How to use likelihood ratios to interpret evidence from randomized trials

Area of Science:

• Biostatistics
• Clinical Trials
• Statistical Inference

Background:

• Assessing evidence from clinical trials often involves comparing a new treatment's effectiveness against a null hypothesis.
• Traditional methods can be complex to interpret for non-statisticians.

Purpose of the Study:

• To present a simple method for deriving and interpreting likelihood ratios from published clinical trial reports.
• To demonstrate how likelihood ratios quantify evidence for competing statistical hypotheses.

Main Methods:

• The likelihood ratio is calculated using the test statistic (z) and the expected value under the alternate hypothesis (A).
• Values for A and z are derived from sample size calculations and observed treatment effects or confidence intervals.
• The logarithm of the likelihood ratio is computed as z·A - A²/2.

Main Results:

• Demonstrated application of likelihood ratios to published trial data, showing examples of strong and moderate evidence for alternate hypotheses.
• Illustrated a case where the likelihood ratio favored the null hypothesis.
• Showcased how likelihood ratios update prior beliefs to posterior beliefs.

Conclusions:

• Likelihood ratios offer a simple, interpretable tool for evaluating evidence in data concerning two competing a priori hypotheses.
• This method enhances the understanding of statistical evidence in clinical research.