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Abstract Background Using four case studies, we aim to provide practical guidance and recommendations for the analysis of cluster randomised controlled trials. Methods Four modelling approaches (Generalized Linear Mixed Models with parameters estimated by maximum likelihood/restricted maximum likelihood; Generalized Linear Models with parameters estimated by Generalized Estimating Equations (1st order or second order) and Quadratic Inference Function, for analysing correlated individual participant level outcomes in cluster randomised controlled trials were identified after we reviewed the literature. We systematically searched the online bibliography databases of MEDLINE, EMBASE, PsycINFO (via OVID), CINAHL (via EBSCO), and SCOPUS. We identified the above-mentioned four statistical analytical approaches and applied them to four case studies of cluster randomised controlled trials with the number of clusters ranging from 10 to 100, and individual participants ranging from 748 to 9,207. Results were obtained for both continuous and binary outcomes using R and SAS statistical packages. Results The intracluster correlation coefficient (ICC) estimates for the case studies were less than 0.05 and are consistent with the observed ICC values commonly reported in primary care and community-based cluster randomised controlled trials. In most cases, the four methods produced similar results. However, in a few analyses, quadratic inference function produced different results compared to the generalized linear mixed model, first-order generalized estimating equations, and second-order generalized estimating equations, especially in trials with small to moderate numbers of clusters. Conclusion This paper demonstrates the analysis of cluster randomised controlled trials with four modelling approaches. The results obtained were similar in most cases, however, for trials with few clusters we do recommend that the quadratic inference function should be used with caution, and where possible a small sample correction should be used. The generalisability of our results is limited to studies with similar features to our case studies, for example, studies with a similar-sized ICC. It is important to conduct simulation studies to comprehensively evaluate the performance of the four modelling approaches.

The usefulness of a new heavy-tailed distribution is studied in this article. The type-I heavy-tailed exponential (TI-HTE) distribution studied here has been suggested in the literature but has not been studied anywhere other than now. Some of its properties, together with graphical representations, were considered. The study utilized the maximum likelihood method in the estimation of the parameters. The primary goal is to create group acceptance sampling plans (GASP) using the TI-HTE model to determine whether units from a production process should be accepted or rejected. Through simulation studies and real-world examples, the importance of the TI-HTE model in identifying extreme behaviors beyond typical distributions like exponential or heavy-tailed distributions is emphasized.

Abstract Background In cluster randomised controlled trials (cRCTs), groups of individuals (rather than individuals) are randomised to minimise the risk of contamination and/or efficiently use limited resources or solve logistic and administrative problems. A major concern in the primary analysis of cRCT is the use of appropriate statistical methods to account for correlation among outcomes from a particular group/cluster. This review aimed to investigate the statistical methods used in practice for analysing the primary outcomes in publicly funded cluster randomised controlled trials, adherence to the CONSORT (Consolidated Standards of Reporting Trials) reporting guidelines for cRCTs and the recruitment abilities of the cluster trials design. Methods We manually searched the United Kingdom’s National Institute for Health Research (NIHR) online Journals Library, from 1 January 1997 to 15 July 2021 chronologically for reports of cRCTs. Information on the statistical methods used in the primary analyses was extracted. One reviewer conducted the search and extraction while the two other independent reviewers supervised and validated 25% of the total trials reviewed. Results A total of 1942 reports, published online in the NIHR Journals Library were screened for eligibility, 118 reports of cRCTs met the initial inclusion criteria, of these 79 reports containing the results of 86 trials with 100 primary outcomes analysed were finally included. Two primary outcomes were analysed at the cluster-level using a generalized linear model. At the individual-level, the generalized linear mixed model was the most used statistical method (80%, 80/100), followed by regression with robust standard errors (7%) then generalized estimating equations (6%). Ninety-five percent (95/100) of the primary outcomes in the trials were analysed with appropriate statistical methods that accounted for clustering while 5% were not. The mean observed intracluster correlation coefficient (ICC) was 0.06 (SD, 0.12; range, − 0.02 to 0.63), and the median value was 0.02 (IQR, 0.001–0.060), although 42% of the observed ICCs for the analysed primary outcomes were not reported. Conclusions In practice, most of the publicly funded cluster trials adjusted for clustering using appropriate statistical method(s), with most of the primary analyses done at the individual level using generalized linear mixed models. However, the inadequate analysis and poor reporting of cluster trials published in the UK is still happening in recent times, despite the availability of the CONSORT reporting guidelines for cluster trials published over a decade ago.

Abstract Background Extensive and indiscriminate use of pesticides gradually destroys the environment (ecosystem), poses serious threats to human health, animal life (especially aquatic), plant forms, soil, water, and also lead to emergence of resilient species of life forms that are becoming resistant to pesticides. The present study focused on evaluating lambda-cyhalothrin oxidative stress and gonad histoarchitecture toxicity potency in Clarias gariepinus. Results A total of 120 C. gariepinus 16 to 40 cm SL and 200 to 250 g bodyweights (assigned into treatments 0.00 (control), 2.5 × 10−4 μg/L, 5.0 × 10−4 μg/L, and 6.25×10−4 μg/L (A-D) lambda-cyhalothrin (LCT), each treatment consisted of 30 fishes, replicated three times, 10 fishes per replicate) were used for this study. On day 7, catalase activity (CAT) and glutathione peroxidase (GPx) significantly increased (p < 0.05) in all treatments compared with control. Day 14, superoxide dismutase (SOD) and GPx significantly increased (p < 0.05). All parameters significantly increased (p < 0.05) on days 21 and 28 except SOD (day 21). All parameters increased significantly on day 28 across the row in all treatments. The significant increase (p < 0.05) in SOD, (malondialdehyde) MDA, GPx, and glutathione reductase (GR) levels returned to normal after 7 days of depuration but CAT level did not return to normal. The testes photomicrographs showed necrotic conditions in the spermatogenic cells with nuclear pyknosis and cytoplasmic swelling while that of the ovary displayed vacuolations, flabby oocytes, and degenerated ovaries changes. Conclusion Lambda-cyhalothrin is toxic to C. gariepinus. The inability of significant increase in CAT to return to normal after 7 days of depuration further confirms our report.

The accumulation of α-synuclein aggregates (α-syn) in the human brain is an occurrence common to all α-synucleinopathies. Non-invasive detection of these aggregates in a living brain with a target-specific radiotracer is not yet possible. We have recently discovered that the inclusion of a methylenedioxy group in the structure of diarylbisthiazole (DABTA)-based tracers improves binding affinity and selectivity to α-syn. Subsequently, complementary in silico modeling and machine learning (ML) of tracer–protein interactions were employed to predict surface sites and structure–property relations for the binding of the ligands. Based on this observation, we developed a small focused library of DABTAs from which 4-(benzo[d][1,3]dioxol-5-yl)-4′-(3-[18F]fluoro-4-methoxyphenyl)-2,2′-bithiazole [18F]d2, 6-(4′-(3-[18F]fluoro-4-methoxyphenyl)-[2,2′-bithiazol]-4-yl)-[1,3]dioxolo[4,5-b]pyridine [18F]d4, 4-(benzo [d][1,3]dioxol-5-yl)-4′-(6-[18F]fluoropyridin-3-yl)-2,2′-bithiazole [18F]d6, and 6-(4′-(6-[18F]fluoropyridin-3-yl)-[2,2′-bithiazol]-4-yl)-[1,3]dioxolo[4,5-b]pyridine [18F]d8 were selected based on their high binding affinity to α-syn and were further evaluated. Binding assay experiments carried out with the non-radioactive versions of the above tracers d2, d4, d6, and d8 showed high binding affinity of the ligands to α-syn: 1.22, 0.66, 1.21, and 0.10 nM, respectively, as well as excellent selectivity over β-amyloid plaques (Aβ) and microtubular tau aggregates (>200-fold selectivity). To obtain the tracers, their precursors were radiolabeled either via an innovative ruthenium-mediated (SNAr) reaction ([18F]d2 and [18F]d4) or typical SNAr reaction ([18F]d6 and [18F]d8) with moderate-to-high radiochemical yields (13% – 40%), and high molar activity > 60 GBq/μmol. Biodistribution experiments carried out with the tracers in healthy mice revealed that [18F]d2 and [18F]d4 showed suboptimal brain pharmacokinetics: 1.58 and 4.63 %ID/g at 5 min post-injection (p.i.), and 1.93 and 3.86 %ID/g at 60 min p.i., respectively. However, [18F]d6 and [18F]d8 showed improved brain pharmacokinetics: 5.79 and 5.13 %ID/g at 5 min p.i.; 1.75 and 1.07 %ID/g at 60 min p.i.; and 1.04 and 0.58 %ID/g at 120 min p.i., respectively. The brain uptake kinetics of [18F]d6 and [18F]d8 were confirmed in a dynamic PET study. Both tracers also showed no brain radiometabolites at 20 min p.i. in initial in vivo stability experiments carried out in healthy mice. [18F]d8 seems very promising based on its binding properties and in vivo stability, thus encouraging further validation of its usefulness as a radiotracer for the in vivo visualization of α-syn in preclinical and clinical settings. Additionally, in silico and ML-predicted values correlated with the experimental binding affinity of the ligands.

This paper adopted the use of artificial neural network (ANN) which is also a nonlinear model in contributing to the debate of comparing different methods of forecasting frequency of rainfall in Umuahia, Abia State of Nigeria. The choice of ANN is informed by articles in literature which have shown that Neural Network models outperform some traditional statistical models in modelling meteorological time series. The data used for the research was obtained from the National Root Crop Research Institute, Umudike, Abia State and it spanned from 2006 to 2016. The forecasting performance of seasonal autoregressive integrated moving average (SARIMA) model and that of seasonal artificial neural network (SANN) were compared with four forecast performance measures:- Forecast Error (FE), Mean Forecast Error (MFE), Mean Squared Error (MSE) and Root Mean Squared Error (RMSE). Results from the study showed that the SARIMA had lower error indicators in forecast performance and thus was adjudged better than SANN in forecasting frequency of rainfall in Umuahia, Abia State. A t-test for significant difference showed that there is no statistical significant difference between both forecast values. Hence, the authors conclude that the two methods can be successfully used as substitutes. Farmers, Construction Companies, Government agencies working in Umuahia are therefore advised to choose SARIMA modelling of monthly rainfall frequency over that of SANN. This study also confirms that ANNs are not utterly better than the traditional statistical models as seen in other works in literature.