Distribution of radon in large workplaces: an analysis performed on radon levels measured in UK schools.

Radon is a radioactive, carcinogenic gas formed by the radioactive decay of uranium and radium that occur naturally in small amounts in all rocks and soils. It is the largest single source of radiation exposure to the UK population, contributing to more than 1 100 lung cancer deaths each year according to an analysis conducted in 2005. Regulations exist to protect employees (and other persons) where radon concentrations exceed the reference level of 300 Bq m-3. Once the reference level is exceeded, annual doses of more than the public dose limit of 1 mSv a-1are considered to be excessive. A radon measurement campaign for schools, which started in 2009, generated a large dataset, including those with high numbers of simultaneous radon measurements. Radon data between buildings (e.g. homes) have been shown to correspond broadly to the lognormal distribution, after the additive contribution of outside air has been removed. However, there are fewer studies of the distribution of radon levels within a single, large property. Radon data collected from 533 UK schools with at least 20 valid, simultaneous results were analysed against several statistical models. In approximately 50% of schools the radon levels could be represented by the lognormal distribution and in 60% by the loglogistic lognormal distribution, the latter being a better fit probably owing to its lower sensitivity to the tails of the distribution. Qualitatively, the lognormal and the loglogistic probability plots appeared to be indistinguishable. These findings indicate that the lognormal and loglogistic might be appropriate models to characterise the distribution of radon in most large workplaces. For each statistical model, the two distribution parameters can be used to provide a better estimate of the average dose to the occupants. However, caution is required when assessing doses, since the average estimator of the radon concentration does not predict the highest value and may significantly underestimate or overestimate the dose in specific areas.

A Bayesian Survival Analysis on Long COVID and non Long COVID patients: A Cohort Study Using National COVID Cohort Collaborative (N3C) Data.

Since the outbreak of COVID-19 pandemic in 2020, numerous researches and studies have focused on the long-term effects of COVID infection. The Centers for Disease Control (CDC) implemented an additional code into the International Classification of Diseases, Tenth Revision, Clinical Modification (ICD-10-CM) for reporting 'Post COVID-19 condition, unspecified (U09.9)' effective on October 1st 2021, representing that Long COVID is a real illness with potential chronic conditions. The National COVID Cohort Collaborative (N3C) provides researchers with abundant electronic health records (EHR) data by aggregating and harmonizing EHR data across different clinical organizations in the United States, making it convenient to build up a survival analysis on Long COVID patients and non Long COVID patients among large amounts of COVID positive patients.

The effect of forest composition on outdoor recreation.

Climate change will shift the composition of northern Minnesota forests from boreal to temperate by the end of the century. This shift in forest composition will likely affect outdoor recreation, a valuable ecosystem service and a key economic driver for the region. In this context, the objective of our paper is to empirically examine the relationship between forest composition and recreation. We analyze the effect of changes in forest composition for seven forest types on seven types of recreation using a lognormal pooled panel regression model for Minnesota's Laurentian Mixed Forest Province. Earlier research showed forest composition affected recreation at the level of broad groups of broadleaved or coniferous species. We find a statistically significant empirical association between forest composition and recreation at the forest type level (forest types within those broad groups). This relationship varies across forest types and recreation categories. For example, big game hunting is positively related to elm-ash-cottonwood and white-red-jack pine and negatively associated with aspen-birch. We find individual forest types within broad groups of broadleaved or coniferous forests, have different relationships with recreation, so that these broad groups are not sufficient in capturing the effect of forest composition on recreation. Our results are of interest in the context of current shifts in forest composition caused by climate change, which could also affect recreation. Our findings suggest adding a forest composition lens to existing policies could facilitate strategies for more effective recreation management and climate change adaptation.

Comparative Analysis of Women's Breast Cancer Survival Time at Three Selected Government Referral Hospitals in Ethiopia's Amhara Region Using Parametric Shared Frailty Models.

Background: One in five people will eventually develop cancer, and one in eleven women will lose their lives to the disease. The main aim of this study is to determinants of survival time of women with breast cancer using appropriate Frailty models. Methods: A study involving 632 Ethiopian women with breast cancer was conducted between 2018 and 2020, utilizing medical records from Felege-Hiwot Referral Hospital, the University of Gondar, and Dessie Referral Hospital. To compare survival, the Kaplan-Meier plot (s) and Log rank test were employed; to assess mean survival, one-way analysis of variance and the t test were utilized. The factors influencing women's survival times from breast cancer were identified using the parametric shared frailty model and the accelerated failure time model. Results: The median time to die for breast cancer patients treated at FHRH, UoGCSH, and DRH was 14.91 months, 11.14 months, and 12.32 months, respectively. The parametric model of shared frailty fit those who were statistically significant in univariate analysis. The results showed that survival of women with breast cancer was significantly influenced by age, tumor size, comorbidity, nodal status, stage, histologic grade, and type of primary treatment initiated. When comparing mean survival times between hospitals, the results showed a significant difference; patients who were treated in FHRH live significantly longer than patients treated in UoGCSH and DRH, whereas patients treated in UoGCSH have comparatively lower survival. Women with stage IV and comorbidities have 22.4% and 27.1% shorter expected survival, respectively. Conclusion: This finding suggests that improving the availability and accessibility of radiation therapy and surgery, eliminating disparities between hospitals, raising awareness of early signs and symptoms of breast cancer and encouraging women to seek clinical help, and highlighting women with comorbidities at diagnosis are important ways to increase survival time.

Joint monitoring of mean and variance using Max-EWMA control chart under lognormal process with application to engine oil data.

The control charts are frequently employed in process monitoring to assess the average and variability of a process, assuming a normal distribution. However, it is worth noting that some process distributions tend to exhibit a positively skewed distribution, such as the lognormal distribution. This article proposed a maximum exponential weighted moving average control chart for joint monitoring of mean and variance under a lognormal process. The proposed control chart is evaluated by using the run length profile such as ARL and SDRL. The Monte Carlo simulation is conducted by using the R language to find the run length profile. An application is presented to demonstrate the design of the proposed control chart.

Quadratic resampling method for the long-term γ-ray background spectra using an HPGe detector.

We developed a novel quadratic resampling method for summing up γ-ray spectra with different calibration parameters. We investigated a long-term environmental background γ-ray spectrum by summing up 114 spectra measured using a 30% HPGe detector between 2017 and 2021. Gain variations in different measurement periods shift γ-ray peak positions by a fractional pulse-height bin size up to around 2 keV. The resampling method was applied to measure low-level background γ-ray peaks in the γ-ray spectrum in a wide energy range from 50 keV to 3 MeV. We additionally document temporal variations in the activities of major γ-ray peaks, such as 40K (1461 keV), 208Tl (2615 keV), and other typical nuclides, along with contributions from cosmic rays. The normal distribution of γ-ray background count rates, as evidenced by quantile-quantile plots, indicates consistent data collection throughout the measurement period. Consequently, we assert that the quadratic resampling method for accumulating γ-ray spectra surpasses the linear method (Bossew, 2005) in various aspects.

Word Length in Political Public Speaking: Distribution and Time Evolution.

In this paper, word length in the texts of public speeches by USA and UK politicians is analyzed. More than 300 speeches delivered over the past two hundred years were studied. It is found that the lognormal distribution better describes the distribution of word length than do the Weibull and Poisson distributions, for example. It is shown that the length of words does not change significantly over time (the average value either does not change or slightly decreases, and the mode slightly increases). These results are fundamentally different from those obtained previously for sentence lengths and indicate that, in terms of quantitative linguistic analysis, the word length in politicians' speech has not evolved over the last 200 years and does not obey the principle of least effort proposed by G. Zipf.

Predicting the Effect of the Loading Rate on the Fracture Toughness of Hydraulic Asphalt Concrete Based on the Weibull Distribution.

The cracking problem of asphalt concrete panels is a crucial consideration in the design of hydraulic asphalt concrete seepage control bodies. Panels experiencing uneven rises or falls of water levels during impoundment may exhibit loading rate effects. Investigating the fracture toughness value of asphalt concrete under varying loading rates is essential. This study employs a statistical method to calculate the fracture index KIC, using the semi-circular bending test (SCB) to examine the effect of loading rates on the Type I fracture mode of hydraulic asphalt concrete. The data are analyzed using the two-parameter Weibull distribution curve, offering insights into the minimum number of KIC test specimens. The results indicate an increase in KIC with loading rate, with greater data dispersion at faster rates. The Weibull distribution curve successfully fits the fracture behavior under different loading rates, providing valuable predictions. This study estimates the minimum number of SCB test specimens to be nine, based on a confidence level of 0.95 and a relative deviation not exceeding 5%.

Exploring the impact of stage and tumor site on colorectal cancer survival: Bayesian survival modeling.

Colorectal cancer is a prevalent malignancy with global significance. This retrospective study aimed to investigate the influence of stage and tumor site on survival outcomes in 284 colorectal cancer patients diagnosed between 2001 and 2017. Patients were categorized into four groups based on tumor site (colon and rectum) and disease stage (early stage and advanced stage). Demographic characteristics, treatment modalities, and survival outcomes were recorded. Bayesian survival modeling was performed using semi-competing risks illness-death models with an accelerated failure time (AFT) approach, utilizing R 4.1 software. Results demonstrated significantly higher time ratios for disease recurrence (TR = 1.712, 95% CI 1.489-2.197), mortality without recurrence (TR = 1.933, 1.480-2.510), and mortality after recurrence (TR = 1.847, 1.147-2.178) in early-stage colon cancer compared to early-stage rectal cancer. Furthermore, patients with advanced-stage rectal cancer exhibited shorter survival times for disease recurrence than patients with early-stage colon cancer. The interaction effect between the disease site and cancer stage was not significant. These findings, derived from the optimal Bayesian log-normal model for terminal and non-terminal events, highlight the importance of early detection and effective management strategies for colon cancer. Early-stage colon cancer demonstrated improved survival rates for disease recurrence, mortality without recurrence, and mortality after recurrence compared to other stages. Early intervention and comprehensive care are crucial to enhance prognosis and minimize adverse events in colon cancer patients.

An Accelerated Failure Time Model to Predict Cause-Specific Survival and Prognostic Factors of Lung and Bronchus Cancer Patients with at Least Bone or Brain Metastases: Development and Internal Validation Using a SEER-Based Study.

BACKGROUND: This study addresses the significant challenge of low survival rates in patients with cause-specific lung cancer accompanied by bone or brain metastases. Recognizing the critical need for an effective predictive model, the research aims to establish survival prediction models using both parametric and non-parametric approaches. METHODS: Clinical data from lung cancer patients with at least one bone or brain metastasis between 2000 and 2020 from the SEER database were utilized. Four models were constructed: Cox proportional hazard, Weibull accelerated failure time (AFT), log-normal AFT, and Zografos-Balakrishnan log-normal (ZBLN). Independent prognostic factors for cause-specific survival were identified, and model fit was evaluated using Akaike's and Bayesian information criteria. Internal validation assessed predictive accuracy and discriminability through the Harriel Concordance Index (C-index) and calibration plots. RESULTS: A total of 20,412 patients were included, with 14,290 (70%) as the training cohort and 6122 (30%) validation. Independent prognostic factors selected for the study were age, race, sex, primary tumor site, disease grade, total malignant tumor in situ, metastases, treatment modality, and histology. Among the accelerated failure time (AFT) models considered, the ZBLN distribution exhibited the most robust model fit for the 3- and 5-year survival, as evidenced by the lowest values of Akaike's information criterion of 6322 and 79,396, and the Bayesian information criterion of 63,495 and 79,396, respectively. This outperformed other AFT and Cox models (AIC = [156,891, 211,125]; BIC = [158,848, 211,287]). Regarding predictive accuracy, the ZBLN AFT model achieved the highest concordance C-index (0.682, 0.667), a better performance than the Cox model (0.669, 0.643). The calibration curves of the ZBLN AFT model demonstrated a high degree of concordance between actual and predicted values. All variables considered in this study demonstrated significance at the 0.05 level for the ZBLN AFT model. However, differences emerged in the significant variations in survival times between subgroups. The study revealed that patients with only bone metastases have a higher chance of survival compared to only brain and those with bone and brain metastases. CONCLUSIONS: The study highlights the underutilized but accurate nature of the accelerated failure time model in predicting lung cancer survival and identifying prognostic factors. These findings have implications for individualized clinical decisions, indicating the potential for screening and professional care of lung cancer patients with at least one bone or brain metastasis in the future.

Evaluation of virus removal in membrane bioreactor (MBR) and conventional activated sludge (CAS) processes based on long-term monitoring at two wastewater treatment plants.

The membrane bioreactor (MBR) process always offers better wastewater treatment than conventional activated sludge (CAS) treatment. However, the difference in their efficacy of virus reduction remains unknown. To investigate this, we monitored virus concentrations before and after MBR and CAS processes over 2 years. Concentrations of norovirus genotypes I and II (NoV GI and GII), aichivirus (AiV), F-specific RNA phage genotypes I, II, and III (GI-, GII-, and GIII-FRNAPHs), and pepper mild mottle virus (PMMoV) were measured by a quantitative polymerase chain reaction (qPCR) method at two municipal wastewater treatment plants (WWTPs A and B) in Japan. Virus concentration datasets containing left-censored data were estimated by using both maximum likelihood estimation (MLE) and robust regression on order statistics (rROS) approaches. PMMoV was the most prevalent at both WWTPs, with median concentrations of 7.5 to 8.8 log10 copies/L before treatment. Log10 removal values (LRVs) of all viruses based on means and standard deviations of concentrations before and after treatment were consistently higher following MBR than following CAS. We used NoV GII as a model pathogen in a quantitative microbial risk assessment of the treated water, and we estimated the additional reductions required following MBR and CAS processes to meet the guideline of 10-6 DALYs pppy for safe wastewater reuse.

A comparison of single- and double-threshold ROC plots for mixture distributions.

The receiver operating characteristics (ROC) analysis is commonly used in clinical settings to check the performance of a single threshold for distinguishing population-wise bimodal-distributed test results. However, for population-wise three-modal distributed test results, a single threshold ROC (stROC) analysis showed poor discriminative performance. The purpose of this study is to use a double-threshold ROC analysis for the three-modal distributed test results to provide better discriminative performance than the stROC analysis. A double-threshold receiver operating characteristic plot (dtROC) is constructed by replacing the single threshold with a double threshold. The sensitivity and specificity coordinates are chosen to maximize sensitivity for a given specificity value. Besides a simulation study assuming a mixture of lognormal, Poisson, and Weibull distributions, a clinical application is examined by a secondary data analysis of palpation test results of the C7 spinous process using the modified thorax-rib static technique. For the assumed mixture models, the discrimination performance of dtROC analysis outperforms the stROC analysis (area under ROC (AUROC) increased from 0.436 to 0.983 for lognormal distributed test results, 0.676 to 0.752 for the Poisson distribution, and 0.674 to 0.804 for Weibull distribution).

Assessing the sensitivity and resistance of communities in a changing environment.

We propose that the ecological resilience of communities to permanent changes of the environment can be based on how variation in the overall abundance of individuals affects the number of species. Community sensitivity is defined as the ratio between the rate of change in the log expected number of species and the rate of change in the log expected number of individuals in the community. High community sensitivity means that small changes in the total abundance strongly impact the number of species. Community resistance is the proportional reduction in expected number of individuals that the community can sustain before expecting to lose one species. A small value of community resistance means that the community can only endure a small reduction in abundance before it is expected to lose one species. Based on long-term studies of four bird communities in European deciduous forests at different latitudes large differences were found in the resilience to environmental perturbations. Estimating the variance components of the species abundance distribution revealed how different processes contributed to the community sensitivity and resistance. Species heterogeneity in the population dynamics was the largest component, but its proportion varied among communities. Species-specific response to environmental fluctuations was the second major component of the variation in abundance. Estimates of community sensitivity and resistance based on data only from a single year were in general larger than those based on estimates from longer time series. Thus, our approach can provide rapid and conservative assessment of the resilience of communities to environmental changes also including only short-term data. This study shows that a general ecological mechanism, caused by increased strength of density dependence due to reduction in resource availability, can provide an intuitive measure of community resilience to environmental variation. Our analyses also illustrate the importance of including specific assumptions about how different processes affect community dynamics. For example, if stochastic fluctuations in the environment affect all species in a similar way, the sensitivity and resistance of the community to environmental changes will be different from communities in which all species show independent responses.

What do surrogate safety metrics measure? Understanding driving safety as a continuum.

Road safety is an important public health issue; technology, policy, and educational interventions to prevent crashes are of significant interest to researchers and policymakers. In particular, there is significant ongoing research to proactively evaluate the safety of new technologies, including autonomous vehicles, before enough crashes occur to directly measure their impact. We analyze the distributional form of five diverse datasets that approximate motor vehicle safety incident severity, including one dataset of hard braking events that characterizes the severity of non-crash incidents. Our empirical analysis finds that all five datasets closely fit a lognormal distribution (Kolmogorov-Smirnov distance < 0.013; significance of loglikelihood ratio with other distributions < 0.000029). We demonstrate a linkage between two well-known but largely qualitative safety frameworks and the severity distributions observed in the data. We create a formal model of the Swiss Cheese Model (SCM) and show through analysis and simulations that this formalization leads to a lognormal distribution of the severity continuum of safety-critical incidents. This finding is not only consistent with the empirical data we examine, but represents a quantitative restatement of Heinrich's Triangle, another heretofore largely qualitative framework that hypothesizes that safety events of increasing severity have decreasing frequency. Our results support the use of more frequent, low-severity events to rapidly assess safety in the absence of less frequent, high-severity events for any system consistent with our formalization of SCM. This includes any complex system designed for robustness to single-point failures, including autonomous vehicles.

Confidence intervals for ratio of means of delta-lognormal distributions based on left-censored data with application to rainfall data in Thailand.

Thailand is a country that is prone to both floods and droughts, and these natural disasters have significant impacts on the country's people, economy, and environment. Estimating rainfall is an important part of flood and drought prevention. Rainfall data typically contains both zero and positive observations, and the distribution of rainfall often follows the delta-lognormal distribution. However, it is important to note that rainfall data can be censored, meaning that some values may be missing or truncated. The interval estimator for the ratio of means will be useful when comparing the means of two samples. The purpose of this article was to compare the performance of several approaches for statistically analyzing left-censored data. The performance of the confidence intervals was evaluated using the coverage probability and average length, which were assessed through Monte Carlo simulation. The approaches examined included several variations of the generalized confidence interval, the Bayesian, the parametric bootstrap, and the method of variance estimates recovery approaches. For (ξ1, ξ2) = (0.10,0.10), simulations showed that the Bayesian approach would be a suitable choice for constructing the credible interval for the ratio of means of delta-lognormal distributions based on left-censored data. For (ξ1, ξ2) = (0.10,0.25), the parametric bootstrap approach was a strong alternative for constructing the confidence interval. However, the generalized confidence interval approach can be considered to construct the confidence when the sample sizes are increase. Practical applications demonstrating the use of these techniques on rainfall data showed that the confidence interval based on the generalized confidence interval approach covered the ratio of population means and had the smallest length. The proposed approaches' effectiveness was illustrated using daily rainfall datasets from the provinces of Chiang Rai and Chiang Mai in Thailand.

Analysis of HepG2 cell response to a wide concentration range of mitomycin C using a multichannel quartz crystal microbalance system with a microscope.

The morphological response of HepG2 cells to mitomycin C was analyzed using a multichannel quartz crystal microbalance system equipped with a home-built movable microscope that enables the simultaneous acquisition of cell images and measurements of eight-channel quartz crystal microbalance. After 24 h of cell seeding, mitomycin C was injected into the culture medium. During the attachment process, the resonant frequency decreased, and the curves fitted well with the first-order lag response. Analysis of the response to mitomycin C revealed that the resonant frequency response curves varied with mitomycin C concentration. When the mitomycin C concentration was <10 µmol L-1, the delay time was observed before the increase in resonant frequency. When the mitomycin C concentration was extremely low, an additional decrease in resonant frequency was observed in the middle of the delay time that fitted well with the cumulative log-normal distribution curve. The resonant frequency response curves after the delay time fitted well with the cumulative log-normal distribution curves. The delay time and mean cumulative log-normal distribution time for the increase in resonant frequency correlated with the mitomycin C concentration; however, the mean time for the additional decrease in the resonant frequency did not show a statistically significant difference as a function of mitomycin C concentration. For mitomycin C concentrations of >20 µmol L-1, the response to the change in resonant frequency was rapid, and the response curves fitted well with the first-order lag response. The first-order lag response indicates that the response occurred simultaneously for all cells. The results showed that the time constant was independent of the tested mitomycin C concentration between 20 and 100 µmol L-1. These results suggested that different cell death processes occurred by mitomycin C. The findings of this study suggest that the system can be used to investigate cell death in adherent cells.

Observation of Weibull, Lognormal, and Gamma Distributions in Electrodeposited Cu and Cu-Ag Particles.

In this work, the nearest-neighbor distances and Voronoi cell features of Cu-Ag deposits were analyzed and fitted with Lognormal, Weibull, and Gamma distributions. The nearest-neighbor distance distributions of the samples were compared with those of complete spatially random points, showing spatial inhomogeneity due to the nucleation exclusion effect. The radial distribution function was calculated, showing both influences from the grain size and the nucleation exclusion effect. Voronoi cells were generated based on the shape of the grains. The size, occupancy, and coordination of the Voronoi cells were examined and fitted. The results show that although the Cu-Ag deposits seemed to be governed by the instantaneous nucleation mode, the spatial distribution of the nuclei was more impacted by the nucleation exclusion effect than the Cu-only samples. This behavior is also justified by the grain size distribution generated with Voronoi cell size and occupancy distributions.

Estimation of the time of exposure based on interval and censored data using the ε-accelerated EM algorithm.

Accurately estimating the timing of pathogen exposure plays a crucial role in outbreak control for emerging infectious diseases, including the source identification, contact tracing, and vaccine research and development. However, since surveillance activities often collect data retrospectively after symptoms have appeared, obtaining accurate data on the timing of disease onset is difficult in practice and can involve "coarse" observations, such as interval or censored data. To address this challenge, we propose a novel likelihood function, tailored to coarsely observed data in rapid outbreak surveillance, along with an optimization method based on an ε $$ \varepsilon $$ -accelerated EM algorithm for faster convergence to find maximum likelihood estimates (MLEs). The covariance matrix of MLEs is also discussed using a nonparametric bootstrap approach. In terms of bias and mean-squared error, the performance of our proposed method is evaluated through extensive numerical experiments, as well as its application to a series of epidemiological surveillance focused on cases of mass food poisoning. The experiments show that our method exhibits less bias than conventional methods, providing greater efficiency across all scenarios.

Skewed distribution of spines is independent of presynaptic transmitter release and synaptic plasticity, and emerges early during adult neurogenesis.

Dendritic spines are crucial for excitatory synaptic transmission as the size of a spine head correlates with the strength of its synapse. The distribution of spine head sizes follows a lognormal-like distribution with more small spines than large ones. We analysed the impact of synaptic activity and plasticity on the spine size distribution in adult-born hippocampal granule cells from rats with induced homo- and heterosynaptic long-term plasticity in vivo and CA1 pyramidal cells from Munc13-1/Munc13-2 knockout mice with completely blocked synaptic transmission. Neither the induction of extrinsic synaptic plasticity nor the blockage of presynaptic activity degrades the lognormal-like distribution but changes its mean, variance and skewness. The skewed distribution develops early in the life of the neuron. Our findings and their computational modelling support the idea that intrinsic synaptic plasticity is sufficient for the generation, while a combination of intrinsic and extrinsic synaptic plasticity maintains lognormal-like distribution of spines.

Modeling income distribution: An econophysics approach.

This study aims to develop appropriate models for income distribution in Iran using the econophysics approach for the 2006-2018 period. For this purpose, the three improved distributions of the Pareto, Lognormal, and Gibbs-Boltzmann distributions are analyzed with the data extracted from the target household income expansion plan of the statistical centers in Iran. The research results indicate that the income distribution in Iran does not follow the Pareto and Lognormal distributions in most of the study years but follows the generalized Gibbs-Boltzmann distribution function in all study years. According to the results, the generalized Gibbs-Boltzmann distribution also properly fits the actual data distribution and could clearly explain the income distribution in Iran. The generalized Gibbs-Boltzmann distribution also fits the actual income data better than both Pareto and Lognormal distributions.