# How to use likelihood ratios to interpret evidence from randomized trials

## Highlights

The likelihood ratio represents evidence from a study about the relative merits of two hypotheses – typically, in a clinical trial, the hypotheses that the new treatment is effective (at a specific level), vs. that it is not.

The likelihood ratio has an intuitive interpretation: a likelihood ratio of 10 means that the hypothesis of effectiveness is 10 times as strongly supported by the data than the hypothesis of ineffectiveness.

The likelihood ratio is based on the same data summary as the P-value (the test statistic), and can be easily computed when the trial result is shown as a measure of effect (a difference in means or a hazard ratio) accompanied by its confidence interval.

The likelihood ratio allows the combination of prior beliefs with evidence provided in one or several clinical trials, by application of the Bayes’ theorem.

The likelihood ratio may be a practical alternative to statistical tests of significance, which are increasingly criticized.

## Abstract

### 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 – A2/2. 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. LEGGI TUTTO

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