A Bayesian Approach to the Estimation of Variance Components for the Unbalanced One-Way Random Model

Bayesian Analysis of ANOVA and Mixed Models on the Log-Transformed Response Variable

The analysis of variance, and mixed models in general, are popular tools for analyzing experimental data in psychology. Bayesian inference for these models is gaining popularity as it allows to easily handle complex experimental designs and data dependence structures. When working on the log of the response variable, the use of standard priors for the variance parameters can create inferential problems and namely the non-existence of posterior moments of parameters and predictive distributions in the original scale of the data. The use of the generalized inverse Gaussian distributions with a careful choice of the hyper-parameters is proposed as a general purpose option for priors on variance parameters. Theoretical and simulations results motivate the proposal. A software package that implements the analysis is also discussed. As the log-transformation of the response variable is often applied when modelling response times, an empirical data analysis in this field is reported.

Affine-transformation invariant clustering models

We develop a cluster process which is invariant with respect to unknown affine transformations of the feature space without knowing the number of clusters in advance. Specifically, our proposed method can identify clusters invariant under (I) orthogonal transformations, (II) scaling-coordinate orthogonal transformations, and (III) arbitrary nonsingular linear transformations corresponding to models I, II, and III, respectively and represent clusters with the proposed heatmap of the similarity matrix. The proposed Metropolis-Hasting algorithm leads to an irreducible and aperiodic Markov chain, which is also efficient at identifying clusters reasonably well for various applications. Both the synthetic and real data examples show that the proposed method could be widely applied in many fields, especially for finding the number of clusters and identifying clusters of samples of interest in aerial photography and genomic data.

Expediting Clinical and Translational Research via Bayesian Instrument Development

Developing valid and reliable instruments is crucial but costly and time-consuming in health care research and evaluation. The Food and Drug Administration and the National Institutes of Health have set up guidelines for developing patient-reported outcome instruments. However, the guidelines are not applicable to cases of small sample sizes. Instead of using an exact estimation procedure to examine psychometric properties, our Bayesian Instrument Development (BID) method integrates expert data and participant data into a single seamless analysis. Using a novel set of priors, we use simulated data to compare BID to classical instrument development procedures and test the stability of BID. To display BID to non-statisticians, a graphical user interface based on R and WINBUGS is developed and demonstrated with data on a small sample of heart failure patients. Costs were saved by eliminating the need for unnecessary continuation of data collection for larger samples as required by the classical instrument development approach.

Bayesian methods to determine performance differences and to quantify variability among centers in multi-center trials: the IHAST trial

Background

To quantify the variability among centers and to identify centers whose performance are potentially outside of normal variability in the primary outcome and to propose a guideline that they are outliers.

Methods

Novel statistical methodology using a Bayesian hierarchical model is used. Bayesian methods for estimation and outlier detection are applied assuming an additive random center effect on the log odds of response: centers are similar but different (exchangeable). The Intraoperative Hypothermia for Aneurysm Surgery Trial (IHAST) is used as an example. Analyses were adjusted for treatment, age, gender, aneurysm location, World Federation of Neurological Surgeons scale, Fisher score and baseline NIH stroke scale scores. Adjustments for differences in center characteristics were also examined. Graphical and numerical summaries of the between-center standard deviation (sd) and variability, as well as the identification of potential outliers are implemented.

Results

In the IHAST, the center-to-center variation in the log odds of favorable outcome at each center is consistent with a normal distribution with posterior sd of 0.538 (95% credible interval: 0.397 to 0.726) after adjusting for the effects of important covariates. Outcome differences among centers show no outlying centers. Four potential outlying centers were identified but did not meet the proposed guideline for declaring them as outlying. Center characteristics (number of subjects enrolled from the center, geographical location, learning over time, nitrous oxide, and temporary clipping use) did not predict outcome, but subject and disease characteristics did.

Conclusions

Bayesian hierarchical methods allow for determination of whether outcomes from a specific center differ from others and whether specific clinical practices predict outcome, even when some centers/subgroups have relatively small sample sizes. In the IHAST no outlying centers were found. The estimated variability between centers was moderately large.

Bayesian methods for cluster randomized trials with continuous responses

Bayesian methods for cluster randomized trials extend the random-effects formulation by allowing both the use of external evidence on parameters and straightforward relaxation of the standard normality and constant variance assumptions. Care is required in specifying prior distributions on variance components, and a number of different options are explored with implied prior distributions for other parameters given in closed form. Markov chain Monte Carlo (MCMC) methods permit the fitting of very general models and the introduction of parameter uncertainty into power calculations. We illustrate these ideas using a published example in which general practices were randomized to intervention or control, and show that different choices of supposedly 'non-informative' prior distributions can have substantial influence on conclusions. We also illustrate the use of forward simulation methods in power calculations with uncertainty on multiple inputs. Bayesian methods have the potential to be very useful but guidance is required as to appropriate strategies for robust analysis. Our current experience leads us to recommend a standard 'non-informative' prior distribution for the within-cluster sampling variance, and an independent prior on the intraclass correlation coefficient (ICC). The latter may exploit background evidence or, as a reference analysis, be a uniform ICC or a 'uniform shrinkage' prior.