### Department of Biostatistics Seminar/Workshop Series

# Likelihood Ratios and Misleading Evidence

## Jeffrey D. Blume, PhD

### Associate Professor and Director Graduate Studies, Department of Biostatistics

Vanderbilt University School of Medicine

### Wednesday, March 11, 1:30-2:30pm, MRBIII Conference Room 1220

### Intended Audience: Persons interested in applied statistics, statistical theory, epidemiology, health services research, clinical trials methodology, statistical computing, statistical graphics, R users or potential users

The Law of Likelihood explains that the strength of statistical evidence in data is measured by likelihood ratios, not p-values or posterior probabilities. I have argued elsewhere that the Law of Likelihood represents a ‘theory of evidence’ and that such a theory is conspicuously absent from modern statistical methodology. But in this talk, I ignore these philosophical arguments and present a pragmatic case for the Law of Likelihood: likelihood ratios are more flexible, more efficient, and more accurate than traditional hypothesis testing methods or Bayesian alternatives.

In particular, I will focus on the frequency of observing misleading evidence, which is naturally bounded and controllable. For example, using a likelihood ratio as a measure of evidence minimizes the overall probability of making an error (either type I or type II), even in situations with multiple endpoints where the type I error is adjusted to avoid inflation. Likelihood ratios also remain seldom misleading even when the study is (statistically) rigged to produce evidence favoring the pet hypothesis over the true hypothesis. I illustrate these theoretical advances in some simple examples and with a real-world example of a study design where the primary endpoint is the time to an event.