Bayesian Methods for Data Analysis
Tom Louis Part 1 (PowerPoint), Part 2 (PDF).
ABSTRACT
Use of Bayesian designs and analyses in biomedical and many other applications is steadily increasing. The formalism enables flexible designs, combining information from similar information sources and appropriate accounting of relevant uncertainties. More generally, Bayesian structuring provides an effective “procedure-generator” for a broad class of inferential goals. The approach is by no means a panacea because valid development and application places additional obligations on the investigative team and it isn’t always worth the effort. However, the investment can pay big dividends, the cost/benefit relation is increasingly attractive, and consequently statisticians and collaborators are increasingly finding Bayesian approaches worthwhile.
In three, one-hour sessions I will provide an introduction to the Bayesian philosophy and formalism using basic and more advanced examples, and one or two case studies.
- Introduction and examples
Bayesian thinking, Combining evidence and shrinkage, Diagnostic testing, Binomial confidence intervals, Bayesian Design, Historical controls, Multiple Comparisons, . . .
- Ranking SNPs using Trend Tests that Accommodate Uncertain Genotyping
Accommodating Uncertainty: High-throughput single nucleotide polymorphism (SNP) arrays provide estimates of genotypes for up to several million loci. Most genotype estimates are very accurate, but genotyping errors do occur and can influence Z-scores for testing the hypothesis of no association, related p-values and ranks. Some SNPs are harder to call than others due to probe properties and other technical/biological factors; uncertainties can be associated with features of interest. SNP- and case-specific genotype posterior probabilities are available, but they are typically not used or used only informally, for example by setting aside the most uncertain calls. I’ll demonstrate that compared to picking a single genotype, possibly setting aside difficult calls, Bayesian accommodation of genotype uncertainty can substantially increase statistical information for detecting a true association and for ranking SNPs, whether the ranking be frequentist or optimal Bayes.
Optimal Bayesian Ranking: Neither ranks based on hypothesis test Z-scores nor those based on parameter estimates directly address the ranking goal and Bayesian structuring produces substantial improvements. I will outline the approach and provide examples of the benefits.
- Bayesian Monitoring of Clinical Trials and Adaptive Design
Bayesian monitoring of clinical trials has been used only infrequently because a broad community holding many different a priori opinions, must be convinced by the study. However, use of adaptive designs based on the Bayesian formalism is increasing in importance. I’ll outline the issues, present after-the-fact monitoring of a clinical trial on the prevention of Toxoplasmosis in HIV/AIDS patients, and present an adaptive design for a clinical trial of treating post-herpetic neuralgia.
