A mixed membership model-based measure for subgroup integration in social networks

Social networks analysis often involves quantifying subgroup structure in which tie density is greater among nodes in the same subgroup than between subgroups. One such measure, subgroup insularity or segregation, is the extent that subgroups are separate from each other. We introduce a new measure, γ, which is a parameter from the mixed membership stochastic blockmodel (MMSBM; Airoldi et al., 2008), and differs from many existing measures in that γ does not depend on node membership. We compare this measure to several well-known measures and use simulation studies and real data analysis to provide insight into how this measure can be used in practice.     

When She Earns More Than He Does: A Longitudinal Study of Dual‐Earner Couples

In a random sample of 286 full‐time‐employed dual‐earner couples, we tested 3 competing hypotheses: when wives earn more than their husbands, (a) each partner's marital‐role quality (MRQ) decreases; (b) his MRQ increases, whereas effects on her MRQ are mixed; and (c) relationships vary with gender‐role beliefs (i.e., gender‐role ideology and subjective rewards of salary). We conceptualized salary as a couple‐level predictor with 4 components, 2 time varying and 2 time invariant, and estimated the relationship between 2 time‐varying components and MRQ. Women's MRQ was not significantly related to change in relative earnings. However, among men, the relationship varied by salary rewards.     

A Bayesian method for safety signal detection in ongoing blinded randomised controlled trials

Sponsors have a responsibility to minimise risk to participants in clinical studies through safety monitoring. The FDA Final Rule for IND Safety Reporting requires routine aggregate safety evaluation, including in ongoing blinded studies. We are interested in estimating the probability that the true adverse event rate in the experimental arm exceeds that in the control arm. We developed a Bayesian approach that specifies an informative meta-analytic predictive prior on the event probability in the control arm and an uninformative prior on that in the experimental arm. We combined these priors with a mixture likelihood that considers each patient in the ongoing blinded study may belong to the experimental or control arm. This allowed us to estimate the quantity of interest without unblinding. We evaluated our method by simulation, pairing scenarios that differed only in whether a safety signal was present or missing, and quantifying the ability of our model to discriminate using signal detection theory. Our approach shows benefit. It detects safety signals more reliably with greater sample sizes and for common rather than rare events. Performance does not deteriorate markedly when historical studies exhibit heterogeneous hazards or non-constant hazards. Our method will allow us to monitor safety signals in ongoing blinded studies with the goal of earlier identification and risk mitigation. Our method could be adapted to use informative priors on both arms or predictive covariates where pertinent data exist. We stress that ongoing safety monitoring should involve a multi-disciplinary team where statistical methods are paired with medical judgement.     

Bayesian regression analysis of data with censored initiating and terminating times: applications to aids

Data with censored initiating and terminating times arises quite frequently in acquired immunodeficiency syndrome (AIDS) epidemiologic studies. Analysis of such data involves a complicated bivariate likelihood, which is difficult to deal with computationally. Bayesian analysis, op the other hand, presents added complexities that have yet to be resolved. By exploiting the simple form of a complete data likelihood and utilizing the power of a Markov Chain Monte Carlo (MCMC) algorithm, this paper presents a methodology for fitting Bayesian regression models to such data. The proposed methods extend the work of Sinha (1997), who considered non-parametric Bayesian analysis of this type of data. The methodology is illustiated with an application to a cohort of HIV infected hemophiliac patients.     

Bayesian quantile inference

The paper proposes a Bayesian interpretation of quantile regression that is shown to be equivalent to scale mixtures of normals leading to a skewed Laplace distribution. This representation of the model facilitates Bayesian analysis by means of Gibbs sampling with data augmentation, and nests regression in the L₁ norm as a special case. The new methods are applied to an analysis of the patents - R&D relationship for U.S. firms and unit root inference for the dollar-deutschemark exchange rate.     

Implementation of a robust bayesian method

In this work we study robustness in Bayesian models through a generalization of the Normal distribution. We show new appropriate techniques in order to deal with this distribution in Bayesian inference. Then we propose two approaches to decide, in some applications, if we should replace the usual Normal model by this generalization. First, we pose this dilemma as a model rejection problem, using diagnostic measures. In the second approach we evaluate the model's predictive efficiency. We illustrate those perspectives with a simulation study, a non linear model and a longitudinal data model.     

Bayesian meta-analysis using skewed elliptical distributions

Meta-analysis refers to a quantitative method for combining results from independent studies in order to draw overall conclusions. We consider hierarchical models including selection models under a skewed heavy tailed error distribution proposed originally by Chen, Dey, and Shao [M. H. Chen, D. K. Dey, Q. M. Shao, A new skewed link model for dichotomous quantal response data, J. Amer. Statist. Assoc. 94 (1983), pp. 1172–1186.] and Branco and Dey [D. Branco and D.K. Dey, A general class of multivariate skew-elliptical distributions, J. Multivariate Anal. 79, pp. 99–113.]. These rich classes of models combine the information of independent studies, allowing investigation of variability both between and within studies and incorporating weight functions. We constructed a detailed computational scheme under skewed normal and skewed Student's t distribution using the MCMC method. Bayesian model selection was conducted by Bayes factor under a different skewed error. Finally, we illustrated our methodology using a real data example taken from Johnson [M.F. Johnson, Comparative efficacy of Naf and SMFP dentifrices in caries prevention: a meta-analysis overview, J Eur. Organ. Caries Res. 27 (1993), pp. 328–336.].     

The Bayesian approach for highly reliable electro-explosive devices using one-shot device testing

Due to the high reliability and high testing cost of electro-explosive devices, even though an accelerated test is performed, one may observe very few failures or even no failures at all due to censoring. In this paper, we consider modelling the reliability of such devices by an exponential lifetime distribution in which the failure rate is assumed to be a function of some covariates and that the observed data are binary. The Bayesian approach, with three different prior settings, is used to develop inference on the failure rate, lifetime and the reliability under some settings. A Monte Carlo simulation study is carried out to show that this approach is quite useful and suitable for analysing data of the considered form, especially when the failure rates are very small. Finally, illustrative data are analysed using this approach.     

Robust estimation of dropout models using hierarchical likelihood

It is very well known that analyses for missing data depend on untestable assumptions. As a consequence, in such settings, sensitivity analyses are often sensible. One such class of analyses assesses the dependence of conclusions on an explicit missing value mechanism. Inevitably, there is an association between such dependence and the actual (but unknown) distribution of the missing data. In a particular parametric framework for dropout in this paper, an approach is presented that reduces (but never removes) the impact of incorrect assumptions on the form of the association. It is shown how these models can be formulated and fitted relatively simply using hierarchical likelihood. These are applied directly to an example involving mastitis in dairy cattle, and an extensive simulation study is described to show the properties of the methods.     

Analysis of bivariate binary data with possible chances of wrong ascertainment

In familial data, ascertainment correction is often necessary to decipher genetic bases of complex human diseases. This is because families usually are not drawn at random or are not selected according to well-defined rules. While there has been much progress in identifying genes associated with a certain phenotype, little attention has been paid so far for familial studies on exploring common genetic influences on different phenotypes of interest. In this study, we develop a powerful bivariate analytical approach that can be used for a complex situation with paired binary traits. In addition, our model has been framed to accommodate the possibility of imperfect diagnosis as traits may be wrongly observed. Thus, the primary focus is to see whether a particular gene jointly influences both phenotypes. We examine the plausibility of this theory in a sample of families ascertained on the basis of at least one affected individual. We propose a bivariate binary mixed model that provides a novel and flexible way to account for wrong ascertainment in families collected with multiple cases. A hierarchical Bayesian analysis using Markov Chain Monte Carlo (MCMC) method has been carried out to investigate the effect of covariates on the disease status. Results based on simulated data indicate that estimates of the parameters are biased when classification errors and/or ascertainment are ignored.