Trends in epidemiology in the 21st century: time to adopt Bayesian methods Tendências da epidemiologia no século XXI: é o tempo dos métodos bayesianos Tendencias de la epidemiología del siglo XXI: es tiempo para los métodos bayesianos

2013 marked the 250th anniversary of the presentation of Bayes’ theorem by the philosopher Richard Price. Thomas Bayes was a figure little known in his own time, but in the 20th century the theorem that bears his name became widely used in many fields of research. The Bayes theorem is the basis of the so-called Bayesian methods, an approach to statistical inference that allows studies to incorporate prior knowledge about relevant data characteristics into statistical analysis. Nowadays, Bayesian methods are widely used in many different areas such as astronomy, economics, marketing, genetics, bioinformatics and social sciences. This study observed that a number of authors discussed recent advances in techniques and the advantages of Bayesian methods for the analysis of epidemiological data. This article presents an overview of Bayesian methods, their application to epidemiological research and the main areas of epidemiology which should benefit from the use of Bayesian methods in coming years. Bayes Theorem; Statistics; Probability Theory Resumo O ano de 2013 marca o 250o aniversário da apresentação do teorema de Bayes pelo filósofo Richard Price à Royal Society em 1763. Thomas Bayes foi uma pessoa pouco conhecida em sua época, mas no século XX o teorema que leva o seu nome tornou-se amplamente utilizado em muitas áreas de pesquisa. O teorema de Bayes é a base dos chamados métodos bayesianos, um procedimento de inferência estatística que permite incorporar na análise o conhecimento prévio sobre características relevantes dos dados. Atualmente, os métodos bayesianos são largamente usados em muitas diferentes áreas como astronomia, economia, marketing, genética, bioinformática e ciências sociais. Em adição, é observado na literatura que muitos autores têm discutido os recentes avanços do uso dos métodos bayesianos na análise de dados epidemiológicos. No presente artigo, apresentamos uma visão global dos métodos bayesianos, sua utilidade na pesquisa epidemiológica e os tópicos em epidemiologia em que estes métodos podem ser extensivamente usados nos próximos anos. Teorema de Bayes; Estatística; Teoria da Probabilidade 703 QUESTÕES METODOLÓGICAS METHODOLOGICAL ISSUES http://dx.doi.org/10.1590/0102-311X00144013 Martinez EZ, Achcar JA 704 Cad. Saúde Pública, Rio de Janeiro, 30(4):703-714, abr, 2014 Introduction The first mathematical formulation using the Bayesian method is attributed to Thomas Bayes, a British Presbyterian minister. Very little is known about his personal history. It is believed that he was born around 1701 in Hertfordshire, England and died in 1761 in Tunbridge. Many facts about his life are speculation such as the exact date of his birth and the authorship of a book on Theology entitled Divine Benevolence: or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures, that concerned the motive behind God’s actions in making the world. In 1719, he began his studies of logic and theology at the University of Edinburgh. The only scientific work published during his lifetime was The Doctrine of Fluxions, in 1736, in which he defended the logical foundation of Isaac Newton’s calculus. Two years after his death, his friend Richard Price (1723-1791) presented the Royal Society with a manuscript authored by Thomas Bayes entitled An Essay Towards Solving a Problem in the Doctrine of Chances 1. Price said he found the essay among Bayes’ papers and in his opinion it “has great merit and well deserves to be preserved” 2 (p. 451). The essay offered the first clear solution to a problem of inverse probability, where Bayes described how we can calculate the probability of the occurrence of an event given the known probability of a certain condition. This formula is known as Bayes’ theorem. It is interesting to note that Richard Price believed that Bayes’ theorem was based on theological arguments and it could prove the existence of God 3. In 1748, the Scottish empiricist philosopher David Hume published a book entitled An Enquiry Concerning Human Understanding. In chapter ten of this work entitled Of Miracles, Hume wrote his famous argument against miracles 4. Today, some authors claim that Hume’s statements were based on arguments taken from Bayes’s theorem 5,6,7. Despite these philosophical ideas, Bayes’ essay seemed to have been forgotten until the publication of the book entitled Théorie Analytique des Probabilités by the French mathematician and astronomer Pierre-Simon Laplace, in 1812. It is believed that Laplace was not familiar with the work of Thomas Bayes and he independently developed a more formal version of Bayes’ theorem. Currently, Bayesian ideas are used in many fields of technology and research, such as modern computers which use Bayesian filters to classify emails and detect spam 8. Another example of the modern use of Bayesian ideas is in robots which, based on a Bayesian framework 9 and a Bayes network based system, distinguished terrestrial rocks from meteorites in the first robotic identification of a meteorite in 2000 in the Elephant Moraine in the Antarctic 10. In addition, NASA’s Mars Exploration Rover mission has been using Bayesian classification algorithms to study the physical properties of the surface of Mars 11. Nowadays, Bayesian methods are widely used in many different fields of research, such as astronomy 12, economics and econometrics 13,14, marketing 15, actuarial science 16, psychological research 17, genetics 18,19, evolutionary biology 20, bioinformatics 21, demography 22, social sciences 23, public health 24, drug development 25 and clinical trials 26,27. The use of Bayesian methods in epidemiological studies has been discussed by several authors 28,29,30,31 and Congdon 32 claims that the Bayesian approach is very useful for modeling epidemiological datasets, since they allow the control of possible confounding influences on disease outcomes and the establishment of causal and dose-response relationships. In addition, Dunson 28 showed that the use of Bayesian techniques in epidemiological studies is a powerful mechanism for incorporating information from previous studies and controlling confounding. Appropriate methods for dealing with interactions between variables and confounding effects are essential for epidemiological studies, and in this respect Bayesian methods can be very useful. Bayesian methods represent a totally different way of thinking about research methods where the researcher’s previous knowledge and experience have an important effect on inference and decision-making. The traditional approach to statistical inference is the frequentist (or classical) technique, where results are interpreted in terms of the frequency of occurrence of an event observed in a hypothetically large number of repetitions of the experiment. Frequentist inferences are based only on observational data, while Bayesian inference assumes that prior knowledge can be formally incorporated into the analytical process. We can therefore say that the Bayesian research method is based both on an empirical world represented by the sample data and on human reasoning represented by the accumulated experience of the researcher. In the present article, we present an overview of the Bayesian approach together with a brief description of the Bayesian statistical inference procedure and comparison with the standard frequentist approach. We also discuss the advantages of the Bayesian approach over the traditional research method applied to the analysis of epidemiological data and discuss some areas of epidemiology which should benefit from the use of Bayesian methods in coming years. TIME TO ADOPT BAYESIAN METHODS 705 Cad. Saúde Pública, Rio de Janeiro, 30(4):703-714, abr, 2014 Are we in the Bayesian era? In 1996, David Moore published an article 33 that discussed the possibility of teaching Bayesian inference on a first statistics course for students from different backgrounds. He argued that Bayesian methods were rarely used in practice and teaching them would deprive students of instruction about more common statistical methods. It is possible that this statement was based on limitations caused by the time needed for software and hardware to analyze data using a Bayesian approach. Major advances in software and hardware in the last 20 years have been one of the factors that has led to a sharp increase in the use of Bayesian methods. To obtain an idea of the current use of Bayesian methods in health research, a search was made in PubMed using the keyword “Bayesian”. The annual number of articles is presented graphically in Figure 1 which shows that the first article using the term “Bayesian” indexed in PubMed was published in 1963 34. After this first publication, we observe a very modest increase in the number of articles up to the middle of the 1980s, after which a large increase can be observed. It is important to remember that portable personal computers only became popular in the middle of the 1980s, significantly contributing to the use of Bayesian methods, since the approach is usually depends on computational algorithms. A large increase in the number of published articles using the term Bayesian can be observed toward the end of 20th century. It is possible that this increase was due to the emergence of new software adapted to Bayesian analysis, such as the free software WinBUGS 35. This software uses simulation methods, such as the popular Markov Chain Monte Carlo (MCMC) methods 36, and was possibly the most important computational advances to have popularized the use of Bayesian methodology. The first version of WinBUGS for Windows was made available in 1997 37. Today, OpenBUGS is the open-source version of WinBUGS and can be freely downloaded from the project website (http://www.openbugs.info/w/Downloads). In 2010, 2.56 in every 1,000 articles indexed in PubMed contained the term Bayesian (Figure 1), showing the growing use of Bayesian methods in health research since the publication of Moore’s article 29 and suggesting that Bayesian statistics is actually an important issue to students who are starting their studies to become researchs. The advantages of the use of Bayesian methods in specific fields of knowledge, such as genetics 18, oncology 38 and para-