Bayesian modeling of time-varying and waning exposure effects

Methodologic issues in the design and analysis of epidemiologic studies of pregnancy outcome

Using epidemiology to elucidate the causes of adverse pregnancy outcomes offers unique opportunities and poses distinctive challenges. The context of pregnancy includes contraception and planning, medical interventions altering the natural history, and the tendency for selective participation in demanding research protocols. Several key pervasive issues are considered in detail: 1) the close temporal proximity of determinants and outcomes, which makes separation of causes and effects difficult and introduces the real possibility of reverse causality; 2) non-random allocation of exposure, often done consciously in response to concerns about having a healthy pregnancy or to the health of the pregnancy itself, making confounding a major concern; 3) heterogeneity of pregnancy outcomes, with endpoints such as pregnancy loss and preterm birth arising through diverse pathways that are not easily identified and if grouped, could diminish the magnitude of observed associations; and 4) racial and ethnic disparities, which pose a public health challenge in the USA and offer a potentially important opportunity for identifying preventable causes of adverse pregnancy outcome. Sophisticated biological and statistical methods are needed to advance epidemiologic research in this area.

Structure detection of semiparametric structural equation models with Bayesian adaptive group lasso

Structural equation models (SEMs) are widely recognized as the most important statistical tool for assessing the interrelationships among latent variables. This study develops a Bayesian adaptive group least absolute shrinkage and selection operator procedure to perform simultaneous model selection and estimation for semiparametric SEMs, wherein the structural equation is formulated using the additive nonparametric functions of observed and latent variables. We propose the use of basis expansions to approximate the unknown functions. By introducing adaptive penalties to the groups of basis expansions, the nonlinear, linear, or non-existent effects of observed and latent variables in the structural equation can be automatically detected. A simulation study demonstrates that the proposed method performs satisfactorily. This paper presents an application of revealing the observed and latent risk factors of diabetic kidney disease.

Finite mixture varying coefficient models for analyzing longitudinal heterogenous data

This paper aims to develop a mixture model to study heterogeneous longitudinal data on the treatment effect of heroin use from a California Civil Addict Program. Each component of the mixture is characterized by a varying coefficient mixed effect model. We use the Bayesian P-splines approach to approximate the varying coefficient functions. We develop Markov chain Monte Carlo algorithms to estimate the smooth functions, unknown parameters, and latent variables in the model. We use modified deviance information criterion to determine the number of components in the mixture. A simulation study demonstrates that the modified deviance information criterion selects the correct number of components and the estimation of unknown quantities is accurate. We apply the proposed model to the heroin treatment study. Furthermore, we identify heterogeneous longitudinal patterns.

Bayesian modeling of multiple episode occurrence and severity with a terminating event

An individual's health condition can affect the frequency and intensity of episodes that can occur repeatedly and that may be related to an event time of interest. For example, bleeding episodes during pregnancy may indicate problems predictive of preterm delivery. Motivated by this application, we propose a joint model for a multiple episode process and an event time. The frequency of occurrence and severity of the episodes are characterized by a latent variable model, which allows an individual's episode intensity to change dynamically over time. This latent episode intensity is then incorporated as a predictor in a discrete time model for the terminating event. Time-varying coefficients are used to distinguish among effects earlier versus later in gestation. Formulating the model within a Bayesian framework, prior distributions are chosen so that conditional posterior distributions are conjugate after data augmentation. Posterior computation proceeds via an efficient Gibbs sampling algorithm. The methods are illustrated using bleeding episode and gestational length data from a pregnancy study.