RESUMO
Copula models have become increasingly popular for modelling the dependence structure in multivariate survival data. The two-parameter Archimedean family of Power Variance Function (PVF) copulas includes the Clayton, Positive Stable (Gumbel) and Inverse Gaussian copulas as special or limiting cases, thus offers a unified approach to fitting these important copulas. Two-stage frequentist procedures for estimating the marginal distributions and the PVF copula have been suggested by Andersen (Lifetime Data Anal 11:333-350, 2005), Massonnet et al. (J Stat Plann Inference 139(11):3865-3877, 2009) and Prenen et al. (J R Stat Soc Ser B 79(2):483-505, 2017) which first estimate the marginal distributions and conditional on these in a second step to estimate the PVF copula parameters. Here we explore an one-stage Bayesian approach that simultaneously estimates the marginal and the PVF copula parameters. For the marginal distributions, we consider both parametric as well as semiparametric models. We propose a new method to simulate uniform pairs with PVF dependence structure based on conditional sampling for copulas and on numerical approximation to solve a target equation. In a simulation study, small sample properties of the Bayesian estimators are explored. We illustrate the usefulness of the methodology using data on times to appendectomy for adult twins in the Australian NH&MRC Twin registry. Parameters of the marginal distributions and the PVF copula are simultaneously estimated in a parametric as well as a semiparametric approach where the marginal distributions are modelled using Weibull and piecewise exponential distributions, respectively.
Assuntos
Teorema de Bayes , Análise de Sobrevida , Algoritmos , Austrália , Interpretação Estatística de Dados , Modelos Estatísticos , Análise MultivariadaRESUMO
Background Molecular mechanisms of plant-pathogen interactions have been studied thoroughly but much about them is still unknown. A better understanding of these mechanisms and the detection of new resistance genes can improve crop production and food supply. Extracting this knowledge from available genomic data is a challenging task. Results Here, we evaluate the usefulness of clustering, data-mining and regression to identify potential new resistance genes. Three types of analyses were conducted separately over two conditions, tomatoes inoculated with Phytophthora infestans and not inoculated tomatoes. Predictions for 10 new resistance genes obtained by all applied methods were selected as being the most reliable and are therefore reported as potential resistance genes. Conclusion Application of different statistical analyses to detect potential resistance genes reliably has shown to conduct interesting results that improve knowledge on molecular mechanisms of plant resistance to pathogens.
Assuntos
Doenças das Plantas/genética , Genes de Plantas , Solanum lycopersicum/genética , Resistência à Doença/genética , Expressão Gênica , Funções Verossimilhança , Classificação , Phytophthora infestans , Mineração de Dados , Produção AgrícolaRESUMO
Publicly available genomic data are a great source of biological knowledge that can be extracted when appropriate data analysis is used. Predicting the biological function of genes is of interest to understand molecular mechanisms of virulence and resistance in pathogens and hosts and is important for drug discovery and disease control. This is commonly done by searching for similar gene expression behavior. Here, we used publicly available Streptococcus pyogenes microarray data obtained during primate infection to identify genes that have a potential influence on virulence and Phytophtora infestance inoculated tomato microarray data to identify genes potentially implicated in resistance processes. This approach goes beyond co-expression analysis. We employed a quasi-likelihood model separated by primate gender/inoculation condition to model median gene expression of known virulence/resistance factors. Based on this model, an influence analysis considering time course measurement was performed to detect genes with atypical expression. This procedure allowed for the detection of genes potentially implicated in the infection process. Finally, we discuss the biological meaning of these results, showing that influence analysis is an efficient and useful alternative for functional gene prediction.
Assuntos
Perfilação da Expressão Gênica , Solanum lycopersicum/genética , Infecções Estreptocócicas/genética , Streptococcus pyogenes/patogenicidade , Algoritmos , Animais , Biologia Computacional/métodos , Feminino , Genômica , Funções Verossimilhança , Solanum lycopersicum/imunologia , Solanum lycopersicum/microbiologia , Masculino , Doenças das Plantas/genética , Doenças das Plantas/imunologia , Doenças das Plantas/microbiologia , Primatas , Infecções Estreptocócicas/imunologia , Infecções Estreptocócicas/microbiologia , Streptococcus pyogenes/genética , Streptococcus pyogenes/imunologia , Fatores de Virulência/genéticaRESUMO
Copula models have become increasingly popular for modeling multivariate survival data. In this paper we review some of the recent work that has been appeared for copula model for bivariate survival data and propose a Bayesian modeling. Our approach is very flexible with respect to the choice of marginal distributions and, depending on the copula model employed, it is possible to have a class of variation for the dependence parameter. We compare some of the copula models using a descriptive diagnostic method and three popular Bayesian model selection criteria. Our methodology is illustrated with the Diabetic Retinopathy Study (1976).