Comparison of Cox proportional hazards model, Cox proportional hazards with time-varying coefficients model, and lognormal accelerated failure time model: Application in time to event analysis of melioidosis patients

Objective: To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time (AFT), Cox proportional hazards (PH), and Cox PH with timevarying coefficient (TVC) models. Methods: A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah, Kedah and Hospital Tuanku Fauziah, Perlis in Northern Malaysia due to confirmed-cultured melioidosis. The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis, and Cox s models and the findings were compared by using the goodness of fit methods. The analyses were done by using Stata SE version 14.0. Results: A total of 242 patients (53.4%) survived. In this study, the median survival time of melioidosis patients was 30.0 days (95% CI 0.0-60.9). Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model. In AFT survival analysis, a total of seven significant prognostic factors were identified. The results were found to be only a slight difference between the identified prognostic factors among the models. AFT survival showed better results compared to Cox's models, with the lowest Akaike information criteria and best fitted Cox-snell residuals. Conclusions: AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.

The Sudden Infant Death Syndrome is a Probability Process.

The Sudden Infant Death Syndrome (SIDS) is sudden-unexpected death of an infant that remains unexplained after thorough forensic autopsy, death scene investigation and review of the infant's medical history. As the results of a few spins of a roulette wheel cannot establish whether the wheel is honest (uniform value distribution), medical investigations of a few SIDS cases have not been able to uncover the mechanistic cause of death. We propose that this is because statistical analyses of large numbers of independent observations may be required to unmask the apparent probability processes that govern these quite different phenomena. The SIDS male fraction ~0.60 appears as a binomial probability sample characteristic of a condition caused by an Xlinked gene. The unique SIDS age distribution (minimum at birth, mode ~63 days, median ~94 days, falling exponentially to zero at ~41.2 months) appears as a probability sample from an underlying Johnson SB (4-parameter lognormal) distribution of ages. The presence of this lognormal distribution is prima facie evidence that a probability process is involved. Matching binomial and SB distribution equations to these physiological phenomena, we propose: The SIDS binomial gender distributions arises from an Xlinked recessive allele (q ≈ 2/3) non-protective against acute anoxic encephalopathy; and SIDS Johnson SB age distributions arise from such genetically susceptible infants having three independent risk factors: neurological prematurity (m + 0.31)-1 decreasing with age in months m; risk of respiratory infection increasing with age (41.2 - m)-1; and risk of physiological anemia rising and falling with age (2ᴨσ2)-1/2[exp(-0.5[(y-μ)/σ]2)] , where y = Log[(m + 0.31)/(41.2 - m)] = μ + σ z, μ is median of y, σ is standard deviation of y, with z a standard normal deviate. We show infant Respiratory Distress Syndrome and Suffocation by Inhalation of Food or Foreign Object have approximately the same male fractions as SIDS, supporting the hypothesis that the same allele of an X-linked gene is responsible for death in all these cases.

Application of statistical distribution of PM10 concentration in air quality management in 5 representative cities of China / 生物医学与环境科学（英文）

<p><b>OBJECTIVE</b>To estimate the frequency of daily average PM10 concentrations exceeding the air quality standard (AQS) and the reduction of particulate matter emission to meet the AQS from the statistical properties (probability density functions) of air pollutant concentration.</p><p><b>METHODS</b>The daily PM10 average concentration in Beijing, Shanghai, Guangzhou, Wuhan, and Xi'an was measured from 1 January 2004 to 31 December 2008. The PM10 concentration distribution was simulated by using the lognormal, Weibull and Gamma distributions and the best statistical distribution of PM10 concentration in the 5 cities was detected using to the maximum likelihood method.</p><p><b>RESULTS</b>The daily PM10 average concentration in the 5 cities was fitted using the lognormal distribution. The exceeding duration was predicted, and the estimated PM10 emission source reductions in the 5 cities need to be 56.58%, 93.40%, 80.17%, 82.40%, and 79.80%, respectively to meet the AQS.</p><p><b>CONCLUSION</b>Air pollutant concentration can be predicted by using the PM10 concentration distribution, which can be further applied in air quality management and related policy making.</p>

Investigating the center of pressure velocity Romberg's quotient for assessing the visual role on the body sway / Avaliando a importância da visão nas oscilações posturais utilizando o quociente de Romberg da velocidade do centro de pressão

The classical Romberg's test based on stabilometric tests in eyes open (EO) and closed (EC) conditions was used for investigating the influence of visual feedback in the body sway control in healthy adult subjects. Stabilograms from 144 subjects (aged 18-40) resting over a force platform were recorded for 30 s in EO and 30 s in EC conditions. The mean velocity was obtained for EO (VmEO) and EC (VmEC) in both anterior-posterior (y) and medial-lateral (x) directions and in the (x,y) plane, and thus used for computing the respective Romberg's quotient (RQ V). All Vm and RQ V parameter histograms presented unimodal asymmetric shapes, which were adequately fitted to lognormal distributions (Kolmogorov-Smirnov test, p > 0.05). These findings suggest a single homogeneous group in terms of visual strategy. Taking the threshold scores (95% confidence interval) of the Vm and RQ V distributions, only four subjects (2.7%) presented values below the lower limit, as expected by the confidence level (two tailed, 5%). A strong dependence was also found between each RQ V and the respective VmEC (Spear correlation > 0.86, R² > 74.0%), with VmEO presenting almost negligible coefficients of determination (R² < 2.9%). One can conclude that RQ V derived from a single stabilometric trial could be not sufficient for the diagnosis of body sway control impairment by vision. Nevertheless, the RQ V could be useful to indicate subjects to carry out additional tests to investigate a possible deficit in the integration of the visual information in the postural control system.

O Teste de Romberg clássico, baseado em testes estabilométricos nas condições de olhos abertos (EO) e fechados (EC), tem sido utilizado para investigar a influência da realimentação visual no controle das oscilações posturais em sujeitos adultos saudáveis. Estabilogramas de 144 sujeitos (18 a 40 anos) em posição ortostática sobre uma plataforma de força foram coletados durante 30 s na condição EO e 30 s em EC. As velocidades médias para EO (VmEO) e EC (VmEC), obtidas nas direções anteroposterior (y), mediolateral (x) e no plano (x,y), foram utilizadas no cálculo dos respectivos quocientes de Romberg (RQV). Os histogramas dos parâmetros Vm e RQV apresentaram morfologia unimodal assimétrica, aos quais foram ajustadas distribuições lognormais (Teste de Kolmogorov-Smirnov, p > 0,05). Tais distribuições sugerem haver um único grupo homogêneo no que concerne à estratégia visual. Considerando o intervalo de confiança de 95%, somente quatro sujeitos (2,7%) apresentaram valores de Vm e QRV abaixo do limite inferior, percentual este compatível com o teste bicaudal. A Correlação de Spear entre o RQV e seu respectivo VmEC foi sempre superior a 0,86, sendo o coeficiente de determinação R2 > 74,0%, enquanto que com VmEO R2 < 2,9%. Tais achados sugerem que o RQV obtido a partir de um único teste estabilométrico não seria adequado ao diagnóstico de problemas de controle das oscilações posturais ocasionados pela visão. No entanto, o RQV pode ser útil para indicar a realização de testes adicionais com vistas a investigar possível déficit na integração da informação visual no sistema de controle postural.

Diversidade de um cerrado sensu stricto com base em modelos de abundância de espécies / Diversity of a cerrado sensu stricto based on species abundance models

Este estudo teve como objetivo avaliar a diversidade de uma comunidade lenhosa de cerrado sensu stricto no sudeste de Goiás, a partir de modelos de distribuição de abundância de espécies. Foram alocadas aleatoriamente 10 parcelas de 20 x 20 m em um trecho de 4 km2 de cerrado sensu stricto preservado, onde todos os indivíduos com DB ≥ 5 cm (diâmetro a altura da base = 30 cm do nível do solo) foram amostrados e identificados. A comunidade apresentou ajuste aos modelos de vara-quebrada (χ 2 = 37,62, P = 0,99) e normal-logarítmico (χ 2 = 2,61, P = 0,63), que refletem equilíbrio ecológico. O modelo normal-logarítmico foi o de melhor ajuste, mostrando que as espécies se distribuem ao longo de mosaicos de recursos, fato corroborado pela diferenciação na distribuição das espécies a partir de uma análise de gradientes (análise de correspondência segmentada - DCA).

This study aimed to evaluate the diversity of the woody community of a cerrado sensu stricto in southeastern of Goiás State (Brazil), through species abundance models. Ten plots of 20 x 20 m were randomly allocated in an undisturbed cerrado sensu stricto area of 4 km2, and all individuals with DSH ≥ 5 cm (diameter at soil height = 30 cm aboveground) were sampled and identified. The broken-stick (χ 2 = 37.62, P = 0.99) and lognormal (χ 2 = 2.61, P = 0.63) models fits to community, reflecting an ecological equilibrium. The lognormal model was the most adequate, showing that the species are distributed along resource patches, in agreement to the pattern found in the gradient analysis (Detrended correspondence analysis - DCA)

Chironomidae assemblage structure in relation to organic enrichment of an aquatic environment / Estrutura da assembléia de chironomidae em relação ao enriquecimento orgânico de um ambiente aquático

In this study we determined the taxonomic diversity of larval Chironomidae upstream and downstream to discharges of the sewage treatment plant (STP) from Agro-industrial District of Anápolis, State of Goiás, Brazil. Additionally, we evaluated the use of the lognormal distribution as a measure of biotic integrity of this system. The Chironomidae communities were sampled in three sites, upstream and downstream of the discharge of the sewage treatment plant (STP). We fitted the truncate lognormal distribution based on a nonlinear regression of the datasets using least squares as loss function in an iterative quasi-Newton procedure. The total of 21,498 individuals were sampled, from 24 Chironomidae genera, Chironomus, Polypedilum, Rheotanytarsus e Thienemanniella, with 73.9 percent, 14.4 percent, 7.1 percent and 4.5 percent, respectively, of all analyzed community; they are generally considered resistant to organic pollution. The assemblage of the site upstream was described for a truncate lognormal distribution. The extreme increase in abundance of some genera in the first site downstream produced a distribution not fitted to lognormal. The second site downstream however, permits a good fit to lognormal, probably due to the decrease in abundance of the dominant groups. These data substantiate the hypothesis that Chironomidae community is not suitably characterized by lognormal distribution at disturbed environments. Consequently, these aquatic communities were ecological disordered by organic pollution which caused the lost of sensible species and the dominance of those tolerants to this sort of impact. Additionally, the study highlighted the distribution lognormal approach as a valuable method to assess environmental impacts.

A diversidade taxonômica da comunidade de Chironomidae em ambientes aquáticos poluídos e não-poluídos foi estudada na área de influência do Distrito Agroindustrial de Anápolis, Anápolis, GO, avaliando-se a distribuição lognormal como indicador da integridade biótica desses sistemas. Larvas de Chironomidae foram coletadas em três pontos a montante e jusante do lançamento do efluente da estação de tratamento de esgoto desse distrito industrial. O ajuste do modelo de distribuição foi realizado utilizando-se o modelo de regressão não-linear, adotando procedimento iterativo quasi-Newton. Foram amostrados 21.498 indivíduos de 24 gêneros de Chironomidae. Chironomus, Polypedilum, Rheotanytarsus e Thienemanniella foram os mais abundantes, visto que são geralmente considerados resistentes à poluição orgânica. A assembléia do ponto a montante do lançamento foi bem descrita pelo modelo de distribuição lognormal truncada. O grande aumento da abundância de alguns gêneros no primeiro ponto a jusante impossibilitou o ajuste da distribuição lognormal truncada. O segundo a jusante, no entanto, possibilitou bom ajuste, possivelmente devido à diminuição na abundância dos grupos dominantes. Esses dados corroboram a hipótese de que as assembléias de chironomideos em ambientes não alterados são bem descritas por uma distribuição lognormal, o que não pode ser observado em ambientes degradados. Desta forma, evidenciou-se que a poluição orgânica causa desestruturação das comunidades aquáticas desse sistema, com perda das espécies sensíveis e dominância das tolerantes a esse tipo de impacto. Além disso, fica evidente que a distribuição lognormal pode ser considerada uma valiosa abordagem para avaliação de impactos ambientais.

Prognostic factors in gastric cancer using log-normal censored regression model.

Background & objectives: Gastric cancer is one of the most common cancers in the world. It is rarely detected early, and the prognosis remains poor. Cox proportional hazard model is used to examine the relationship between survival and covariates. Parametric survival models such as log normal regression model can also be used for this analysis. We used log normal regression model in this study to evaluate prognostic factors in gastric cancer and compared with Cox model. Methods: We retrospectively studied the 746 patients diagnosed with gastric cancer admitted in a referral hospital in Tehran, Iran, from February 2003 through January 2007. Age at diagnosis, sex, extent of wall penetration, histology type, tumour grade, tumour size, pathologic stage, lymph node metastasis and presence of metastasis were entered into a log normal model. Hazard rate (HR) was employed to interpret the risk of death and the results were compared with Cox regression. The AIC (Akaike Information Criterion) was employed to compare the efficiency of models. Results: Univariate analysis indicated that with increasing age the risk of death increased significantly in both log normal and Cox models. Patients with grater tumour size were also in higher risk of death followed by those with poorly differentiated and moderately differentiated in tumour grade and advanced pathologic stage. The presence of metastasis was significant prognostic factor only in log normal analysis. In final multivariate model, age was still a significant prognostic factor in Cox regression but it was not significant in log normal model. Presence of metastasis followed by histology type were other prognostic features found significant in log normal results. Based on AIC, log normal model performed better than Cox. Interpretation & conclusion: Our results suggest that early detection of patients in younger age and in primary stages and grade of tumour could be important to decrease the risk of death in patients with gastric cancer. Comparison between Cox and log normal models indicated that log normal regression model can be a useful statistical model to find prognostic factors instead of Cox.

Comments about some species abundance patterns: classic, neutral, and niche partitioning models

The literature on species abundance models is extensive and a great deal of new and important contributions have been published in the last three decades. Broadly speaking, one can recognize five families of species abundance models: i) purely statistical or classic models (Broken-stick, Log-normal, Logarithmic and Geometric series); ii) branching process (Zipf-Mandelbrot and Fractal branching models); iii) population dynamics (Neutral models included); iv) spatial distribution of individuals (Multifractal and HEAP models) and v) niche partitioning (Sugihara's breakage and Tokeshi models). Among these the neutral, the classic and the niche partitioning models have been the most applied to natural communities, the former having been more extensively discussed than the others in the last years. The objective of this paper is to comment some aspects of the classic, neutral and niche partitioning models in a way that the proposed distributions may contribute to the analysis of the empirical patterns of species abundance. In spite of the variety of models, the distributions in general vary between the log-normal and the logarithmic series. From these models the Power-Fraction, together with independent niche dimensions measures, are amenable to experimental tests and may offer answers on which resources are important in the structuring of biological communities.

A literatura sobre modelos de espécie-abundância é extensa e importantes contribuições têm sido publicadas nas últimas três décadas. De forma geral, são reconhecidos cinco grandes grupos de modelos: i) os que descrevem distribuições puramente estatísticas ou modelos clássicos (Broken-stick, log-normal, série logarítmica e série geométrica); ii) os que simulam processos de ramificação hierárquica (modelos Zipf-Mandelbrot e Fractal); iii) de dinâmica de populações (modelos Neutros); iv) de distribuição espacial de indivíduos (modelos Multifractal e HEAP); e v) de partição de nicho (modelos de Sugihara e de Tokeshi). Os modelos clássicos, os de partição de nicho e principalmente os modelos neutros têm sido os mais utilizados em estudos de comunidades naturais. O objetivo deste artigo é discutir de que forma as distribuições geradas por estes três grupos, bem com as suas bases conceituais, podem contribuir com a análise de padrões empíricos de espécie-abundância. Em geral, estes padrões variam entre as curvas log-normal e série logarítmica. Dentre a variedade de modelos existentes, o Power-fraction possibilita a simulação de uma grande amplitude de padrões de abundância relativa e é de utilização relativamente simples, podendo ser utilizado em testes experimentais de perturbação ou de sucessão ecológica. Aliado a medidas independentes de dimensões de nicho, este modelo pode ainda oferecer respostas sobre quais recursos são essenciais à estruturação de comunidades biológicas.

Comments about some species abundance patterns: classic, neutral, and niche partitioning models / Comentários sobre alguns padrões de espécie-abundância: modelos clássicos, neutros e de partição de nicho

The literature on species abundance models is extensive and a great deal of new and important contributions have been published in the last three decades. Broadly speaking, one can recognize five families of species abundance models: i) purely statistical or classic models (Broken-stick, Log-normal, Logarithmic and Geometric series); ii) branching process (Zipf-Mandelbrot and Fractal branching models); iii) population dynamics (Neutral models included); iv) spatial distribution of individuals (Multifractal and HEAP models) and v) niche partitioning (Sugihara's breakage and Tokeshi models). Among these the neutral, the classic and the niche partitioning models have been the most applied to natural communities, the former having been more extensively discussed than the others in the last years. The objective of this paper is to comment some aspects of the classic, neutral and niche partitioning models in a way that the proposed distributions may contribute to the analysis of the empirical patterns of species abundance. In spite of the variety of models, the distributions in general vary between the log-normal and the logarithmic series. From these models the Power-Fraction, together with independent niche dimensions measures, are amenable to experimental tests and may offer answers on which resources are important in the structuring of biological communities.

A literatura sobre modelos de espécie-abundância é extensa e importantes contribuições têm sido publicadas nas últimas três décadas. De forma geral, são reconhecidos cinco grandes grupos de modelos: i) os que descrevem distribuições puramente estatísticas ou modelos clássicos (Broken-stick, log-normal, série logarítmica e série geométrica); ii) os que simulam processos de ramificação hierárquica (modelos Zipf-Mandelbrot e Fractal); iii) de dinâmica de populações (modelos Neutros); iv) de distribuição espacial de indivíduos (modelos Multifractal e HEAP); e v) de partição de nicho (modelos de Sugihara e de Tokeshi). Os modelos clássicos, os de partição de nicho e principalmente os modelos neutros têm sido os mais utilizados em estudos de comunidades naturais. O objetivo deste artigo é discutir de que forma as distribuições geradas por estes três grupos, bem com as suas bases conceituais, podem contribuir com a análise de padrões empíricos de espécie-abundância. Em geral, estes padrões variam entre as curvas log-normal e série logarítmica. Dentre a variedade de modelos existentes, o Power-fraction possibilita a simulação de uma grande amplitude de padrões de abundância relativa e é de utilização relativamente simples, podendo ser utilizado em testes experimentais de perturbação ou de sucessão ecológica. Aliado a medidas independentes de dimensões de nicho, este modelo pode ainda oferecer respostas sobre quais recursos são essenciais à estruturação de comunidades biológicas.

An overview of boron, lithium, and strontium in human health and profiles of these elements in urine of Japanese

The biological, medical and environmental roles of trace elements have attracted considerable attention over the years. In spite of their relevance in nutritional, occupational and toxicological aspects, there is still a lack of consistent and reliable measurement techniques and reliable information on reference values. In this review our understandings of the urinary profilings of boron, lithium and strontium are summarized and fundamental results obtained in our laboratory are discussed.Over the past decade we have successfully used inductively coupled plasma emission spectrometry for the determination of reference values for urinary concentrations of boron, lithium and strontium. Taking into account the short biological half-life of these elements and the fact that their major excretion route is via the kidney, urine was considered to be a suitable material for monitoring of exposure to these elements. We confirmed that urinary concentrations of boron, lithium and strontium follow a lognormal distribution. The geometric mean reference values and 95% confidence intervals were 798 μg/l (398-1599 μg/l) for boron, 23.5 μg/l (11.0-50.5 μg/l) for lithium and 143.9 μg/l (40.9-505.8 μg/l) for strontium. There were no discrepancies between our values and those previously reported. Our reference values and confidential intervals can be used as guidelines for the health screening of Japanese individuals to evaluate environmental or occupational exposure to these elements.

An Overview of Boron, Lithium, and Strontium in Human Health and Profiles of These Elements in Urine of Japanese

The biological, medical and environmental roles of trace elements have attracted considerable attention over the years. In spite of their relevance in nutritional, occupational and toxicological aspects, there is still a lack of consistent and reliable measurement techniques and reliable information on reference values. In this review our understandings of the urinary profilings of boron, lithium and strontium are summarized and fundamental results obtained in our laboratory are discussed. Over the past decade we have successfully used inductively coupled plasma emission spectrometry for the determination of reference values for urinary concentrations of boron, lithium and strontium. Taking into account the short biological half-life of these elements and the fact that their major excretion route is via the kidney, urine was considered to be a suitable material for monitoring of exposure to these elements. We confirmed that urinary concentrations of boron, lithium and strontium follow a lognormal distribution. The geometric mean reference values and 95% confidence intervals were 798 μg/l (398–1599 μg/l) for boron, 23.5 μg/l (11.0–50.5 μg/l) for lithium and 143.9 μg/l (40.9–505.8 μg/l) for strontium. There were no discrepancies between our values and those previously reported. Our reference values and confidential intervals can be used as guidelines for the health screening of Japanese individuals to evaluate environmental or occupational exposure to these elements.

Determination of reference concentrations of strontium in urine by inductively coupled plasma atomic emission spectrometry

<p><b>OBJECTIVE</b>The aim of this study was to establish reference concentrations of urinary strontium by inductively coupled plasma atomic emission spectrometry (ICP-AES).</p><p><b>METHODS</b>For the determination of strontium, urine samples were collected from healthy Japanese (n=146; 115 males, 31 females; mean age, 33±9 years; age range, 18 to 58 years). The urine samples stored at or below -20°C were thawed with incubation at 40°C for 30 min and sediments were dissolved by vigorous shakings. Then, the samples were centrifuged at 3000 g for 5 min, and the supernatant was directly aspired into a P-5200-3600/1200 ICP-AES system from Hitachi Ltd., Tokyo, Japan.</p><p><b>RESULTS</b>A steeper increase in the S/N ratio and a good effective linearity of the calibration line was obtained at 407.771 nm in the range of 0-300 μg/L strontium standard solution. Urine samples having the same background signal as that of 18 MΩ cm ultrapure blank water, a good correspondence of the single peak pattern of the spectra, accuracy and precision of spike recovery were also confirmed. Urinary strontium concentrations showed a log-normal distribution and a geometric mean concentration of 143.9 μg/L, with 5-95% confidential interval of 40.9-505.8 μg/L.</p><p><b>CONCLUSION</b>The results of this study will be useful as guidelines for the biological monitoring of strontium in normal subjects and in individuals therapeutically or environmentally exposed to strontium.</p>

Determination of Reference Concentrations of Strontium in Urine by Inductively Coupled Plasma Atomic Emission Spectrometry

Objective: The aim of this study was to establish reference concentrations of urinary strontium by inductively coupled plasma atomic emission spectrometry (ICP-AES). Methods: For the determination of strontium, urine samples were collected from healthy Japanese (n=146; 115 males, 31 females; mean age, 33±9 years; age range, 18 to 58 years). The urine samples stored at or below −20°C were thawed with incubation at 40°C for 30 min and sediments were dissolved by vigorous shakings. Then, the samples were centrifuged at 3000 g for 5 min, and the supernatant was directly aspired into a P-5200-3600/1200 ICP-AES system from Hitachi Ltd., Tokyo, Japan. Results: A steeper increase in the S/N ratio and a good effective linearity of the calibration line was obtained at 407.771 nm in the range of 0–300 μg/L strontium standard solution. Urine samples having the same background signal as that of 18 MΩ cm ultrapure blank water, a good correspondence of the single peak pattern of the spectra, accuracy and precision of spike recovery were also confirmed. Urinary strontium concentrations showed a log-normal distribution and a geometric mean concentration of 143.9 μg/L, with 5–95% confidential interval of 40.9–505.8 μg/L. Conclusion: The results of this study will be useful as guidelines for the biological monitoring of strontium in normal subjects and in individuals therapeutically or environmentally exposed to strontium.