysis is sometimes used as a primary statistical analysis for a longitudinal randomized clinical trial. When the MMRM analysis is implemented in ordinary statistical software, the standard error of the treatment effect is estimated by assuming orthogonality between the fixed effects and covariance parameters, based on the characteristics of the normal distribution. However, orthogonality does not hold unless the normality assumption of the error distribution holds, and/or the missing data are derived from the missing completely at random structure. Therefore, assuming orthogonality in the MMRM analysis is not preferable. However, without the assumption of orthogonality, the small-sample bias in the standard error of the treatment effect is significant. Nonetheless, there is no method to improve small-sample performance. Furthermore, there is no software that can easily implement inferences on treatment effects without assuming orthogonality. Hence, we propose two small-sample adjustment methods inflating standard errors that are reasonable in ideal situations and achieve empirical conservatism even in general situations. We also provide an R package to implement these inference processes. The simulation results show that one of the proposed small-sample adjustment methods performs particularly well in terms of underestimation bias of standard errors; consequently, the proposed method is recommended. When using the MMRM analysis, our proposed method is recommended if the sample size is not large and between-group heteroscedasticity is expected.

Navigating the Social Environment: Linking Motivations, Impressions, and Behaviors Via a Sampling Approach to Trustworthiness.

Our understanding of impression formation comes from experiments constraining participants' control over information sampling. This limits our understanding of how people sample information when forming impressions as well as the effects of self-generated samples on impressions. Our paradigm allows participants to actively collect information samples. This work investigates how people explore the social environment and how sampled information informs resulting impressions. Four experiments tested theoretically-driven predictions regarding information sampling patterns under interested and disinterested information search. Under interested search, participants truncated the sampling of social targets showing early untrustworthy behavior. Under disinterested search, participants sampled extensively and systematically, avoiding small-sample biases. The sampled information, once obtained, accurately determines final impressions. Moreover, we documented a direct link between sampled information and subsequent behaviors (partner selection in trust games, trustworthiness expectations). By investigating sampling-based trustworthiness impressions, the present research informs the origins of trustworthiness and sampling accounts of judgment and decision-making.

Factors affecting intraperitoneal pressure (IPP) and its prognostic value in predicting leak risk and gastrointestinal symptoms in adult peritoneal dialysis patients: a systematic review and meta-analysis.

Intraperitoneal pressure measurementoffers therapeutic and prognostic benefits in predicting leak risks and gastrointestinal symptoms in Peritoneal Dialysis (PD) patients. This systematic review aims to evaluate the prognostic utility of intraperitoneal pressure measurements and different estimated intraperitoneal pressure equations in predicting the risk of non-infectious complications in PD patients. Databases including MEDLINE, EMBASE and Cochrane were searched up to July 2023. Randomised and non-randomised trials were included, focusing on End-Stage Kidney Disease (ESKD) patients undergoing PD. Primary outcomes were variables associated with intraperitoneal pressure, while secondary outcomes included PD-related non-infectious complications and gastrointestinal symptoms. Data synthesis combined meta-analysis with narrative synthesis.This review has been registered on PROSPERO (CRD42023475138). Out of 1828 identified studies, 12 were included for systematic review and 10 for meta-analysis. Body Mass Index (BMI) and Body Surface Area (BSA) showed a consistent positive correlation with intraperitoneal pressure (BMI: r = 0.49, 95% CI 0.35-0.61, I2 = 67.39%, p = 0.003; BSA: r = 0.2, 95% CI 0.08-0.31, I2 = 14.10%, p = 0.324). Conversely, the association between intraperitoneal pressure and age, intraperitoneal volume, and Charlson Comorbidity Index were less consistent. Subgroup analysis demonstrated an association between higher intraperitoneal pressure in patients with increased BMI and BSA. However, the relationship between intraperitoneal pressure and non-infectious mechanical complications remained inconclusive. This review underscores a significant association between intraperitoneal pressure and anthropometric measures (BMI and BSA). The majority of the studies identified included a small sample and considerable bias. However, the association between intraperitoneal pressure and clinically relevant outcomes was not clear. While increasing body mass index and body surface areas are associated with increasing intraperitoneal pressure, the clinical relevance of measuring intraperitoneal pressure in an adult population remains unclear, particularly given the absence of an association with clinically relevant non-infectious outcomes.

Recommendations for analysing and meta-analysing small sample size software engineering experiments

ContextSoftware engineering (SE) experiments often have small sample sizes. This can result in data sets with non-normal characteristics, which poses problems as standard parametric meta-analysis, using the standardized mean difference (StdMD) effect size, assumes normally distributed sample data. Small sample sizes and non-normal data set characteristics can also lead to unreliable estimates of parametric effect sizes. Meta-analysis is even more complicated if experiments use complex experimental designs, such as two-group and four-group cross-over designs, which are popular in SE experiments.ObjectiveOur objective was to develop a validated and robust meta-analysis method that can help to address the problems of small sample sizes and complex experimental designs without relying upon data samples being normally distributed.MethodTo illustrate the challenges, we used real SE data sets. We built upon previous research and developed a robust meta-analysis method able to deal with challenges typical for SE experiments. We validated our method via simulations comparing StdMD with two robust alternatives: the probability of superiority (p^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{p}$$\\end{document}) and Cliffs’ d.ResultsWe confirmed that many SE data sets are small and that small experiments run the risk of exhibiting non-normal properties, which can cause problems for analysing families of experiments. For simulations of individual experiments and meta-analyses of families of experiments, p^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{p}$$\\end{document} and Cliff’s d consistently outperformed StdMD in terms of negligible small sample bias. They also had better power for log-normal and Laplace samples, although lower power for normal and gamma samples. Tests based on p^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{p}$$\\end{document} always had better or equal power than tests based on Cliff’s d, and across all but one simulation condition, p^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{p}$$\\end{document} Type 1 error rates were less biased.ConclusionsUsing p^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{p}$$\\end{document} is a low-risk option for analysing and meta-analysing data from small sample-size SE randomized experiments. Parametric methods are only preferable if you have prior knowledge of the data distribution.

Detecting statistically significant changes in connectedness: A bootstrap-based technique

Connectedness quantifies the extent of interlinkages within economies or markets based on a network approach. Connectedness is measured by the Diebold–Yilmaz spillover index, and abrupt increases in this measure are thought to result from major events. However, formal statistical evidence of events causing such increases is scant. We develop a bootstrap-based technique to evaluate the probability that the value of the spillover index changes at a statistically significant level following an exogenously defined event. We further show how our procedure can detect the dates of unknown events endogenously. The results of a simulation exercise support the effectiveness of our method. We revisit the original dataset from Diebold and Yilmaz’s seminal work and obtain statistical support that the spillover index increases quickly in the wake of adverse shocks. Our methodology accounts for small sample bias and is robust with respect to modifications of the pre-event period and forecast horizon.

Reparametrized Firth's Logistic Regressions for Dose-Finding Study With the Biased-Coin Design.

Finding an adequate dose of the drug by revealing the dose-response relationship is very crucial and a challenging problem in the clinical development. The main concerns in dose-finding study are to identify a minimum effective dose (MED) in anesthesia studies and maximum tolerated dose (MTD) in oncology clinical trials. For the estimation of MED and MTD, we propose two modifications of Firth's logistic regression using reparametrization, called reparametrized Firth's logistic regression (rFLR) and ridge-penalized reparametrized Firth's logistic regression (RrFLR). The proposed methods are designed by directly reducing the small-sample bias of the maximum likelihood estimate for the parameter of interest. In addition, we develop a method on how to construct confidence intervals for rFLR and RrFLR using profile penalized likelihood. In the up-and-down biased-coin design, numerical studies confirm the superior performance of the proposed methods in terms of the mean squared error, bias, and coverage accuracy of confidence intervals.

Exploring the Linkages between farm efficiency, farm environmental performance, and agri-environmental scheme adoption: Lessons from France

The agricultural detrimental effects on the environment are a source of concern. Public mea-sures, such as agri-environmental schemes (AES), have been designed to incentivize farmers to adopt more sound environmental practices on the farm. In this study, we examine the effects of past initial economic and environmental performances on AES adoption by focusing on crop farms. Using Firth's logistic regression to address small sample bias with French FADN data from 1997 to 2007, we mainly find that technical efficiency has heterogeneous effects on AES adoption, depending on environmental indexes. This result suggests the presence of windfall effects. We also show complex interactions (antagonism or synergy) between economic and environmental performances in adoption decisions, and heterogeneous effects depending on the type of farming.The agricultural detrimental effects on the environment are a source of concern. Public mea-sures, such as agri-environmental schemes (AES), have been designed to incentivize farmers to adopt more sound environmental practices on the farm. In this study, we examine the effects of past initial economic and environmental performances on AES adoption by focusing on crop farms. Using Firth's logistic regression to address small sample bias with French FADN data from 1997 to 2007, we mainly find that technical efficiency has heterogeneous effects on AES adoption, depending on environmental indexes. This result suggests the presence of windfall effects. We also show complex interactions (antagonism or synergy) between economic and environmental performances in adoption decisions, and heterogeneous effects depending on the type of farming.

Cox proportional hazards regression in small studies of predictive biomarkers

Predictive biomarkers are essential for personalized medicine since they select the best treatment for a specific patient. However, of all biomarkers that are evaluated, only few are eventually used in clinical practice. Many promising biomarkers may be erroneously abandoned because they are investigated in small studies using standard statistical techniques which can cause small sample bias or lack of power. The standard technique for failure time endpoints is Cox proportional hazards regression with a multiplicative interaction term between binary variables of biomarker and treatment. Properties of this model in small studies have not been evaluated so far, therefore we performed a simulation study to understand its small sample behavior. As a remedy, we applied a Firth correction to the score function of the Cox model and obtained confidence intervals (CI) using a profile likelihood (PL) approach. These methods are generally recommended for small studies of different design. Our results show that a Cox model estimates the biomarker-treatment interaction term and the treatment effect in one of the biomarker subgroups with bias, and overestimates their standard errors. Bias is however reduced and power is increased with Firth correction and PL CIs. Hence, the modified Cox model and PL CI should be used instead of a standard Cox model with Wald based CI in small studies of predictive biomarkers.

Abstract 1305: Comparison of HPV-DNA testing to PET-CT imaging as prognostic test following definitive treatment for cervical cancer: A retrospective proof-of-concept study

Abstract Cervical cancer is a significant global health issue, with oncogenic HPV-High Risk (HPV) responsible for over 99% of cases. Despite the prevalence of HPV-related malignancies, current guidelines by the National Comprehensive Cancer Center (NCCN) do not recommend post-treatment HPV-DNA testing. Instead, PET-CT imaging is recommended as a prognostic test. This retrospective proof-of-concept study aims to evaluate current NCCN guidelines and examines whether post-treatment HPV-HR DNA testing is a cost-effective, reliable alternative to PET-CT imaging in cervical cancer prognosis. Methods: The study included female patients diagnosed with cervical or vaginal carcinomas (2011-2021), ensuring comprehensive records of both pre-treatment and post-treatment high-risk HPV (HPV-HR) testing, alongside PET-CT imaging results. Utilizing the FDA-approved HPV-HR DNA test, capable of detecting 14 oncogenic HPV strains, the study conducted rigorous statistical analyses via STATA software to determine significance of the study results. Results: Our analysis of 53 patients who met the inclusion criteria demonstrated that post-treatment assessments using both HPV status and PET-CT imaging exhibited high levels of sensitivity and specificity, as well as impressive negative and positive predictive values (NPV and PPV, respectively). There was a statistically significant correlation between the likelihood of cancer recurrence and the results obtained from HPV status and PET-CT imaging post-treatment (p-value < 0.001). A critical observation was the superior sensitivity and improved NPV of post-treatment HPV status compared to PET-CT scans. Specifically, the sensitivity for HPV status post-treatment was quantified at 92.31, surpassing the 76.92 sensitivity rating of PET-CT scans. Furthermore, the NPV for post-treatment HPV status was measured at 97.44, which is better than the 92.31 NPV for PET-CT scans. Notably, no patients with negative post-treatment HPV-HR tests had a recurrence. Discussion: The results of this study underscore the clinical significance of assessing HPV-HR DNA status post-treatment, particularly when HPV-HR DNA is negative. If future prospective studies confirm these findings, it may eliminate the need for post-treatment PET-CT scans, providing significant survivorship benefits for patients by reducing follow-up visits and eliminating unnecessary imaging. This would also result in substantial financial savings, estimated to be over $75,000,000 per year in the US alone, based on 2023 data. The limitations of the study include small sample size, single-institution data, and biases associated with retrospective studies. Future multi-institutional prospective studies are necessary to improve current guidelines further and validate the findings of this study. Citation Format: Cameron Huddleston, Aya Bou Fakhreddine, Stephanie Stroever, Robert Young, Naresh Sah, Komaraiah Palle, Mark Reedy. Comparison of HPV-DNA testing to PET-CT imaging as prognostic test following definitive treatment for cervical cancer: A retrospective proof-of-concept study [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 1305.

Test-Retest Repeatability of Patlak Slopes versus Standardized Uptake Values for Hypermetabolic Lesions and Normal Organs in an Oncologic PET/CT Population.

We aimed to determine the test-retest repeatability of quantitative metrics based on the Patlak slope (PS) versus the standardized uptake value (SUV) among lesions and normal organs on oncologic [18F]FDG-PET/CT. This prospective, single-center study enrolled adults undergoing standard-of-care oncologic [18F]FDG-PET/CTs. Early (35-50min post-injection) and late (75-90min post-injection) SUV and PS images were reconstructed from dynamic whole-body PET data. Repeat imaging occurred within 7days. Relevant quantitative metrics were extracted from lesions and normal organs. Repeatability was assessed via mean test-retest percent changes [T-RT %Δ], within-subject coefficients of variation (wCVs), and intra-class correlation coefficients (ICCs). Nine subjects (mean age, 61.7 ± 6.2years; 6 females) completed the test-retest protocol. Four subjects collectively had 17 [18F]FDG-avid lesions. Lesion wCVs were higher (i.e., worse repeatability) for PS-early-max (16.2%) and PS-early-peak (15.6%) than for SUV-early-max (8.9%) and SUV-early-peak (8.1%), with similar early metric ICCs (0.95-0.98). Lesion wCVs were similar for PS-late-max (8.5%) and PS-late-peak (6.4%) relative to SUV-late-max (9.7%) and SUV-late-peak (7.2%), with similar late metric ICCs (0.93-0.98). There was a significant bias toward higher retest SUV and PS values in the lesion analysis (T-RT %Δ [95% CI]: SUV-late-max, 10.0% [2.6%, 17.0%]; PS-late-max, 20.4% [14.3%, 26.4%]) but not in the normal organ analysis. Among [18F]FDG-avid lesions, the repeatability of PS-based metrics is similar to equivalent SUV-based metrics at late post-injection time points, indicating that PS-based metrics may be suitable for tracking response to oncologic therapies. However, further validation is required in light of our study's limitations, including small sample size and bias toward higher retest values for some metrics.

Does renewable energy promote green economic growth in emerging market economies?

PurposeWhile sustainable growth extends the use of resources, it is crucial to explore green growth (GG) that ensures growth sustainability through the adoption of renewable energy. Thus, this study is motivated to investigate the influence of renewable energy on GG in 19 emerging countries spanning a decade and a half (2000–2020). This study aims to provide a quantitative examination of how renewable energy contributes to sustainable economic growth.Design/methodology/approachThis study uses advanced dynamic common correlated effect techniques to assess the long-term effectiveness of renewable energy on GG. Additionally, it uses Dumitrescu and Hurlin causality tests to identify synchronicity between the respective variables.FindingsThe findings of this study reveal that the adoption and utilisation of renewable energy effectively promote GG in emerging economies. However, in contrast, the significantly greater negative influence of trade openness on GG compared to renewable energy highlights the inadequacy and limited impact of cleaner energy alone.Originality/valueTo the best of the authors’ knowledge, existing literature predominantly focuses on investigating the relationship between renewable energy and economic growth, with only a limited number of studies exploring the impact on GG. To the best of the authors’ knowledge, this study would be the first to analyse this relationship in these emerging countries. Furthermore, previous estimation frameworks used in prior studies often overlook the crucial factor of cross-sectional dependence (CSD) among countries. Therefore, this study addresses this issue using a contemporary econometric approach that deals not only with CSD but other biases, like endogeneity, autocorrelation, small sample bias, etc.

Meta-analyses of partial correlations are biased: Detection and solutions.

We demonstrate that all meta-analyses of partial correlations are biased, and yet hundreds of meta-analyses of partial correlation coefficients (PCCs) are conducted each year widely across economics, business, education, psychology, and medical research. To address these biases, we offer a new weighted average, UWLS+3 . UWLS+3 is the unrestricted weighted least squares weighted average that makes an adjustment to the degrees of freedom that are used to calculate partial correlations and, by doing so, renders trivial any remaining meta-analysis bias. Our simulations also reveal that these meta-analysis biases are small-sample biases (n < 200), and a simple correction factor of (n - 2)/(n - 1) greatly reduces these small-sample biases along with Fisher's z. In many applications where primary studies typically have hundreds or more observations, partial correlations can be meta-analyzed in standard ways with only negligible bias. However, in other fields in the social and the medical sciences that are dominated by small samples, these meta-analysis biases are easily avoidable by our proposed methods.

Finite-Sample Bias of the Linear Excess Relative Risk in Cohort Studies of Computed Tomography-Related Radiation Exposure and Cancer.

The linear excess relative risk (ERR) is the most commonly reported measure of association in radiation epidemiological studies, when individual dose estimates are available. While the asymptotic properties of the ERR estimator are well understood, there is evidence of small sample bias in case-control studies of treatment-related radiation exposure and second cancer risk. Cohort studies of cancer risk after exposure to low doses of radiation from diagnostic procedures, e.g., computed tomography (CT) examinations, typically have small numbers of cases and risks are small. Therefore, understanding the properties of the estimated ERR is essential for interpretation and analysis of such studies. We present results of a simulation study that evaluates the finite-sample bias of the ERR estimated by time-to-event analyses and its confidence interval using simulated data, resembling a retrospective cohort study of radiation-related leukemia risk after CT examinations in childhood and adolescence. Furthermore, we evaluate how the Firth-corrected estimator reduces the finite-sample bias of the classical estimator. We show that the ERR is overestimated by about 30% for a cohort of about 150,000 individuals, with 42 leukemia cases observed on average. The bias is reduced for higher baseline incidence rates and for higher values of the true ERR. As the number of cases increases, the ERR is approximately unbiased. The Firth correction reduces the bias for all cohort sizes to generally around or under 5%. Epidemiological studies showing an association between radiation exposure from pediatric CT and cancer risk, unless very large, may overestimate the magnitude of the relationship, while there is no evidence of an increased chance for false-positive results. Conducting large studies, perhaps by pooling individual studies to increase the number of cases, should be a priority. If this is not possible, Firth correction should be applied to reduce small-sample bias.

Compare the marginal effects for environmental exposure and biomonitoring data with repeated measurements and values below the limit of detection.

Environmental exposure and biomonitoring data with repeated measurements from environmental and occupational studies are commonly right-skewed and in the presence of limits of detection (LOD). However, existing model has not been discussed for small-sample properties and highly skewed data with non-detects and repeated measurements. Marginal modeling provides an alternative to analyzing longitudinal and cluster data, in which the parameter interpretations are with respect to marginal or population-averaged means. We outlined the theories of three marginal models, i.e., generalized estimating equations (GEE), quadratic inference functions (QIF), and generalized method of moments (GMM). With these approaches, we proposed to incorporate the fill-in methods, including single and multiple value imputation techniques, such that any measurements less than the limit of detection are assigned values. We demonstrated that the GEE method works well in terms of estimating the regression parameters in small sample sizes, while the QIF and GMM outperform in large-sample settings, as parameter estimates are consistent and have relatively smaller mean squared error. No specific fill-in method can be deemed superior as each has its own merits. Marginal modeling is firstly employed to analyze repeated measures data with non-detects, in which only the mean structure needs to be correctly provided to obtain consistent parameter estimates. After replacing non-detects through substitution methods and utilizing small-sample bias corrections, in a simulation study we found that the estimating approaches used in the marginal models have corresponding advantages under a wide range of sample sizes. We also applied the models to longitudinal and cluster working examples.

Transdiagnostic Psychological Interventions for Symptoms of Common Mental Disorders Delivered by Non‐Specialist Providers in Low‐ and Middle‐Income Countries: A Systematic Review and Meta‐Analysis

There is a treatment gap for Common Mental Disorders (CMDs) such as anxiety, depression, and post‐traumatic stress disorder (PTSD), as well as non‐specific psychological distress (NPD) in low‐ and middle‐income countries (LAMIC), due to the lack of available clinicians and locally appropriate interventions. Task‐shifting using non‐specialist providers (NSP) and transdiagnostic approaches may address this. Transdiagnostic approaches can be effective at treating CMDs and NPD in high‐income countries (HIC), but currently, there is no comprehensive synthesis of evidence regarding their effectiveness in LAMICs. This review addressed this gap by examining the effectiveness of transdiagnostic psychological interventions for symptoms of CMDs and NPD delivered by NSPs in LAMICs. Three databases were searched (Embase, PsycInfo, and PubMed). Hedge’s g’s were calculated using random‐effect models to correct for small sample bias. Twenty‐one transdiagnostic interventions across 20 studies were included. Moderate reductions at posttreatment were found in psychological distress (g = −0.64; 95% CI: −0.81 to −0.46), symptoms of anxiety (g = −0.61; 95% CI: −0.80 to −0.42), depression (g = −0.59; 95% CI: −0.75 to −0.44), and PTSD/trauma (g = −0.38; 95% CI: −0.59 to −0.16), with significant small reductions maintained at follow‐up ranging from 13 to 26 weeks for NPD (SMD = − 0.37; 95% CI: −0.57 to −0.17), anxiety (g = − 0.41; 95% CI: −0.91 to 0.09), depression (g = −0.38; 95% CI: −0.59 to −0.16), and trauma symptoms (g = −0.23; 95% CI: −0.42 to −0.05). These findings are important and suggest that transdiagnostic approaches delivered by NSPs are effective at treating symptoms of CMDs and NPD in LAMICs. Future research should consider comparing task‐shifting approaches with disorder‐specific interventions and explore the effectiveness of longer sessions across various mental health conditions.

A NEWCLASS OF TAN-G FAMILY OF DISTRIBUTIONS WITH PROPERTIES AND APPLICATIONS

This research article is dedicated to the exploration of a novel family of distributions that is based on a tangent transformation. The new class of distributions, which we have named the new class tan-G (NCT-G) family, has been developed using the ratio of the cumulative distribution function (CDF) G(x) and 1+G(x) of a baseline distribution. We provide an overview of the general properties of this family of distributions. To demonstrate the applicability of the NCT-G family, we have utilized the inverse Weibull distribution as a baseline and introduced a new member of the suggested family. This new distribution exhibits a reverse-J, increasing, or inverted bathtub-shaped hazard function. We have also explored some statistical properties of this distribution, as well as its associated parameters estimated through maximum likelihood estimation (MLE). To evaluate the accuracy of the estimation procedure, we have conducted a Monte Carlo simulation. We found that even for small sample sizes, biases and mean square errors decrease as the sample size increases. Additionally, we have applied the NCT-IW distribution to two real data sets. By using model selection criteria and goodness of fit test statistics, we empirically proved that our suggested model outperforms other existing models, most of which have a greater number of parameters.

Loneliness and firearm acquisition among low-income U.S. veterans: Findings from the National Veteran Homeless and Other Poverty Experiences (NV-HOPE) study

RationaleThere are theoretical reasons to expect loneliness related to firearm purchasing. For instance, loneliness might amplify social isolation and feelings of insecurity, anxiety, perceived danger, and need for self-reliance. Purchasing a firearm might be seen as a way to bolster one's security and gain a sense of control when faced with potential threats, yet there is a lack of research assessing this possibility. ObjectiveThis study aimed to examine the relationship between loneliness and purchasing a firearm among a sample of low-income U.S. military veterans. MethodsData are from a national survey of 1,004 low-income U.S. veterans collected in December 2022 and January 2023. Firth logistic regression—a rare event logistic regression model to address small-sample bias stemming from rare outcomes through a penalized likelihood approach—was used to estimate the adjusted association between loneliness and purchasing a firearm in the past year. ResultsApproximately 5.4% reported the purchase of a new firearm in the past year, and respondents reported an average loneliness score of 1.82 (standard deviation = 1.96; range = 0–6). Results of Firth Logit regression analyses found that net of control variables for demographic, socioeconomic, and household characteristics, loneliness was positively associated with purchasing a firearm in the past year (OR = 1.167, 95% CI = 1.006, 1.352). ConclusionThe findings indicate that loneliness among U.S. military veterans is associated with firearm purchasing. Considering the risks posed by both loneliness and firearm ownership for veteran suicide, the findings suggest the need for greater focus and synergistic strategies to address loneliness and safe firearm practices among U.S. veterans.

Statistically validated coeherence and intensity in temporal networks of information flows

We propose a method for characterizing the local structure of weighted multivariate time series networks. We draw intensity and coherence of network motifs, i.e. statistically recurrent subgraphs, to characterize the system behavior via higher-order structures derived upon effective transfer entropy networks. The latter consists of a model-free methodology enabling to correct for small sample biases affecting Shannon transfer entropy, other than conducting inference on the estimated directional time series information flows. We demonstrate the usefulness of our proposed method with an application to a set of global commodity prices. Our main result shows that, despite simple triadic structures are the most intense, coherent and statistically recurrent over time, their intensity suddenly decreases after the Global Financial Crisis, in favor of most complex triadic structures, while all types of subgraphs tend to become more coherent thereafter.