Microarrays measure the abundance of DNA transcripts for thousands of gene sequences, simultaneously facilitating genomic comparisons across tissue types or disease status. These experiments are used to understand fundamental aspects of growth and development and to explore the underlying genetic causes of many diseases. The data from most microarray studies are found in open-access online databases. Bayesian models are ideal for the analysis of microarray data because of their ability to integrate prior information; however, most current Bayesian analyses use empirical or flat priors. We present a Perl script to build an informative prior by mining online databases for similar microarray experiments. Four prior distributions are investigated: a power prior including information from multiple previous experiments, an informative prior using information from one previous experiment, an empirically estimated prior, and a flat prior. The method is illustrated with a two-sample experiment to determine the preferential regulation of genes by tamoxifen in breast cancer cells.

Submitted by (ana.araujo@ufrpe.br) on 2016-05-25T16:16:39Z No. of bitstreams: 1 Cicero Carlos Felix de Oliveira.pdf: 934310 bytes, checksum: 4f4332b0b319f6bf33cdc1d615c36324 (MD5) / Made available in DSpace on 2016-05-25T16:16:39Z (GMT). No. of bitstreams: 1 Cicero Carlos Felix de Oliveira.pdf: 934310 bytes, checksum: 4f4332b0b319f6bf33cdc1d615c36324 (MD5) Previous issue date: 2011-07-08 / This dissertation is being dealt with a discrete distribution based on Bernoulli trials, which is the Negative Binomial distribution. The main objective is to propose a new non-informative prior distribution for the Negative Binomial model, which is being termed as a possible prior distribution Beta(0; 0), which is an improper distribution. This distribution is also known for the Binomial model as Haldane prior, but for the Negative Binomial model there are no studies to date. The study of the behavior of this prior was based on Bayesian and classical contexts. The idea of using a non-informative prior is the desire to make statistical inference based on the minimum of information prior subjective as possible. Well, makes it possible to compare the results of classical inference that uses only sample information, for example, the maximum likelihood estimator. When is compared the Beta(0; 0) distribution with the Bayes-Laplace prior and Jeffreys prior, based on the Bayesian estimators (posterior mean and posterior mode) and the maximum likelihood estimator, note that the possible Beta(0; 0) prior is less informative than the others prior. It is also verified that is prior possible is a limited distribution in parameter space, thus, an important feature for non-informative prior. The main argument shows that the possible Beta(0; 0) prior is adequate, when it is applied in a predictive posterior distribution for Negative Binomial model, leading the a Beta-Negative Binomial distribution (which corresponds the a hypergeometric multiplied by a probability). All observations citas are strengthened by several studies, such as: basic concepts related to Bayesian Inference and concepts of the negative binomial distribution and Beta-Negative Binomial (a mixture of Beta with the negative binomial) distribution. / Nesta dissertação está sendo abordado uma distribuição discreta baseada em ensaios de Bernoulli, que é a distribuição Binomial Negativa. O objetivo principal é prôpor uma nova distribuição a priori não informativa para o modelo Binomial Negativa, que está sendo denominado como uma possível distribuição a priori Beta(0; 0), que é uma distribuição imprópria. Essa distribuição também é conhecida para o modelo Binomial como a priori de Haldane, mas para o modelo Binomial Negativa não há nenhum estudo até o momento. O estudo do comportamento desta a priori foi baseada nos contextos bayesiano e clássico. A ideia da utilização de uma a priori não informativa é o desejo de fazer inferência estatística baseada no mínimo de informação subjetiva a priori quanto seja possível. Assim, torna possível a comparação com os resultados da inferência clássica que só usa informação amostral, como por exemplo, o estimador de máxima verossimilhança. Quando é comparado a distribuição Beta(0; 0) com a priori de Bayes - Laplace e a priori de Jeffreys, baseado-se nos estimadores bayesiano (média a posteriori e moda a posteriori) e no estimador de máxima verossimilhança, nota-se que a possível a priori Beta(0; 0) é menos informativa do que as outras a priori. É verificado também, que esta possível a priori é uma distribuição limitada no espaço paramétrico, sendo assim, uma característica importante para a priori não informativa. O principal argumento mostra que a possível a priori Beta(0; 0) é adequada, quando ela é aplicada numa distribuição a posteriori preditiva para modelo Binomial Negativa, levando a uma distribuição Beta Binomial Negativa (que corresponde a uma hipergeométrica multiplicada por uma probabilidade). Todas as observações citadas são fortalecidas por alguns estudos feitos, tais como: conceitos básicos associados à Inferência Bayesiana e conceitos das distribuições Binomial Negativa e Beta Binomial Negativa (que uma mistura da Beta com a Binomial Negativa).

<p><strong>ABSTRACT</strong></p> <p><strong>Background and Objectives</strong>:<strong> </strong>Informed health care decision making depends on the available evidence base. Where the available evidence comes from different sources methods are required that can synthesise all of the evidence. The synthesis of different types of evidence poses various methodological challenges. The objective of this thesis is to investigate the use of Bayesian methods for combining evidence on effects from randomised and non-randomised studies and additional evidence from the literature with patient level trial data. <strong> </strong></p> <p><strong>Methods</strong>: Using a Bayesian three-level hierarchical model an approach was proposed to combine evidence from randomised and non-randomised studies while adjusting for potential imbalances in patient covariates. The proposed approach was compared to four other Bayesian methods using a case study of endovascular versus open surgical repair for the treatment of abdominal aortic aneurysms. In order to assess the performance of the proposed approach beyond this single applied example a simulation study was conducted. The simulation study examined a series of Bayesian approaches under a variety of scenarios. The subsequent research focussed on the use of informative prior distributions to integrate additional evidence with patient level data in a Bayesian cost-effectiveness analysis comparing endovascular and open surgical repair in terms of incremental costs and life years gained.</p> <p><strong>Results and Conclusions</strong>: The shift in the estimated odds ratios towards those of the more balanced randomised studies, observed in the case study, suggested that the proposed Bayesian approach was capable of adjusting for imbalances. These results were reinforced in the simulation study. The impact of the informative priors in terms of increasing estimated mean life years in the control group, demonstrated the potential importance of incorporating all available evidence in the context of an economic evaluation. In addressing these issues this research contributes to comprehensive evidence based decision making in health care.</p> / Doctor of Philosophy (PhD)