CLUSTER ANALYSIS IDENTIFIES VARIABLES RELATED TO PROGNOSIS OF BREAST CANCER DISEASE

This work presents a cluster analysis approach aiming to determine distinct groups based on clinicopathological data from patients with breast cancer (BC). For this purpose, the clinical variables were considered: age at diagnosis, weight, height, lymph nodal invasion (LN), tumor-node-metastasis (TNM) staging and body mass index (BMI). Ward's hierarchical clustering algorithm was used to form specific groups. Based on this, BC patients were separated into four groups. The Kruskal-Wallis test was performed to assess the differences among the clusters. The intensity of the influence of variables on the prognosis of BC was also evaluated by calculating the Spearman's correlation. Positive correlations were obtained between weight and BMI, TNM and LN invasion in all analyzes. Negative correlations between BMI and height were obtained in some of the analyzes. Finally, a new correlation was obtained, based on this approach, between weight and TNM, demonstrating that the trophic-adipose status of BC patients can be directly related to disease staging.

ANALYSIS OF COVID-19 CONTAMINATION AND DEATHS CASES IN BRAZIL ACCORDING TO THE NEWCOMB-BENFORD

The use of the Newcomb-Benford Law in assessing the quality of health and / orepidemiological information systems can allow relevant decisions to be made to improve these systems. In this context, this research aimed to carry out an assessment of the conformity of theinformation regarding the number of cases of contamination and deaths by COVID-19 in Brazil according to the Newcomb-Benford Law, from the moment of the occurrence of the first case of the disease and from the first death by COVID-19 in the country until the month of September 2020. With the aid of descriptive statistics and the use of metrics related to the Z test and themean absolute deviation it was possible to observe that, both from a national and longitudinal perspective as for the transversal-state perspective, the quantitative data referring to the cases of contamination by the coronavirus and the deaths that occurred as a result of COVID-19 did not present the expected behavior according to the Newcomb-Benford Law. Due to the lack of conformity in relation to the Newcomb-Benford Law, it is suspected that some level of conformity specific to this type of data has occurred, in the Brazilian context, since there are already studies that suggest the existence of proper levels of conformity for certain types of data.

INCIDENCE AND LETHALITY OF COVID-19 CLUSTERS IN BRAZIL VIA CIRCULAR SCAN METHOD

The COVID-19 pandemic has spread rapidly around the world in a frightening way. In Brazil, the third country with the highest number of infected and deaths from the disease, it is important for government health authorities to identify the federation units that stand out in cases and deaths from this disease to target resources. The circular scan statistic proposed by Martin Kulldorff allows to identify with some statistical significance the units of the federation that stand out in relation to the number of cases and deaths of COVID-19 in Brazil. Such units of federation are known as clusters. Once these clusters were identified, we used the coefficients of incidence and lethality to better describe the behavior of these clusters during three phases of the pandemic: the initial phase, the peak phase, and also the stability and fall phase. We observed changes in the location of the clusters identified in these three phases and used the R software and also the SaTScan software to obtain the maps and results, which were consistent with what was reported by the Brazilian media.

BEST LINEAR UNBIASED LATENT VALUES PREDICTORS FOR FINITE POPULATION LINEAR MODELS WITH DIFFERENT ERROR SOURCES

We develop best linear unbiased predictors (BLUP) of the latent values of labeled sample units selected from a finite population when there are two distinct sources of measurement error: endogenous, exogenous or both. Usual target parameters are the population mean, the latent values associated to a labeled unit or the latent value of the unit that will appear in a given position in the sample. We show how both types of measurement errors affect the within unit covariance matrices and indicate how the finite population BLUP may be obtained via standard software packages employed to fit mixed models in situations with either heteroskedastic or homoskedastic exogenous and endogenous measurement errors.

UROCHLOA GRASS GROWTH AS A FUNCTION OF NITROGEN AND PHOSPHORUS FERTILIZATION

The urochloa grass (Urochloa mosambicensis) is a perennial grass, C4 plant, with a high photosynthetic rate and CO2 fixation, persistent to water deficit, adapted to a wide diversity of soils and hot climate regions. Thus, the objective was to evaluate the urochloa grass growth and define the best models to estimate plant height as a function of nitrogen and phosphate fertilization. The experimental design was completely randomized, in the 2 x 2 factorial design (presence and absence of nitrogen presence and absence of phosphorus), with four replications. Was used a dose of nitrogen and phosphorus equivalent to 100 kg.ha-1 of N and 150 kg.ha-1 of P2O5, respectively. The following models were used: linear, power, gamma andlogistic to estimate plant height as a function of the following explanatory variables: days after planting, nitrogen and phosphorus doses. The criteria used to determine the best model(s) were as follows: higher adjusted coefficient of determination, lower Akaike information criterion, lower sum of square of residuals and high Willmott index. The plant height in the absence of nitrogen and phosphorus and when applied 100 kg.ha-1 of N and 150 kg.ha-1 of P2O5 was estimated more accurately by the Gamma model with high power of explanation. The adoption of the Gamma model allows to estimate the U. mosambicensis plant height, in a non-destructive manner, with high precision, speed and low cost, depending of age plant and nitrogen and phosphate fertilization.

AN APPLICATION OF THE POISSON-WEIBULL MODEL FOR CENSURED DATA

In this paper, we proposed the Poisson-Weibull distribution for the modeling of survival data. The motivation to study this model since, in addition to generalizing the Weibull distribution, which is widely used in several areas of knowledge among them the Survival and Reliability analysis, it presents great exibility in the forms of the hazard function. The Poisson-Weibull distribution was created in a composition of discrete and continuous distributions where there is no information about which factor was responsible for the component failure, only the minimum lifetime value among all risks is observed. The maximum likelihood approach was used to estimate the parameters of the model. Also was conducted a simulation study to examine the mean, the bias, and the root of the mean square error of the maximum likelihood estimates of the proposed model according to the censoring percentages and sample sizes. The model selection criteria were also applied, in addition to graphic techniques such as TTT-Plot and Kaplan-Meier. Application to the real data set was used to illustrate the usefulnessof the distribution.

Comparações entre métodos de desvio padrões aleatórios em experimentos fatoriais com dois níveis por fator e sem repetição.

Para obter a estimativa da variância aleatória em experimentos fatoriais completos e fracionados com dois níveis por fator avaliados sem repetições, Hamada e Balakrishnan (1998) fornecem uma lista de vários métodos. Assim, com base nessa revisão, o objetivo do presente trabalho consistiu em comparar as estimativas dos desvios-padrão com apenas influências das causas aleatórias de acordo com quatro métodos: de Lenth (1989), de Juan e Pena (1992), de Dong (1993) e sem nenhuma restrição aos dados, aqui denominado de desvio-padrão total. Para isso, foi simulada uma variável aleatória normal com 10.000 valores, cuja simulação foi repetida 16 vezes. Posteriormente, foram substituídos em cada um dos 16 conjuntos de dados, 0%, 1%, 2%, 3% e 4% dos valores aleatórios por outliers com o objetivo de quebrar a aleatoriedade da variável simulada. Com base na estimativa do erro percentual médio absoluto (EPMA) obtida em relação ao desvio-padrão aleatório paramétrico, concluiu-se, por meio da análise de regressão, que ela aumentou em função do aumento do percentual de substituição dos valores aleatórios por outliers, com exceção à obtida de acordo com o método de Juan e Pena (1992). Mesmo assim, para conjuntos de dados com até 3,68% de outliers, os melhores métodos de estimação do desvio-padrão aleatório (Saleatório) foram os de Lenth (1989) e de Dong (1993), por terem fornecido as menores estimativas do EPMA. Acima desse percentual e até 4% de outliers, o método de Juan e Pena (1992) mostrou-se ser melhor. No entanto, como a maior estimativa do EPMA proporcionada pelos três métodos de estimação foi muito baixa (4,00%), e ainda, como as diferenças observadas entre eles foram, praticamente, desprezíveis, concluiu-se que os três métodos forneceram boas estimativas do Saleatório e que, consequentemente, podem ser recomendados para estimar o quadrado médio do resíduo em experimentos fatoriais completos e fracionados com dois níveis por fator e com observações individuais por tratamento. Por outro lado, o método do desvio-padrão total não conseguiu evitar o efeito da não aleatoriedade sobre a estimativa do Saleatório.

INEQUALITY AND DISABILITY: IN STATISTICAL TERMS, WHAT ELSE DO WE NEED TO KNOW?

Social inequality is the phenomenon that differentiates between people in the context of the same society, placing some individuals in structurally more advantageous conditions than others. It manifests itself in all aspects: political, economic among others. The main causes of inequality are investment lack in social areas, health and education. Among the consequences of inequality, we highlight: increased violence, poverty, delay in economic progress; hunger, destruction and infant mortality; young marginalization people, and finally; rising unemployment. Among the main inequality types, we highlight: people with and without disabilities, regions, races; income and sex. To measure this inequality, we highlight HDI, Theil and MPI. A person with a disability is any person who presents a loss or abnormality that generates an inability to perform one or more activities, and these characteristics hinder their social inclusion, access to the labor market, transportation, education, financing and training; urban and environmental barriers, and finally; ignorance of employers. Situations like these provide disabilities people with lower wages when employed, worse purchasing power, less social participation providing greater exclusion and disadvantaged situations when compared to those without disabilities. For this work we used exploratory analysis techniques considering data sets from the 2010 IBGE Census and UNDP.

Análise de sobrevivência aplicada ao tempo de permanência em planos de saúde.

Apesar dos lucros auferidos no segmento de saúde suplementar, o número de segurados vinculados a ele oscilou entre 2015 e 2018, em contraste com o comportamento apresentado entre 2000 e 2014, quando só cresceu. Para compreender parte desse fluxo, isto é, a saída dos segurados desse mercado, objetiva-se analisar o tempo de permanência do segurado em planos de saúde, a partir de dados compostos por 122.381 segurados (e ex-segurados) acompanhados entre os anos de 1984 e 2018. Utilizando-se da análise de sobrevivência tradicional, por meio do estimador de Kaplan-Meier e de modelos paramétricos e semiparamétricos, destacam-se os seguintes resultados: a) a mediana do tempo de permanência no plano é de 4,62 anos; b) a massa de seguradoras é composta (ao longo dos anos observados) predominantemente por mulheres, solteiras, jovens, titulares e aderentes ao contrato de individual/familiar; c) conforme o modelo de Cox selecionado, ser homem (em relação à mulher), ser jovem (em relação ao adulto), ser dependente (em relação ao titular) e ser casado (em relação ao amasiado) aumentam o risco de saída da operadora analisada. Espera-se que esses resultados auxiliem a operadora analisada a (re)direcionar suas políticas comerciais e de subscrição de riscos.

A CASE STUDY ON ANIMAL BEHAVIOR ANALYSIS USING GAMLSS

Animal behavior studies usually produce large amounts of data and a wide variety of data structures, including nonlinear relationships, interaction effects, nonconstant variance, correlated measures, overdispersion, and zero inflation, among others. We aimed to explore here the potential of generalized additive models for location, scale and shape (GAMLSS) in analyzing data from animal behavior studies. Data from 20 Romane ewes from two genetic lineages submitted to brushing by a familiar observer were analyzed. Behavioral responses through ear posture changes, a count random variable, and the proportion of time to perform the horizontal ear posture, a continuous random variable on the interval (0,1), with non-null probabilities in zero and one, were analyzed. The Poisson, negative binomial, and their zero-inflated and zero-adjusted extensions models were considered for the count data, whereas the beta distribution and its inflated versions were evaluated for the proportions. Random effects were also included to consider the multilevel structure of the experiment. The zero adjusted negative binomial model has better fitted the count data, whereas the inflated beta distribution performed the best for the proportions. Both models allowed us to properly assess the effects of social separation, brushing, and genetic lineages on sheep behavioral. We may conclude that GAMLSS is a flexible framework to analyze animal behavior data.