Scientific article
Open access

How to use likelihood ratios to interpret evidence from randomized trials

ContributorsPerneger, Thomas
Published inJournal of clinical epidemiology, vol. 136, p. 235-242
Publication date2021-08
First online date2021-04-27

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.

  • Clinical trials
  • Confidence interval
  • Evidence
  • Likelihood ratio
  • P-value
  • Statistical inference
  • Data Accuracy
  • Data Interpretation, Statistical
  • Humans
  • Likelihood Functions
  • Models, Statistical
  • Proportional Hazards Models
  • Randomized Controlled Trials as Topic / standards
  • Randomized Controlled Trials as Topic / statistics & numerical data
  • Research Design / standards
  • Research Design / statistics & numerical data
Citation (ISO format)
PERNEGER, Thomas. How to use likelihood ratios to interpret evidence from randomized trials. In: Journal of clinical epidemiology, 2021, vol. 136, p. 235–242. doi: 10.1016/j.jclinepi.2021.04.010
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Article (Published version)
ISSN of the journal0895-4356

Technical informations

Creation10/05/2022 9:10:00 AM
First validation10/05/2022 9:10:00 AM
Update time03/16/2023 10:51:29 AM
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