PSS Health: como calcular tamanho de amostra para estimar média, proporção e correlação / PSS Health: how to calculate a sample size to estimate means, proportions, and correlations

A ferramenta PSS Health (Power and Sample Size for Health Researchers) foi desenvolvida com o propósito de facilitar o cálculo do tamanho amostral e do poder de testes de hipóteses para diferentes objetivos de estudo, usando interface amigável e terminologia comum à área da saúde. Este é o primeiro de uma série de artigos que pretendem orientar o usuário na utilização da ferramenta PSS Health para o planejamento de uma pesquisa. Neste artigo, se ensina como utilizar o PSS Health quando o objetivo principal do estudo é estimar uma média, estimar uma proporção (prevalência ou incidência) ou estimar uma correlação. São disponibilizados vídeos demonstrando o uso da ferramenta em cada um dos contextos citados. (AU)

The PSS Health (Power and Sample Size for Health Researchers) tool was developed with the purpose of facilitating the calculation of sample size and power of hypothesis tests for different study objectives, based on a user-friendly interface and common health care terminology. This is the first in a series of articles intending to guide the user in how to use the PSS Health tool for planning a research project. This article teaches how to use PSS Health when the main objective of the study is to estimate means, proportions (prevalence or incidence), or correlations. Videos showing how to use the tool in each of the mentioned contexts are available. (AU)

Power and sample size for health researchers: uma ferramenta para cálculo de tamanho amostral e poder do teste voltado a pesquisadores da área da saúde / Power and sample size for health researchers: a tool for calculating sample size and statistical power designed for health researchers

Nas próximas edições da seção de Bioestatística da revistaClinical & Biomedical Researchuma nova série de artigos será publicada abordando um assunto de grande importância ao planejar uma pesquisa: o tamanho de amostra mínimo necessário para atingir os objetivos do estudo. Nessa série será apresentado como calcular o tamanho de uma amostra usando a ferramenta PSSHealth(Power and Sample Size for Health Researchers), construído em linguagem R por meio do pacote Shiny, para diferentes tipos e objetivos de estudo, direcionado à pesquisadores da área da saúde, utilizando termos e conceitos comumente utilizados nesta área. Além disso, o pacote fornece uma sugestão de texto com as informações consideradas no cálculo, e como devem ser descritas, com a finalidade de minimizar problemas de interpretação por parte dos pesquisadores. Neste primeiro artigo será apresentada essa ferramenta desenvolvida pela Unidade de Bioestatística do Grupo de Pesquisa e Pós-Graduação do Hospital de Clínicas de Porto Alegre, que permite calcular não apenas o tamanho de amostra, mas também o poder de um teste de hipóteses. (AU)

In the next issues ofClinical and Biomedical Research, the Biostatistics section will introduce a new series of articles addressing a very important subject for research planning: the minimum sample size to achieve the aim of a study. This series will show how to calculate sample size using PSS Health (Power and Sample Size for Health Researchers). This tool was built using R language through the Shiny package. It can be used for different types of study and is designed for health researchers by using terms and concepts commonly used in this area. PSS Health also suggests a text with information considered in the calculation to minimize problems of interpretation by the researchers. In this first article, a general overview of PSS Health will be presented. This tool, which was developed by the Research and Graduate Group Biostatistics Unit of the Hospital de Clínicas de Porto Alegre, is useful not only to calculate sample size but also to determine power of a hypothesis test. (AU)

Mathematical Modeling of the Quorum Sensing in Vibrio harveyi / Modelado Matemático de la Detección de Quórum en Vibrio harveyi

Abstract One of the most used bacteria in the Quorum Sensing (QS) experimental works is the Vibrio harveyi, which is used as reporter bacteria to detect the Autoinducers-2 (AI-2) activity of other bacteria. Nevertheless, the description of its QS mechanism by the mathematical modeling is an approach still unexploited. For biological systems, it is necessary to consider the high variability of the experimental data, thus identifiability and parametric reliability analyses must be performed before a model could be used. The following work describes a methodology for parameter fitting and parametric identifiability analysis in a model that describes the dynamics of AI-2 in V. harveyi bacteria. Identifiability analyses showed that all parameters are identifiable, but parametric dependency analyses showed two linearly dependent parameters. According to our results, the model is adequate to describe the AI-2 dynamics in V. harveyi.

Resumen Una de las bacterias más utilizadas en los trabajos experimentales de detección de quorum (QS) es la Vibrio harveyi, que se utiliza como bacteria reportera para detectar la actividad de Autoinductores-2 (AI-2) de otras bacterias. Sin embargo, la descripción de su mecanismo de QS por medio del modelado matemático es un enfoque aún no explotado. En el caso de los sistemas biológicos, es necesario considerar la alta variabilidad de los datos experimentales, por lo que deben realizarse análisis de identificabilidad y fiabilidad paramétrica antes de que un modelo pueda ser usado. El siguiente trabajo describe una metodología para el ajuste de parámetros y el análisis de la identificabilidad paramétrica en un modelo que describe la dinámica de la AI-2 en las bacterias V. harveyi. Los análisis de identificabilidad mostraron que todos los parámetros son identificables, pero los análisis de dependencia paramétrica mostraron dos parámetros linealmente dependientes. De acuerdo con los resultados, el modelo es adecuado para describir la dinámica AI-2 en V. harveyi.

Parameter estimation for sigmoid E(max) models in exposure-response relationship

The purpose of this simulation study is to explore the limitation of the population PK/PD analysis using data from a clinical study and to help to construct an appropriate PK/PD design that enable precise and unbiased estimation of both fixed and random PD parameters in PK/PD analysis under different doses and Hill coefficients. Seven escalating doses of virtual drugs with equal potency and efficacy but with five different Hill coefficients were used in simulations of single and multiple dose scenarios with dense sampling design. A total of 70 scenarios with 100 subjects were simulated and estimated 100 times applying 1-compartment PK model and sigmoid E(max) model. The bias and precision of the parameter estimates in each scenario were assessed using relative bias and relative root mean square error. For the single dose scenarios, most PD parameters of sigmoid E(max) model were accurately and precisely estimated when the C(max) was more than 85% of EC₅₀, except for typical value and inter-individual variability of EC₅₀ which were poorly estimated at low Hill coefficients. For the multiple dose studies, the parameter estimation performance was not good. This simulation study demonstrated the effect of the relative range of sampled concentrations to EC₅₀ and sigmoidicity on the parameter estimation performance using dense sampling design.

Logistic growth models of China pinks, cultivated on seven substrates, as a function of degree days / Modelo logístico de crescimento de cravina de jardim cultivada em sete substratos em função da soma térmica

ABSTRACT: The objective of this study was to characterize the height (H) and leaf number (LN) of China pinks, grown in seven substrates, as a function of degree days, using the logistic growth model. H and LN were measured from 56 plants per substrate, for 392 plants in total. Plants that were grown on substrates formed of 50% soil with 50% rice husk ash (50% S + 50% RH) and 80% rice husk ash with 20% worm castings (80% RH + 20% W) had the longest vegetative growth period (74d), corresponding to 1317.9ºCd. The logistic growth model, adjusted for H, showed differences in the estimation of maximum expected height (α) between the substrates, with values between 10.47cm for 50% S + 50% RH and 35.75cm for Mecplant(r). When α was estimated as LN, variation was also observed between the different substrates, from approximately 30 leaves on plants growing on 50% S + 50% RH to 34 leaves on the plants growing on the substrate formed of 80% RH + 20% W. Growth of China pinks can be characterized using H or LN in the logistic growth model as a function of degree days, being the provided plants adequately fertilized. The best substrates in terms of maximum height and leaf number were 80% soil + 20% worm castings and Mecplant(r). However, users must recalibrate the model with the estimated parameters before applying it to different growing conditions.

RESUMO: O objetivo do estudo foi caracterizar a altura (H) e o número de folhas (NF), pelo modelo logístico, de cravina de jardim cultivada em sete substratos em função da soma térmica. Foram avaliadas a H e o NF de 56 plantas por substrato, totalizando 392 plantas ajustadas. As plantas dos substratos compostos de: 50% de solo e 50% de cinzas de casca de arroz (50% S + 50% CA); e 80% cinzas de casca de arroz e 20% húmus de minhoca (80% CA + 20% H) tiveram o maior ciclo, de 74 dias, e o completaram com soma térmica de 1317,9ºC dia. O modelo logístico ajustado para H apresentou diferenças para a estimativa da altura máxima esperada (α) entre os substratos, com valores de 10,47cm para 50% S + 50% CA e, 35,75cm, para o substrato Mecplant(r). Para o NF, observou-se que α teve menor variação entre os substratos, desde aproximadamente 30 folhas, nas plantas do substrato 50% S + 50% CA até 34 folhas, nas plantas do substrato 80% CA + 20% H. O crescimento de cravina de jardim, a partir das variáveis estudadas, pode ser caracterizado pelo modelo logístico, em função da soma térmica acumulada, quando as plantas estão sem restrições nutricionais. Considerando a altura máxima e o número máximo de folhas, os melhores substratos foram o composto de 80% de solo + 20% húmus de minhoca e o Mecplant(r). Entretanto, os usuários devem testar as calibrações do modelo, com os parâmetros sugeridos, antes de aplicar o modelo para outras condições climáticas.

Applying fuzzy logic to estimate the parameters of the length-weight relationship / O uso da lógica fuzzy para estimar os parâmetros da relação entre peso e comprimento

Abstract We evaluated three mathematical procedures to estimate the parameters of the relationship between weight and length for Cichla monoculus: least squares ordinary regression on log-transformed data, non-linear estimation using raw data and a mix of multivariate analysis and fuzzy logic. Our goal was to find an alternative approach that considers the uncertainties inherent to this biological model. We found that non-linear estimation generated more consistent estimates than least squares regression. Our results also indicate that it is possible to find consistent estimates of the parameters directly from the centers of mass of each cluster. However, the most important result is the intervals obtained with the fuzzy inference system.

Resumo Empregamos três procedimentos matemáticos, regressão com mínimos quadrados ordinários com dados log-transformados, estimação não-linear e uma combinação de análise multivariada e lógica fuzzy para estimar os parâmetros da relação peso × comprimento para Cichla monoculus. Nosso objetivo foi apresentar uma abordagem alternativa que considere as incertezas inerentes ao modelo. Observamos que as estimativas da estimação não-linear foram mais consistentes que as obtidas por regressão linear sobre dados log-transformados. Nossos resultados também mostraram que é possível obter estimativas dos parâmetros diretamente dos centros de máximos formados dos grupos por uma análise de agrupamento k-means. No entanto, os resultados mais importantes foram os intervalos obtidos com o sistema de inferência fuzzy.

Parameter estimation of an artificial respiratory system under mechanical ventilation following a noisy regime

Abstract Introduction: This work concerns the assessment of a novel system for mechanical ventilation and a parameter estimation method in a bench test. The tested system was based on a commercial mechanical ventilator and a personal computer. A computational routine was developed do drive the mechanical ventilator and a parameter estimation method was utilized to estimate positive end-expiratory pressure, resistance and compliance of the artificial respiratory system. Methods The computational routine was responsible for establishing connections between devices and controlling them. Parameters such as tidal volume, respiratory rate and others can be set for standard and noisy ventilation regimes. Ventilation tests were performed directly varying parameters in the system. Readings from a calibrated measuring device were the basis for analysis. Adopting a first-order linear model, the parameters could be estimated and the outcomes statistically analysed. Results Data acquisition was effective in terms of sample frequency and low noise content. After filtering, cycle detection and estimation took place. Statistics of median, mean and standard deviation were calculated, showing consistent matching with adjusted values. Changes in positive end-expiratory pressure statistically imply changes in compliance, but not the opposite. Conclusion The developed system was satisfactory in terms of clinical parameters. Statistics exhibited consistent relations between adjusted and estimated values, besides precision of the measurements. The system is expected to be used in animals, with a view to better understand the benefits of noisy ventilation, by evaluating the estimated parameters and performing cross relations among blood gas, ultrasonography and electrical impedance tomography.

Improved calibration of a solid substrate fermentation model

Background: Calibration of dynamic models in biotechnology is challenging. Kinetic models are usually complex and differential equations are highly coupled involving a large number of parameters. In addition, available measurements are scarce and infrequent, and some key variables are often non-measurable. Therefore, effective optimization and statistical analysis methods are crucial to achieve meaningful results. In this research, we apply a metaheuristic scatter search algorithm to calibrate a solid substrate cultivation model. Results: Even though scatter search has shown to be effective for calibrating difficult nonlinear models, we show here that a posteriori analysis can significantly improve the accuracy and reliability of the estimation. Conclusions: Sensibility and correlation analysis helped us detect reliability problems and provided suggestions to improve the design of future experiments.