PCorteSoft - Sistema para la determinación del punto de corte óptimo en escalas predictivas y la categorización de variables continuas

Al desarrollar modelos de predicción para su aplicación en la práctica clínica, los profesionales de la salud suelen categorizar las variables clínicas que son de naturaleza continua. En muchas ocasiones estos modelos constituyen la base para la confección de escalas predictivas, a partir de las cuales se estratifica a los pacientes en varias categorías atendiendo al fenómeno estudiado. En estos casos se requiere la determinación de uno o varios puntos de cortes que permitan dividir el recorrido de la variable, variables continuas o puntuaciones de una escala, en dos o más categorías. El presente trabajo tiene como objetivo la automatización de diferentes métodos para dicotomizar variables continuas en modelos de predicción clínica, donde la variable respuesta es dicotómica, y determinar el punto de corte óptimo en la estratificación de pacientes en dos categorías, a partir de escalas de predicción. Para ello se elaboró un software en el lenguaje de programación R, que implementa diferentes métodos para la determinación del punto de corte óptimo, lo cual agiliza el trabajo investigativo de los especialistas de salud en el proceso de elaboración de modelos predictivos y/o escalas de predicción.

When developing predictive models for application in clinical practice, health professionals often categorize clinical variables that are continuous in nature. In many cases, these models are the basis for the development of predictive scales from which patients are stratified into various categories according to the phenomenon under study. In both cases, it is necessary to determine one or more cut-off points that allow dividing the path of the variable, continuous variables, or scores of a scale into two or more categories. The aim of the present work is to automate different existing methods for dichotomizing continuous variables in clinical prediction models where the response variable is dichotomous, as well as to determine the optimal cut-off point for stratifying patients into two categories, based on prediction scales. For this purpose, a software was developed in the R programming language, which implements different existing methods for the determination of the optimal cut-off point, speeding up the research work of health specialists in the process of developing predictive models and/or prediction scales.

TTS package: Computational tools for the application of the Time Temperature Superposition principle.

The TTS package has been developed in R software to predict the mechanical properties of viscoelastic materials, at short and long observation times/frequencies by applying the Time Temperature Superposition (TTS) principle. TTS is a physical principle used in material science to estimate mechanical properties beyond the experimental range of observed times/frequencies by shifting data curves obtained at other temperatures relative to a reference temperature in the dataset. It is a methodology related to accelerated life-tests and reliability, whereas the TTS library is one of the first open source computational tool to apply the TTS principle. This R package provides free computational tools to obtain master curves that characterize materials from a thermal-mechanical approach. The TTS package also proposes, implements and explains our own method to obtain the shift factors and the master curve in a TTS analysis, based on horizontal shifting of the first derivative function of viscoelastic properties. This procedure provides shift factors estimates and smooth master curve estimates using B-spline fitting, in a fully automatic way, without assuming any parametric expression. Williams-Landel-Ferry (WLF) and Arrhenius TTS parametric models are also implemented in the TTS package. They can be fitted from shifts obtained by the our first derivative based method.

The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications.

In this paper, we propose and derive a new regression model for response variables defined on the open unit interval. By reparameterizing the unit generalized half-normal distribution, we get the interpretation of its location parameter as being a quantile of the distribution. In addition, we can evaluate effects of the explanatory variables in the conditional quantiles of the response variable as an alternative to the Kumaraswamy quantile regression model. The suitability of our proposal is demonstrated with two simulated examples and two real applications. For such data sets, the obtained fits of the proposed regression model are compared with that provided by a Kumaraswamy regression model.

An Introductory Tutorial on Cohort State-Transition Models in R Using a Cost-Effectiveness Analysis Example.

Decision models can combine information from different sources to simulate the long-term consequences of alternative strategies in the presence of uncertainty. A cohort state-transition model (cSTM) is a decision model commonly used in medical decision making to simulate the transitions of a hypothetical cohort among various health states over time. This tutorial focuses on time-independent cSTM, in which transition probabilities among health states remain constant over time. We implement time-independent cSTM in R, an open-source mathematical and statistical programming language. We illustrate time-independent cSTMs using a previously published decision model, calculate costs and effectiveness outcomes, and conduct a cost-effectiveness analysis of multiple strategies, including a probabilistic sensitivity analysis. We provide open-source code in R to facilitate wider adoption. In a second, more advanced tutorial, we illustrate time-dependent cSTMs.

An overview on parametric quantile regression models and their computational implementation with applications to biomedical problems including COVID-19 data.

Quantile regression allows us to estimate the relationship between covariates and any quantile of the response variable rather than the mean. Recently, several statistical distributions have been considered for quantile modeling. The objective of this study is to provide a new computational package, two biomedical applications, one of them with COVID-19 data, and an up-to-date overview of parametric quantile regression. A fully parametric quantile regression is formulated by first parameterizing the baseline distribution in terms of a quantile. Then, we introduce a regression-based functional form through a link function. The density, distribution, and quantile functions, as well as the main properties of each distribution, are presented. We consider 18 distributions related to normal and non-normal settings for quantile modeling of continuous responses on the unit interval, four distributions for continuous response, and one distribution for discrete response. We implement an R package that includes estimation and model checking, density, distribution, and quantile functions, as well as random number generators, for distributions using quantile regression in both location and shape parameters. In summary, a number of studies have recently appeared applying parametric quantile regression as an alternative to the distribution-free quantile regression proposed in the literature. We have reviewed a wide body of parametric quantile regression models, developed an R package which allows us, in a simple way, to fit a variety of distributions, and applied these models to two examples with biomedical real-world data from Brazil and COVID-19 data from US for illustrative purposes. Parametric and non-parametric quantile regressions are compared with these two data sets.

Characterization of the chemical composition (mineral, lead and centesimal) in pine nut (Araucaria angustifolia (Bertol.) Kuntze) using exploratory data analysis.

In this study, mineral composition, centesimal composition and lead were evaluated in pine nut seeds (raw and cooked) from five Brazilian states. Mineral composition was determined by ICP OES and lead by GF AAS. The results for minerals were evaluated by Boxplot, PCA and HCA, using the R software. Average minerals in raw and cooked samples (mg 100 g-1) were: 15.2 and 10.8 (Ca), 0.168 and 0.113 (Cu), 0.506 and 0.330 (Fe), 536 and 420 (K), 51.3 and 40.6 (Mg), 0.373 and 0.208 (Mn), 132 and 102 (P) and 0.746 and 0.520 (Zn). The average centesimal composition (raw and cooked) was: 53.5 and 47.2% (moisture), 1.76 and 1.26% (ash), 3.90 and 3.53% (protein), 40.8 and 48.0% (carbohydrate) and 179 and 206 kcal/100 g (total caloric value) and Pb was not detected. The chemometric analysis showed a distinction of raw and cooked samples due to significant nutrient losses after thermal processing.

Modeling Mortality Based on Pollution and Temperature Using a New Birnbaum-Saunders Autoregressive Moving Average Structure with Regressors and Related-Sensors Data.

Environmental agencies are interested in relating mortality to pollutants and possible environmental contributors such as temperature. The Gaussianity assumption is often violated when modeling this relationship due to asymmetry and then other regression models should be considered. The class of Birnbaum-Saunders models, especially their regression formulations, has received considerable attention in the statistical literature. These models have been applied successfully in different areas with an emphasis on engineering, environment, and medicine. A common simplification of these models is that statistical dependence is often not considered. In this paper, we propose and derive a time-dependent model based on a reparameterized Birnbaum-Saunders (RBS) asymmetric distribution that allows us to analyze data in terms of a time-varying conditional mean. In particular, it is a dynamic class of autoregressive moving average (ARMA) models with regressors and a conditional RBS distribution (RBSARMAX). By means of a Monte Carlo simulation study, the statistical performance of the new methodology is assessed, showing good results. The asymmetric RBSARMAX structure is applied to the modeling of mortality as a function of pollution and temperature over time with sensor-related data. This modeling provides strong evidence that the new ARMA formulation is a good alternative for dealing with temporal data, particularly related to mortality with regressors of environmental temperature and pollution.

Disjoint and Functional Principal Component Analysis for Infected Cases and Deaths Due to COVID-19 in South American Countries with Sensor-Related Data.

In this paper, we group South American countries based on the number of infected cases and deaths due to COVID-19. The countries considered are: Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Peru, Paraguay, Uruguay, and Venezuela. The data used are collected from a database of Johns Hopkins University, an institution that is dedicated to sensing and monitoring the evolution of the COVID-19 pandemic. A statistical analysis, based on principal components with modern and recent techniques, is conducted. Initially, utilizing the correlation matrix, standard components and varimax rotations are calculated. Then, by using disjoint components and functional components, the countries are grouped. An algorithm that allows us to keep the principal component analysis updated with a sensor in the data warehouse is designed. As reported in the conclusions, this grouping changes depending on the number of components considered, the type of principal component (standard, disjoint or functional) and the variable to be considered (infected cases or deaths). The results obtained are compared to the k-means technique. The COVID-19 cases and their deaths vary in the different countries due to diverse reasons, as reported in the conclusions.

Discrimination of soils managed with different sources of fertilization and plant species in organic and conventional farming through near-infrared spectroscopy and chemometrics.

BACKGROUND: The combination of near-infrared (NIR) spectroscopy and chemometrics can be used to group or discriminate soils based on spectral response. In this study, we conducted discrimination and classification analyses on soils managed with different sources of fertilization and plant species grown in organic and conventional farming systems. RESULTS: Principal component analysis explained 96% (PC1) and 3% (PC2) of the data variability and separated the soil samples of organic and conventional management systems. The wavenumbers that contributed most to the separation of the management systems were in the range of 3600 and 7300 cm-1 , especially the absorption peaks of 3700 and 4600 cm-1 (characteristic of CH and NH combinations), and 5200 and 7000 cm-1 (typical of OH combinations). Machine learning analysis using k-nearest neighbor and random forest algorithms was efficient in classifying soil samples according to management system with an accuracy of 97.8% and can therefore be used for future classification studies. CONCLUSION: Based on the results, we strongly recommend the use of NIR spectroscopy associated with chemometrics for discriminating soils grown with Malus domestica, Musa spp., Oryza sativa and Solanum tuberosum L. under organic and conventional management systems through spectral response. © 2021 Society of Chemical Industry.

Strategy for the Analysis and Visualization of Electronic Medical Record Data for Public Hospitals in the City of Buenos Aires.

Through the development of a dashboard with participative methodology we present a centralized strategy to analyze and visualize EMRs data for the management of 15 public hospitals from Buenos Aires City. This approach could constitute an efficient option for public health systems from developing countries.

On a new type of Birnbaum-Saunders models and its inference and application to fatigue data.

The Birnbaum-Saunders distribution is a widely studied model with diverse applications. Its origins are in the modeling of lifetimes associated with material fatigue. By using a motivating example, we show that, even when lifetime data related to fatigue are modeled, the Birnbaum-Saunders distribution can be unsuitable to fit these data in the distribution tails. Based on the nice properties of the Birnbaum-Saunders model, in this work, we use a modified skew-normal distribution to construct such a model. This allows us to obtain flexibility in skewness and kurtosis, which is controlled by a shape parameter. We provide a mathematical characterization of this new type of Birnbaum-Saunders distribution and then its statistical characterization is derived by using the maximum-likelihood method, including the associated information matrices. In order to improve the inferential performance, we correct the bias of the corresponding estimators, which is supported by a simulation study. To conclude our investigation, we retake the motivating example based on fatigue life data to show the good agreement between the new type of Birnbaum-Saunders distribution proposed in this work and the data, reporting its potential applications.

Migración sur-sur y desigualdad: alteraciones en la incorporación laboral de migrantes peruanos en la Ciudad de Córdoba, Argentina, 2001-2010 / South-South migration and inequality: alterations in the labor incorporation of peruvian migrants in the City of Córdoba, Argentina, 2001-2010

Resumen Objetivo: analizar la incorporación laboral de los migrantes peruanos en la ciudad de Córdoba, Argentina, en el periodo 2001-2010. Métodos: Se realiza análisis estadístico descriptivo en la primera fase y análisis de correspondencias múltiples en la segunda fase (ACM), ambos en perspectiva comparada con la población nativa. Resultados: los hombres aumentan la participación en la industria, tanto los nativos como los migrantes. Sin embargo, en mayor magnitud para los hombres peruanos. Las mujeres nativas ven poco alterada su estructura ocupacional en el periodo. Para las mujeres nacidas en Perú el movimiento hacia el sector de la industria también se aprecia. Sin embargo, el rasgo más destacable para este grupo es la desconcentración de la categoría más frecuente: el trabajo doméstico, en un proceso que va en dirección a diversificar el espectro de ocupaciones. Conclusiones: en relación a los migrantes peruanos, el clivaje de género presenta estabilidad como un mecanismo que explica las inserciones diferenciales, donde las mujeres persisten en ocupaciones específicas en el periodo considerado. Esto apoya la hipótesis de una incorporación segmentada para las mujeres. Sin embargo, también se observa una variación, ya que aunque la categoría más frecuente sea el trabajo doméstico en ambos momentos censales, la menor proporción de ellas allí empleadas en el 2010, indica que otras ocupaciones adquieren relevancia. En el caso de los hombres el principal rasgo es el trasvase hacia la industria.

Abstract Objective: to analyze the labor incorporation of Peruvian migrants in the city of Córdoba, Argentina, in the period 2001-2010. Methods: We use descriptive statistical analysis in the first step and analysis of multiple correspondences in the second step (MCA), both in comparative perspective with the native population. Results: men increase participation in the industry, both natives and migrants. However, the magnitude is greater for Peruvian men. For native women, the change in the occupational structure is small. For women born in Peru the movement towards the industry sector is also appreciated. However, the most remarkable feature for this group is the scattering of the most frequent category: domestic work, in a process that goes in the direction of diversifying the spectrum of occupations. Conclusions: in relation to Peruvian migrants, gender cleavage presents stability as a mechanism that explains differential incorporation, where women persist in specific occupations in the period considered. This supports the hypothesis of a segmented incorporation for women. However, there is also a variation, since although the most frequent category is domestic work in both census periods, the lower proportion of them employed there in 2010 indicates that other occupations acquire relevance. In the case of men, the main feature is the transfer to industry.

Data supporting the role of enzymes and polysaccharides during cassava postharvest physiological deterioration.

This data article is referred to the research article entitled The role of ascorbate peroxidase, guaiacol peroxidase, and polysaccharides in cassava (Manihot esculenta Crantz) roots under postharvest physiological deterioration by Uarrota et al. (2015). Food Chemistry 197, Part A, 737-746. The stress duo to PPD of cassava roots leads to the formation of ROS which are extremely harmful and accelerates cassava spoiling. To prevent or alleviate injuries from ROS, plants have evolved antioxidant systems that include non-enzymatic and enzymatic defence systems such as ascorbate peroxidase, guaiacol peroxidase and polysaccharides. In this data article can be found a dataset called "newdata", in RData format, with 60 observations and 06 variables. The first 02 variables (Samples and Cultivars) and the last 04, spectrophotometric data of ascorbate peroxidase, guaiacol peroxidase, tocopherol, total proteins and arcsined data of cassava PPD scoring. For further interpretation and analysis in R software, a report is also provided. Means of all variables and standard deviations are also provided in the Supplementary tables ("data.long3.RData, data.long4.RData and meansEnzymes.RData"), raw data of PPD scoring without transformation (PPDmeans.RData) and days of storage (days.RData) are also provided for data analysis reproducibility in R software.

Avaliação de medidas morfoestruturais em equinos da raça quarto de milha utilizando análises de imagens / Evaluation morphostructural measures in horses of the Quarter horse Breed using image analysis

Objetivou-se avaliar técnicas de avaliação morfométrica por análise de imagem em equinos Quartode Milha, a fim de estimar sua viabilidade na rotina da equinocultura brasileira. Foram avaliados 18 animais adultos de ambos os sexos da raça Quarto de Milha. Foram utilizadas três técnicas diferentes: avaliação morfométrica tradicional, avaliação morfométrica por análise de imagens através de software (ImageJ®) sem adesivos reflexivos e avaliação morfométrica por análise de imagens através de software (ImageJ®) com adesivos reflexivos. As medidas corporais foram obtidas foram altura de cernelha (AC), altura de garupa (AG), comprimento corporal (CC), comprimento do pescoço até a cernelha (CPC), comprimento do pescoço até a escápula (CPE), comprimento dorso-lombar (CL), comprimento de garupa (CG), comprimento torácico (CT), comprimento de escápula (ESC), comprimento de úmero (UME), comprimento de rádio/ulna (R/U), comprimento de metacarpo (ME). Para comparação das metodologias foram utilizados o teste de Dunnet a 5% de probabilidade GLM, a correlação entre as metodologias foi avaliada pelo procedimento CORR (StatisticalAnalysis System, versão 9.3), bem como sua acurácia e precisão e análises por variáveis canônicas e deagrupamento pelos métodos de otimização de Tocher. Medidas morfométricas relacionadas com a altura doanimal não diferiram (P > 0,05) entre as metodologias avaliadas. Os dados referentes à acurácia e precisão da avaliação morfométrica por imagens apresentaram um elevado grau de proximidade com o observado pela técnica tradicional. O software ImageJ® pode ser utilizado como técnica alternativa de avaliação morfométrica de equinos da raça Quarto-de-milha

Objective was to evaluate morphometric evaluation techniques by image analysis in horses Quarter Horse breed in order to assess its feasibility in routine Brazilian Equine. We evaluating 18 adult animals of both sexes of bred Quarter Horse. Three different techniques were used: traditional morphometric analysis, morphometric evaluation by image analysis without reflexives adhesives (software ImageJ®) and morphometric evaluation by image analysis with reflexives adhesives (software ImageJ®). Evaluations of body measurements were the withers height (HW), rump height (RH), body length (BL), neck to the withers length (NWL), neck toscapula length (NSL), dorsolumbar length (DL), rump length (RL), thoracic length (TL), scapula length (SL),humerus length (HL), radio/ulna length (R/U) pastern length (PL). To compare the methodology we used the Dunnett test at 5% of probability using PROC GLM, the correlation between the methodologies was evaluated by the CORR procedure (Statistical Analysis System, version 9.3), as well as their accuracy and precision and analysis by canonical variables and cluster analysis by Torcher method. Morphometric measurements related with the height of the animal showed no statistical differences (P > 0.05) among the evaluation methodology.However the measures BL, NWL, NSL, SL, HL, R/U and PL presented statistical differences between the evaluation methodology. Data referring to accuracy and precision of morphometric evaluation by images presented a large degree of proximity to the observed by the traditional technique. The ImageJ® software can be used as alternative technique of morphometric evaluation of equine Quarter Horse breed

Avaliação de medidas morfoestruturais em equinos da raça quarto de milha utilizando análises de imagens / Evaluation morphostructural measures in horses of the Quarter horse Breed using image analysis

Objetivou-se avaliar técnicas de avaliação morfométrica por análise de imagem em equinos Quartode Milha, a fim de estimar sua viabilidade na rotina da equinocultura brasileira. Foram avaliados 18 animais adultos de ambos os sexos da raça Quarto de Milha. Foram utilizadas três técnicas diferentes: avaliação morfométrica tradicional, avaliação morfométrica por análise de imagens através de software (ImageJ®) sem adesivos reflexivos e avaliação morfométrica por análise de imagens através de software (ImageJ®) com adesivos reflexivos. As medidas corporais foram obtidas foram altura de cernelha (AC), altura de garupa (AG), comprimento corporal (CC), comprimento do pescoço até a cernelha (CPC), comprimento do pescoço até a escápula (CPE), comprimento dorso-lombar (CL), comprimento de garupa (CG), comprimento torácico (CT), comprimento de escápula (ESC), comprimento de úmero (UME), comprimento de rádio/ulna (R/U), comprimento de metacarpo (ME). Para comparação das metodologias foram utilizados o teste de Dunnet a 5% de probabilidade GLM, a correlação entre as metodologias foi avaliada pelo procedimento CORR (StatisticalAnalysis System, versão 9.3), bem como sua acurácia e precisão e análises por variáveis canônicas e deagrupamento pelos métodos de otimização de Tocher. Medidas morfométricas relacionadas com a altura doanimal não diferiram (P > 0,05) entre as metodologias avaliadas. Os dados referentes à acurácia e precisão da avaliação morfométrica por imagens apresentaram um elevado grau de proximidade com o observado pela técnica tradicional. O software ImageJ® pode ser utilizado como técnica alternativa de avaliação morfométrica de equinos da raça Quarto-de-milha(AU)

Objective was to evaluate morphometric evaluation techniques by image analysis in horses Quarter Horse breed in order to assess its feasibility in routine Brazilian Equine. We evaluating 18 adult animals of both sexes of bred Quarter Horse. Three different techniques were used: traditional morphometric analysis, morphometric evaluation by image analysis without reflexives adhesives (software ImageJ®) and morphometric evaluation by image analysis with reflexives adhesives (software ImageJ®). Evaluations of body measurements were the withers height (HW), rump height (RH), body length (BL), neck to the withers length (NWL), neck toscapula length (NSL), dorsolumbar length (DL), rump length (RL), thoracic length (TL), scapula length (SL),humerus length (HL), radio/ulna length (R/U) pastern length (PL). To compare the methodology we used the Dunnett test at 5% of probability using PROC GLM, the correlation between the methodologies was evaluated by the CORR procedure (Statistical Analysis System, version 9.3), as well as their accuracy and precision and analysis by canonical variables and cluster analysis by Torcher method. Morphometric measurements related with the height of the animal showed no statistical differences (P > 0.05) among the evaluation methodology.However the measures BL, NWL, NSL, SL, HL, R/U and PL presented statistical differences between the evaluation methodology. Data referring to accuracy and precision of morphometric evaluation by images presented a large degree of proximity to the observed by the traditional technique. The ImageJ® software can be used as alternative technique of morphometric evaluation of equine Quarter Horse breed(AU)

Uso de métodos estatísticos robustos na análise ambiental / Use of robust statistical methods to analyze environmental data

Dados ambientais frequentemente apresentam valores censurados, perdidos e/ou discrepantes (outliers). Além disto, as amostras devem ser consideradas dependentes por terem componentes espaciais e temporais. Outro fato frequente nestes dados é que dificilmente seguem uma distribuição Normal ou Log-normal. Devido a estas características e outras, técnicas estatísticas convencionais não devem ser utilizadas. O presente trabalho apresenta um estudo de caso do rio das Velhas, Minas Gerais, utilizando métodos estatísticos robustos após o tratamento adequado dos dados. A análise de componentes principais detectou as variáveis que mais contribuem para a degradação da qualidade das águas do rio das Velhas e a visualização espacial dos escores mostrou onde esta contaminação está mais evidente.

Environmental data often presents censored, lost and/or outlier values. In addition, samples should be considered dependent for having spatial and temporal components. Another fact is that, frequently, these data won't follow a Normal or Log-normal distribution. Because of these and other characteristics, conventional statistical techniques should not be used. This article presents a case study of the Das Velhas river, Minas Gerais, using robust statistical methods after appropriate treatment of the data. The analysis of the main components found the variables that contribute the most for the degradation of water quality in the river, and the spatial visualization of the scores showed where this contamination is most evident.

Estimativas de variância genética aditiva em populações selecionadas e não-selecionadas via simulação Monte Carlo utilizando o software R / Additive genetic variance estimates in selected and unselected populations via Monte Carlo simulation using the R software

Para disponibilizar um sistema de fornecimento de dados que objetivando-se subsidiar pesquisas de Melhoramento Genético Animal direcionadas à comparação de metodologias de avaliação genética, foi avaliado o comportamento da variância genética aditiva de populações selecionadas e não selecionadas, por seis gerações sucessivas, via simulação Monte Carlo. Por meio de um modelo genético aditivo, foram simuladas populações de 40 animais (20 machos e 20 fêmeas), sob seleção e acasalamento aleatório. Da geração zero até a quinta geração notou-se na população selecionada uma redução de 44,4 por cento na variância genética aditiva, devido a um aumento de 11,58 por cento no coeficiente de endogamia. Na população não selecionada a redução da variância genética aditiva foi menor (27,46 por cento) em relação à população selecionada, também devido a aumento de 10,26 por cento no coeficiente de endogamia.

The additive genetic variance in selected and unselected populations was evaluated in six successive generations via Monte Carlo simulation. The aim was to build a data system to help researches compare genetic evaluation methodologies in Animal Breeding. By means of an additive genetic model, populations of 40 individuals (20 males and 20 females) were simulated, under selected and random mating system. From the generation zero until the fifth generation, the selected population showed reduction of 44.4 percent in additive genetic variance due to an increase of 11.58 percent in inbreeding coefficient. In the unselected population the reduction in additive genetic variance was lower (27.46 percent) in relation to the selected population, due to the increasing of 10.26 percent in inbreeding coefficient.