Abstract: In the area of survival analysis the most popular regression model is the Cox proportional hazards (PH) model. Unfortunately, in practice not all data sets satisfy the PH condition and thus the PH model cannot be used. To overcome the problem, the proportional odds (PO) model ( Pettitt 1982 and Bennett 1983a) and the generalized proportional odds (GPO) model ( Dabrowska and Doksum, 1988) were proposed, which can be considered in some sense generalizations of the PH model. However, there are examples indicating that the use of the PO or GPO model is not appropriate. As a consequence, a more general model must be considered. In this paper, a new model, called the proportional generalized odds (PGO) model, is introduced, which covers PO and GPO models as special cases. Estimation of the regression parameters as well as the underlying survival function of the GPO model is discussed. An application of the model to a data set is presented.
Abstract: Affymetrix high-density oligonucleotide microarray makes it possible to simultaneously measure, and thus compare the expression profiles of hundreds of thousands of genes in living cells. Genes differentially expressed in different conditions are very important to both basic and medical research. However, before detecting these differentially expressed genes from a vast number of candidates, it is necessary to normalize the microarray data due to the significant variation caused by non-biological factors. During the last few years, normalization methods based on probe level or probeset level intensities were proposed in the literature. These methods were motivated by different purposes. In this paper, we propose a multivariate normalization method, based on partial least squares regression, aiming to equalize the central tendency, reduce and equalize the variation of the probe level intensities in any probeset across the replicated arrays. By so doing, we hope that one can precisely estimate the gene expression indexes.
Abstract: The association between bivariate binary responses has been studied using Pearson’s correlation coefficient, odds ratio, and tetrachoric correlation coefficient. This paper introduces a copula to model the association. Numerical comparisons between the proposed method and the existing methods are presented. Results show that these methods are comparative. However, the copula method has a clearer interpretation and is easier to extend to bivariate responses with three or more ordinal categories. In addition, a goodness-of-fit test for the selection of a model is performed. Applications of the method on two real data sets are also presented.
Abstract: A new family of copulas generated by a univariate distribution function is introduced, relations between this copula and other well-known ones are discussed. The new copula is applied to model the dependence of two real data sets as illustrations.