How to use likelihood ratios to interpret evidence from randomized trials

Objective: The likelihood ratio is a method for assessing evidence regarding two simple statistical hypotheses. Its interpretation is simple - for example, a value of 10 means that the first hypothesis is 10 times as strongly supported by the data as the second. A method is shown for deriving likelihood ratios from published trial reports. Study design: The likelihood ratio compares two hypotheses in light of data: that a new treatment is effective, at a specified level (alternate hypothesis: for instance, the hazard ratio equals 0.7), and that it is not (null hypothesis: the hazard ratio equals 1). The result of the trial is summarised by the test statistic z (ie, the estimated treatment effect divided by its standard error). The expected value of z is 0 under the null hypothesis, and A under the alternate hypothesis. The logarithm of the likelihood ratio is given by z.A - A(2)/2. The values of A and z can be derived from the alternate hypothesis used for sample size computation, and from the observed treatment effect and its standard error or confidence interval. Results: Examples are given of trials that yielded strong or moderate evidence in favor of the alternate hypothesis, and of a trial that favored the null hypothesis. The resulting likelihood ratios are applied to initial beliefs about the hypotheses to obtain posterior beliefs. Conclusions: The likelihood ratio is a simple and easily understandable method for assessing evidence in data about two competing a priori hypotheses. (C) 2021 The Author(s). Published by Elsevier Inc.

Automated summary

The likelihood ratio is a method for comparing evidence between two simple statistical hypotheses, providing a straightforward way to assess the support for each hypothesis based on data.