Estimation of the correlation coefficient using the Bayesian Approach and its applications for epidemiologic research

BACKGROUND: The Bayesian approach is one alternative for estimating correlation coefficients in which knowledge from previous studies is incorporated to improve estimation. The purpose of this paper is to illustrate the utility of the Bayesian approach for estimating correlations using prior knowledge. METHODS: The use of the hyperbolic tangent transformation (ρ = tanh ξ and r = tanh z) enables the investigator to take advantage of the conjugate properties of the normal distribution, which are expressed by combining correlation coefficients from different studies. CONCLUSIONS: One of the strengths of the proposed method is that the calculations are simple but the accuracy is maintained. Like meta-analysis, it can be seen as a method to combine different correlations from different studies

Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves

<p>Abstract</p> <p>Background</p> <p>The results of Randomized Controlled Trials (RCTs) on time-to-event outcomes that are usually reported are median time to events and Cox Hazard Ratio. These do not constitute the sufficient statistics required for meta-analysis or cost-effectiveness analysis, and their use in secondary analyses requires strong assumptions that may not have been adequately tested. In order to enhance the quality of secondary data analyses, we propose a method which derives from the published Kaplan Meier survival curves a close approximation to the original individual patient time-to-event data from which they were generated.</p> <p>Methods</p> <p>We develop an algorithm that maps from digitised curves back to KM data by finding numerical solutions to the inverted KM equations, using where available information on number of events and numbers at risk. The reproducibility and accuracy of survival probabilities, median survival times and hazard ratios based on reconstructed KM data was assessed by comparing published statistics (survival probabilities, medians and hazard ratios) with statistics based on repeated reconstructions by multiple observers.</p> <p>Results</p> <p>The validation exercise established there was no material systematic error and that there was a high degree of reproducibility for all statistics. Accuracy was excellent for survival probabilities and medians, for hazard ratios reasonable accuracy can only be obtained if at least numbers at risk or total number of events are reported.</p> <p>Conclusion</p> <p>The algorithm is a reliable tool for meta-analysis and cost-effectiveness analyses of RCTs reporting time-to-event data. It is recommended that all RCTs should report information on numbers at risk and total number of events alongside KM curves.</p

Desempenho de sistemas consorciados de cenoura e alface avaliados através de métodos uni e multivariados Biological performance of carrot and lettuce intercropping systems as assessed through uni- and multivariate methods

A análise de dados provenientes de experimentos de consorciação geralmente é mais complexa do que as advindas de experimentos em cultivo solteiro. Nesta situação, vários tipos de análises são recomendados, como análise univariada de variância do rendimento das culturas componentes separadamente; dos rendimentos combinados dos sistemas consorciados; da eficiência produtiva por modelos de análise de envoltória de dados (DEA) ou de métodos de análise multivariada dos rendimentos das culturas associadas. Neste trabalho, o objetivo foi avaliar o desempenho biológico de sistemas consorciados de cenoura e alface crespa através de métodos uni e multivariados. Dois experimentos (um consorciado e outro solteiro) foram conduzidos em blocos casualizados completos, com quatro repetições. O experimento consorciado foi conduzido em esquema fatorial 2 x 4 + 2, com os tratamentos provenientes da combinação de duas cultivares de cenoura (Alvorada e Brasília) com quatro cultivares de alface crespas (Lucy Brown, Tainá, Laurel e Verônica) e as duas cvs. de cenoura sem consorciação. Os tratamentos do experimento solteiro consistiram das quatros cvs. de alface testadas. As características avaliadas na alface e cenoura foram massa fresca da parte aérea e rendimento de raízes comerciais, respectivamente. Análises uni e multivariadas de variância foram realizadas nas características avaliadas tanto na alface como na cenoura em função dos fatores tratamentos testados. O método multivariado mostrou-se bastante informativo, em função da maior capacidade discriminante, além da descrição da superioridade relativa dos tratamentos por meio da técnica das variáveis canônicas. Os índices combinados de medida de eficiência dos sistemas consorciados tiveram comportamento similar na discriminação dos melhores sistemas de cultivo consorciados quando avaliados pelo método univariado. Na avaliação de todos os sistemas consorciados, observou-se diferença significativa entre os valores dos índices combinados (produtividade equivalente de cenoura, eficiência produtiva, uso eficiente da terra e escore da variável canônica) apenas quando eles foram avaliados através do escore normalizado da variável canônica, com maior eficiência dos sistemas quando a cenoura foi consorciada com a alface 'Lucy Brown'. Os sistemas consorciados de cenoura 'Alvorada' + alface 'Lucy Brown' ou de cenoura 'Brasília' + alface 'Lucy Brown' são aqueles a serem indicados ao produtor.<br>Intercropping experiments' data analysis is usually a complex task, as compared to those data analysis from sole crops. In these cases are recommended univariate analysis of variance for each crop yield; intercropping combined systems yields; productive efficiency measured with data envelopment analysis (DEA) models; and multivariate analysis. In this work we evaluated the biological performance of carrot and crisphead lettuce intercropping systems through uni- and multivariate methods. Two experiments (one in intercropping and another in sole crop) were carried out in a randomized complete block design with four replications. The intercropping experiment was designed in a 2 x 4 + 2 factorial scheme, with the treatments stemmed from the combination of two carrot cultivars (Alvorada and Brasília) with four crisphead lettuce cultivars (Lucy Brown, Tainá, Laurel and Verônica) plus two carrot cultivars in sole crop. The treatments of the experiment in sole crop consisted of those crisphead lettuce cvs. tested in intercropping experiment. The evaluated traits in lettuce and carrot crops were shoot fresh mass and commercial root yield, respectively. Uni- and multivariate analyses of variance were accomplished on these crop traits in function of the tested treatment-factors. The multivariate approach was more informative as compared to the univariated method, as it allowed better discrimination of the treatment-factors, beyond the description of the treatments' relative superiority through the canonic variable technique. The combined efficiency indices showed similar results in the discrimination of the best intercropping systems as assessed through univariate method. Significant differences were observed among the combined indices (carrot equivalent yield index, productive efficiency for DEA, land equivalent ratio, and score of canonic variable) in all evaluated intercropping systems, when evaluated through normalized score of the canonic variable, with the highest efficiency of the systems as the carrot was intercropped with lettuce 'Lucy Brown'. The intercropping systems of carrot 'Alvorada' + lettuce 'Lucy Brown' or carrot 'Brasília' + lettuce 'Lucy Brown' are those to be indicated to the farmers