A Bayesian model for cross-study differential gene expression

In this paper we define a hierarchical Bayesian model for microarray expression data collected from several studies and use it to identify genes that show differential expression between two conditions. Key features include shrinkage across both genes and studies, and flexible modeling that allows for interactions between platforms and the estimated effect, as well as concordant and discordant differential expression across studies. We evaluated the performance of our model in a comprehensive fashion, using both artificial data, and a "split-study" validation approach that provides an agnostic assessment of the model's behavior not only under the null hypothesis, but also under a realistic alternative. The simulation results from the artificial data demonstrate the advantages of the Bayesian model. The 1 - AUC values for the Bayesian model are roughly half of the corresponding values for a direct combination of t- and SAM-statistics. Furthermore, the simulations provide guidelines for when the Bayesian model is most likely to be useful. Most noticeably, in small studies the Bayesian model generally outperforms other methods when evaluated by AUC, FDR, and MDR across a range of simulation parameters, and this difference diminishes for larger sample sizes in the individual studies. The split-study validation illustrates appropriate shrinkage of the Bayesian model in the absence of platform-, sample-, and annotation-differences that otherwise complicate experimental data analyses. Finally, we fit our model to four breast cancer studies employing different technologies (cDNA and Affymetrix) to estimate differential expression in estrogen receptor positive tumors versus negative ones. Software and data for reproducing our analysis are publicly available.     

Optical services in the UK: A study of a professional labour market

What is the optimum size of a profession and how should it be determined? If norms about working standards exist and if it can be assumed that its geographical distribution and organisation are optimal, then man-power planning can be reduced to an arithmetical exercise; and the ideal number of places offered on qualifying courses in Colleges and Universities will be determined by pass-rates. However, in most cases, the problems are more complex. A proper concern for professional freedom leads society to tolerate wide variations in professional behaviour and working practice. One aim of policy, whether developed by a Government department or by a professional association or both, may be to promote efficiency, but not at the expense of individual discretion. In such circumstances, working norms do not exist. If, in addition, there is little hard information about the extent of part-time working, actual working practices and so on, it is difficult at first to see how to decide the future size of the profession. The aim of this paper is to illustrate how a simulation exercise combined with a sensitivity analysis was able to contribute to the solution of this problem in the case of one profession, that of opticians. It is hoped that the approach can be adapted to deal with similar problems in other professions who sell their services directly to the public.