Bayesian prediction of spatial count data using generalized linear mixed models

Spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a Bayesian approach and Markov chain Monte Carlo. Informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling. Furthermore, we demonstrate that so-called Langevin-Hastings updates are useful for efficient simulation of the posterior distributions, and we discuss computational issues concerning prediction.     

Modeling continuous auxiliary covariate data in generalized linear mixed models using the kernel smoother

Auxiliary covariate data are often collected in biomedical studies when the primary exposure variable is only assessed on a subset of the study subjects. In this study, we investigate a semiparametric‐estimated likelihood estimation for the generalized linear mixed models (GLMM) in the presence of a continuous auxiliary variable. We use a kernel smoother to handle continuous auxiliary data. The method can be used to deal with missing or mismeasured covariate data problems in a variety of applications when an auxiliary variable is available and cluster sizes are not too small. Simulation study results show that the proposed method performs better than that which ignores the random effects in GLMM and that which only uses data in the validation data set. We illustrate the proposed method with a real data set from a recent environmental epidemiology study on the maternal serum 1,1‐dichloro‐2,2‐bis(p‐chlorophenyl) ethylene level in relationship to preterm births.     

Clustering in linear‐mixed models with a group fused lasso penalty

A method is proposed that aims at identifying clusters of individuals that show similar patterns when observed repeatedly. We consider linear‐mixed models that are widely used for the modeling of longitudinal data. In contrast to the classical assumption of a normal distribution for the random effects a finite mixture of normal distributions is assumed. Typically, the number of mixture components is unknown and has to be chosen, ideally by data driven tools. For this purpose, an EM algorithm‐based approach is considered that uses a penalized normal mixture as random effects distribution. The penalty term shrinks the pairwise distances of cluster centers based on the group lasso and the fused lasso method. The effect is that individuals with similar time trends are merged into the same cluster. The strength of regularization is determined by one penalization parameter. For finding the optimal penalization parameter a new model choice criterion is proposed.     

Hierarchical Bayesian modeling of heterogeneous cluster‐ and subject‐level associations between continuous and binary outcomes in dairy production

The augmentation of categorical outcomes with underlying Gaussian variables in bivariate generalized mixed effects models has facilitated the joint modeling of continuous and binary response variables. These models typically assume that random effects and residual effects (co)variances are homogeneous across all clusters and subjects, respectively. Motivated by conflicting evidence about the association between performance outcomes in dairy production systems, we consider the situation where these (co)variance parameters may themselves be functions of systematic and/or random effects. We present a hierarchical Bayesian extension of bivariate generalized linear models whereby functions of the (co)variance matrices are specified as linear combinations of fixed and random effects following a square‐root‐free Cholesky reparameterization that ensures necessary positive semidefinite constraints. We test the proposed model by simulation and apply it to the analysis of a dairy cattle data set in which the random herd‐level and residual cow‐level effects (co)variances between a continuous production trait and binary reproduction trait are modeled as functions of fixed management effects and random cluster effects.     

Harvest-based Bayesian estimation of sika deer populations using state-space models

We have estimated the number of sika deer, Cervus nippon, in Hokkaido, Japan, with the aim of developing a management program that will reduce the level of agricultural damage caused by these deer. A population index that is defined by the population divided by the population of 1993 is first estimated from the data obtained during a spotlight survey. A generalized linear mixed model (GLMM) with corner point constraints is used in this estimation. We then estimate the population from the index by evaluating the response of index to the known amount of harvest, including hunting. A stage-structured model is used in this harvest-based estimation. It is well-known that estimates of indices suffer from large observation errors when the probability of the observation fluctuates widely; therefore, we apply state-space modeling to the harvest-based estimation to remove the observation errors. We propose the use of Bayesian estimation with uniform prior-distributions as an approximation of the maximum likelihood estimation, without permitting an arbitrary assumption that the parameters fluctuate following prior-distributions. We are able to demonstrate that the harvest-based Bayesian estimation is effective in reducing the observation errors in sika deer populations, but the stage-structured model requires many demographic parameters to be known prior to running the analyses. These parameters cannot be estimated from the observed time-series of the index if there is insufficient data. We then construct a univariate model by simplifying the stage-structured model and show that the simplified model yields estimates that are nearly identical to those obtained from the stage-structured model. This simplification of the model simultaneously clarifies which parameter is important in estimating the population. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The use of mixed logit models to reflect heterogeneity in capture-recapture studies

We examine issues in estimating population size N with capture-recapture models when there is variable catchability among subjects. We focus on a logistic-normal mixed model, for which the logit of the probability of capture is an additive function of a random subject and a fixed sampling occasion parameter. When the probability of capture is small or the degree of heterogeneity is large, the log-likelihood surface is relatively flat and it is difficult to obtain much information about N. We also discuss a latent class model and a log-linear model that account for heterogeneity and show that the log-linear model has greater scope. Models assuming homogeneity provide much narrower intervals for N but are usually highly overly optimistic, the actual coverage probability being much lower than the nominal level.     

Bayesian analysis of censored response data in family‐based genetic association studies

Biomarkers are subject to censoring whenever some measurements are not quantifiable given a laboratory detection limit. Methods for handling censoring have received less attention in genetic epidemiology, and censored data are still often replaced with a fixed value. We compared different strategies for handling a left‐censored continuous biomarker in a family‐based study, where the biomarker is tested for association with a genetic variant, , adjusting for a covariate, X. Allowing different correlations between X and , we compared simple substitution of censored observations with the detection limit followed by a linear mixed effect model (LMM), Bayesian model with noninformative priors, Tobit model with robust standard errors, the multiple imputation (MI) with and without in the imputation followed by a LMM. Our comparison was based on real and simulated data in which 20% and 40% censoring were artificially induced. The complete data were also analyzed with a LMM. In the MICROS study, the Bayesian model gave results closer to those obtained with the complete data. In the simulations, simple substitution was always the most biased method, the Tobit approach gave the least biased estimates at all censoring levels and correlation values, the Bayesian model and both MI approaches gave slightly biased estimates but smaller root mean square errors. On the basis of these results the Bayesian approach is highly recommended for candidate gene studies; however, the computationally simpler Tobit and the MI without are both good options for genome‐wide studies.     

BMA‐Mod: A Bayesian model averaging strategy for determining dose‐response relationships in the presence of model uncertainty

Successful pharmaceutical drug development requires finding correct doses. The issues that conventional dose‐response analyses consider, namely whether responses are related to doses, which doses have responses differing from a control dose response, the functional form of a dose‐response relationship, and the dose(s) to carry forward, do not need to be addressed simultaneously. Determining if a dose‐response relationship exists, regardless of its functional form, and then identifying a range of doses to study further may be a more efficient strategy. This article describes a novel estimation‐focused Bayesian approach (BMA‐Mod) for carrying out the analyses when the actual dose‐response function is unknown. Realizations from Bayesian analyses of linear, generalized linear, and nonlinear regression models that may include random effects and covariates other than dose are optimally combined to produce distributions of important secondary quantities, including test‐control differences, predictive distributions of possible outcomes from future trials, and ranges of doses corresponding to target outcomes. The objective is similar to the objective of the hypothesis‐testing based MCP‐Mod approach, but provides more model and distributional flexibility and does not require testing hypotheses or adjusting for multiple comparisons. A number of examples illustrate the application of the method.     

A genome‐wide association study suggests several novel candidate genes for carcass traits in Chinese Simmental beef cattle

A genome‐wide association study (GWAS) was conducted for two carcass traits in Chinese Simmental beef cattle. The experimental population consisted of 1301 individuals genotyped with the Illumina BovineHD SNP BeadChip (770K). After quality control, 671 990 SNPs and 1217 individuals were retained for the GWAS. The phenotypic traits included carcass weight and bone weight, which were measured after the cattle were slaughtered at 16 to 18 months of age. Three statistical models—a fixed polygene model, a random polygene model and a composite interval mapping polygene model—were used for the GWAS. The genome‐wide significance threshold after Bonferroni correction was 7.44E‐08 (= 0.05/671 990). In this study, we detected eight and seven SNPs significantly associated with carcass weight and bone weight respectively. In total, 11 candidate genes were identified within or close to these significant SNPs. Of these, we found several novel candidate genes, including PBX1, GCNT4, ALDH1A2, LCORL and WDFY3, to be associated with carcass weight and bone weight in Chinese Simmental beef cattle, and their functional roles need to be verified in further studies.