Bayesian estimation in animal breeding using the Dirichlet process prior for correlated random effects

In the case of the mixed linear model the random effects are usually assumed to be normally distributed in both the Bayesian and classical frameworks. In this paper, the Dirichlet process prior was used to provide nonparametric Bayesian estimates for correlated random effects. This goal was achieved by providing a Gibbs sampler algorithm that allows these correlated random effects to have a nonparametric prior distribution. A sampling based method is illustrated. This method which is employed by transforming the genetic covariance matrix to an identity matrix so that the random effects are uncorrelated, is an extension of the theory and the results of previous researchers. Also by using Gibbs sampling and data augmentation a simulation procedure was derived for estimating the precision parameter M associated with the Dirichlet process prior. All needed conditional posterior distributions are given. To illustrate the application, data from the Elsenburg Dormer sheep stud were analysed. A total of 3325 weaning weight records from the progeny of 101 sires were used.     

Semiparametric Bayes Multiple Testing: Applications to Tumor Data

Summary In National Toxicology Program (NTP) studies, investigators want to assess whether a test agent is carcinogenic overall and specific to certain tumor types, while estimating the dose‐response profiles. Because there are potentially correlations among the tumors, a joint inference is preferred to separate univariate analyses for each tumor type. In this regard, we propose a random effect logistic model with a matrix of coefficients representing log‐odds ratios for the adjacent dose groups for tumors at different sites. We propose appropriate nonparametric priors for these coefficients to characterize the correlations and to allow borrowing of information across different dose groups and tumor types. Global and local hypotheses can be easily evaluated by summarizing the output of a single Monte Carlo Markov chain (MCMC). Two multiple testing procedures are applied for testing local hypotheses based on the posterior probabilities of local alternatives. Simulation studies are conducted and an NTP tumor data set is analyzed illustrating the proposed approach.     

Distinguishing effects on tumor multiplicity and growth rate in chemoprevention experiments

In some types of cancer chemoprevention experiments and short-term carcinogenicity bioassays, the data consist of the number of observed tumors per animal and the times at which these tumors were first detected. In such studies, there is interest in distinguishing between treatment effects on the number of tumors induced by a known carcinogen and treatment effects on the tumor growth rate. Since animals may die before all induced tumors reach a detectable size, separation of these effects can be difficult. This paper describes a flexible parametric model for data of this type. Under our model, the tumor detection times are realizations of a delayed Poisson process that is characterized by the age-specific tumor induction rate and a random latency interval between tumor induction and detection. The model accommodates distinct treatment and animal-specific effects on the number of induced tumors (multiplicity) and the time to tumor detection (growth rate). A Gibbs sampler is developed for estimation of the posterior distributions of the parameters. The methods are illustrated through application to data from a breast cancer chemoprevention experiment.