A varying‐coefficient generalized odds rate model with time‐varying exposure: An application to fitness and cardiovascular disease mortality

Varying‐coefficient models have become a common tool to determine whether and how the association between an exposure and an outcome changes over a continuous measure. These models are complicated when the exposure itself is time‐varying and subjected to measurement error. For example, it is well known that longitudinal physical fitness has an impact on cardiovascular disease (CVD) mortality. It is not known, however, how the effect of longitudinal physical fitness on CVD mortality varies with age. In this paper, we propose a varying‐coefficient generalized odds rate model that allows flexible estimation of age‐modified effects of longitudinal physical fitness on CVD mortality. In our model, the longitudinal physical fitness is measured with error and modeled using a mixed‐effects model, and its associated age‐varying coefficient function is represented by cubic B‐splines. An expectation‐maximization algorithm is developed to estimate the parameters in the joint models of longitudinal physical fitness and CVD mortality. A modified pseudoadaptive Gaussian‐Hermite quadrature method is adopted to compute the integrals with respect to random effects involved in the E‐step. The performance of the proposed method is evaluated through extensive simulation studies and is further illustrated with an application to cohort data from the Aerobic Center Longitudinal Study.     

Stochastic risk assessment of water quality using advection dispersion equation and Bayesian approximation: A case study

The influence of various heterogeneous parameters, stochastic uncertain factors, and pollutant particles from the industrial effluents in the water system is investigated using advection dispersion equation (ADE) and the Bayesian approximation. Here, the decay coefficient is decomposed into the exact part and the deviation part. The coefficient is used to find out the errors and deviation in decay during the flow of pollutants. Two Bayesian models are developed to analyze the posterior distributions and to find out the Bayes factor for the stochastic covariance estimation. The Bayesian calibration focused the characteristics of both on mechanistic and statistical approximation. The efficiency and accuracy of the developed models are checked from the results obtained on the basis of the confidence interval. Markov chain Monte Carlo simulation is used to acquire the convergence point of parameters for the posterior estimation. The stochastic covariance or white noise represents the effect of random factors on the river system. The analysis revealed that the rate of decay is dependent upon the duration and distance traveled by the pollutants. The collaboration of ADE and Bayesian approximation encourage the water-quality management and environmental modeling.     

Prediction analysis for microbiome sequencing data

One goal of human microbiome studies is to relate host traits with human microbiome compositions. The analysis of microbial community sequencing data presents great statistical challenges, especially when the samples have different library sizes and the data are overdispersed with many zeros. To address these challenges, we introduce a new statistical framework, called predictive analysis in metagenomics via inverse regression (PAMIR), to analyze microbiome sequencing data. Within this framework, an inverse regression model is developed for overdispersed microbiota counts given the trait, and then a prediction rule is constructed by taking advantage of the dimension‐reduction structure in the model. An efficient Monte Carlo expectation‐maximization algorithm is proposed for maximum likelihood estimation. The method is further generalized to accommodate other types of covariates. We demonstrate the advantages of PAMIR through simulations and two real data examples.     

How placebo responses are formed: a learning perspective

Despite growing scientific interest in the placebo effect and increasing understanding of neurobiological mechanisms, theoretical conceptualization of the placebo effect remains poorly developed. Substantial mechanistic research on this phenomenon has proceeded with little guidance by any systematic theoretical paradigm. This review seeks to present a theoretical perspective on the formation of placebo responses. We focus on information processing, and argue that different kinds of learning along with individuals' genetic make-up evolved as the proximate cause for triggering behavioural and neural mechanisms that enable the formation of individual expectations and placebo responses. Conceptualizing the placebo effect in terms of learning offers the opportunity for facilitating scientific investigation with a significant impact on medical care.     

Early‐life conditions impact juvenile telomere length,but do not predict later life‐history strategies or fitness in a wild vertebrate

Environmental conditions experienced during early life may have long‐lasting effects on later‐life phenotypes and fitness. Individuals experiencing poor early‐life conditions may suffer subsequent fitness constraints. Alternatively, individuals may use a strategic “Predictive Adaptive Response” (PAR), whereby they respond—in terms of physiology or life‐history strategy—to the conditions experienced in early life to maximize later‐life fitness. Particularly, the Future Lifespan Expectation (FLE) PAR hypothesis predicts that when poor early‐life conditions negatively impact an individual''s physiological state, it will accelerate its reproductive schedule to maximize fitness during its shorter predicted life span. We aimed to measure the impact of early‐life conditions and resulting fitness across individual lifetimes to test predictions of the FLE hypothesis in a wild, long‐lived model species. Using a long‐term individual‐based dataset, we investigated how early‐life conditions are linked with subsequent fitness in an isolated population of the Seychelles warbler Acrocephalus sechellensis. How individuals experience early‐life environmental conditions may vary greatly, so we also tested whether telomere length—shorter telomers are a biomarker of an individual''s exposure to stress—can provide an effective measure of the individual‐specific impact of early‐life conditions. Specifically, under the FLE hypothesis, we would expect shorter telomeres to be associated with accelerated reproduction. Contrary to expectations, shorter juvenile telomere length was not associated with poor early‐life conditions, but instead with better conditions, probably as a result of faster juvenile growth. Furthermore, neither juvenile telomere length, nor other measures of early‐life conditions, were associated with age of first reproduction or the number of offspring produced during early life in either sex. We found no support for the FLE hypothesis. However, for males, poor early‐life body condition was associated with lower first‐year survival and reduced longevity, indicating that poor early‐life conditions pose subsequent fitness constraints. Our results also showed that using juvenile telomere length as a measure of early‐life conditions requires caution, as it is likely to not only reflect environmental stress but also other processes such as growth.     

Back to basics for Bayesian model building in genomic selection

Numerous Bayesian methods of phenotype prediction and genomic breeding value estimation based on multilocus association models have been proposed. Computationally the methods have been based either on Markov chain Monte Carlo or on faster maximum a posteriori estimation. The demand for more accurate and more efficient estimation has led to the rapid emergence of workable methods, unfortunately at the expense of well-defined principles for Bayesian model building. In this article we go back to the basics and build a Bayesian multilocus association model for quantitative and binary traits with carefully defined hierarchical parameterization of Student's t and Laplace priors. In this treatment we consider alternative model structures, using indicator variables and polygenic terms. We make the most of the conjugate analysis, enabled by the hierarchical formulation of the prior densities, by deriving the fully conditional posterior densities of the parameters and using the acquired known distributions in building fast generalized expectation-maximization estimation algorithms.     

On the Estimation of the Mean with Random Number Of Observations. (Comments on a Paper by M. Singh and V. K. Gupta)

In this paper we study the problem of estimating the mean when the number of observations taken on each unit is a random variable. The estimator proposed by M. Singh and V. K. Gupta (1980) is discussed and modified. It is argued, however, that the arithmetic mean is a more appropriate choice of estimator.