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# A computational tool for applying bayesian methods in simple situations

Luis Carlos Silva Ayçaguer. Senior researcher of the Escuela Nacional de Salud Pública from La Habana, Cuba; member of the development team of Epidat. Degree in Mathematics from Universidad de La Habana (1976), PhD from Universidad Carolina (Praga, 1982), Doctor of Science from Universidad de Ciencias Médicas (La Habana, 1999), Titular Academic from República de Cuba.

Email: lcsilva@infomed.sld.cu

Soly Santiago Pérez. Technical statistician at Dirección Xeral de Innovación e Xestión da Saúde Pública (General Directorate of Public Health, Spain) from 1996 to present; member of the development team of Epidat. Degree in Mathematics from Universidad de Santiago de Compostela (Spain, 1994). Specialist in Statistics and Operational Research.

In this post, we present a user friendly tool for applying bayesian methods in simple situations. This tool is part of a free distribution software package, Epidat, that is being developed by the Dirección Xeral de Innovación e Xestión da Saúde Pública (Xunta de Galicia, Spain) since the early 90’s. The general purpose of Epidat is to provide an alternative to other statistical packages for performing analysis of data; more specifically, it brings together a broad range of statistical and epidemiological techniques under a common interface. At present, the fourth version of Epidat, developed in Java, is freely available from the web page: http://dxsp.sergas.es; to download the program, registration is required.

As stated above, one of the methods or “modules” included in Epidat 4 is Bayesian analysis, a tool for the application of bayesian techniques to basic problems, like the estimation and comparison of means and proportions. The module provides a simple approach to Bayesian methods, not based on hierarchical models that go beyond the scope of Epidat.

The module of Bayesian analysis is organized into several sub-modules with the following scheme:

• Bayes’ theorem
• Odds ratio
• Proportion
• One population
• Estimation of a proportion
• Assessment of hypotheses
• Two populations
• Estimation of effects
• Assessment of hypotheses
• Mean
• One population
• Estimation of a mean
• Assessment of hypotheses
• Two populations
• Estimation of a difference
• Assessment of hypotheses
• Bayesian approach to conventional tests

The first option of the module can be used to apply Bayes’ theorem. The following three options (Odds ratio, Proportion and Mean) are designed to solve basic inferential problems under Bayesian logic: estimation of odds ratios, proportions and means, as well as differences or ratios of these two last parameters. The punctual estimation is accompanied by the corresponding credibility interval. The techniques available in these options also include methods related to hypothesis testing. Finally, the last sub-module allows the evaluation of conventional tests from a Bayesian perspective.

Some specific options of Bayesian analysis require the use of simulation techniques. Nevertheless, the user does not need to understand the simulation process to use the program and interpret the results correctly. In addition, the module has a user-friendly interface that allows the user to plot the a priori distribution and choose the values of its parameters (see figure above). The output of Bayesian analysis includes both numerical and graphical results, and the graphics can be edited and modified by the user. In addition, the contents of the output window can be saved as a file in several formats: *.epi, *.pdf, *.odf, or *.rtf.

Finally, like all modules of Epidat, Bayesian analysis has a useful help feature which can be accessed on the help menu in pdf format. This facility has been developed with a didactic and critical approach, including statistical basics of the methods, bibliographic references, and examples of the different options.