Background: Meta-analysis is used to combine evidence from relevant studies in systematic reviews. However, the evidential value of the observed result is not properly evaluated because most statistical analyses are conducted and presented in terms of a frequentist paradigm. This is a fundamentally flawed approach because it attempts to measure evidence using data that was not observed. We have described how the likelihood function (LF) of the data may be used to quantify the relative support (evidence) for all plausible single-group dichotomous hypotheses. We now apply it to measuring and meta-analysis of the evidence for treatment/exposure effects in two-group comparisons.

Objectives: To illustrate how the evidential value of data from comparing two treatment groups using a likelihood approach (LA) can be computed; focusing on analytical inference of rare events using the odds ratio (OR), and meta-analytic evidence synthesis of multiple studies.

Methods & Results: The OR, within and over all studies, and the heterogeneity of the OR between studies are evaluated using a likelihood function for the OR and a log-normal weighting distribution. Point estimation is by computing the most supported value (MSV). Interval estimation is by pre-specifying a minimally acceptable ‘level of support’ and deriving the respective support interval (SI) from the LF. Point hypotheses can be naturally tested using likelihood ratios. We compare the results with the standard frequentist analysis.

Conclusions: The likelihood approach, though computationally challenging, is a better justified approach to evaluating and depicting the evidence from data. The interpretation of the LF provides a relevant meaning to the point and interval estimates as well as a more intuitive way to select the width of the interval. It provides superior intervals, when there are few or no events.