A Bayesian method for the synthesis of evidence from qualitative and quantitative reports: the example of...

Bayesian meta-analysis is a frequently cited but very little-used method for synthesizing qualitative and quantitative research findings. The only example published to date used qualitative data to generate an informative prior probability and quantitative data to generate the likelihood. We developed a method to incorporate both qualitative and quantitative evidence in the likelihood in a Bayesian synthesis of evidence about the relationship between regimen complexity and medication adherence.

Data were from 11 qualitative and six quantitative studies. We updated two different non-informative prior distributions with qualitative and quantitative findings to find the posterior distribution for the probabilities that a more complex regimen was associated with lower adherence and that a less complex regimen was associated with greater adherence.

The posterior mode for the qualitative findings regarding more complex regimen and lesser adherence (using the uniform prior with Jeffreys' prior yielding highly similar estimates) was 0.588 (95% credible set limits 0.519, 0.663) and for the quantitative findings was 0.224 (0.203, 0.245); due to non-overlapping credible sets, we did not combine them. The posterior mode for the qualitative findings regarding less complex regimen and greater adherence was 0.288 (0.214, 0.441) and for the quantitative findings was 0.272 (0.118, 0.437); the combined estimate was 0.299 (0.267, 0.334).

The utility of Bayesian methods for synthesizing qualitative and quantitative research findings at the participant level may depend on the nature of the relationship being synthesized and on how well the findings are represented in the individual reports.