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

2021 
Abstract Objective The likelihood ratio is a method for assessing evidence regarding two simple statistical hypotheses. Its interpretation is simple – e.g., 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: the logarithm of the hazard ratio equals A), and that it is not (null hypothesis: the logarithm of the hazard ratio equals 0). The result of the trial is summarised by the test statistic z (i.e., the estimated treatment effect divided by its standard error). The logarithm of the likelihood ratio is given by z∙A – A2/2. The value of A is usually provided in a trial report, and the value of z can be obtained from the estimated treatment effect and its 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.
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