Traditional Bayes: Diagnostic Testing, Genetic Data Analyses, Bayes and Drug Trials

Abstract

In clinical research where the base rate for a disease is very low and the diagnostic test is far from perfect, there will be a pretty high probability of a positive result that is false positive. Traditional Bayesian statistics uses the ratios of posterior and prior test odds, where the odds is again the ratio of patients being true positive (having some disease) and that of being true negative (having none disease). The methodology has been traditionally used for three main purposes:

• 1. diagnostic testing,

• 2. genetic data analyses,

• 3. finding the probability in drug trials that a new drug will really work.

The current chapter will review the three purposes. We will give examples, including examples of populations with

• rare diseases,

• more common,

• common,

• very common like a genetic disease with 50% gene carrier ship,

• very common with 75% prevalence.

Also examples will be given of Bayesian statistics applied for genetic data analysis, and for analyzing drug trials with type I and type II errors assessed in the form of Bayesian prior probability estimates.