What makes the results differ for fixed-effects models vis-à-vis random effects models? The Cochrane Collaboration's website indicated that two models can produce different results for a meta analysis. I would like to understand this point better.
The incorporation, or lack, of a measure of statistical heterogeneity (Tau2) between the data sets into the pooled effect estimate is the main difference between the two models. If there is minimal (to almost no) between data statistical heterogeneity, then the results are almost identical. On other hand, the more heterogeneity, the wider the confidence intervals in a random-effects model. In most circumstances, it has been shown that a random-effects model is more conservative and gives wider confidence intervals than a fixed effect model. There have been examples when this is not the case. In addition, in a random-effects model, the amount of weight given to each data set is not only based on variance and studies with relatively larger variance (e.g. smaller studies) get more weight than they would in a fixed-effect model. This is also called the 'small study bias' with a random-effects model.
It really helps to visualize these concepts and there are lots of slides online from systematic review courses. Also, a PubMed search will reveal a lot of intro meta-analysis papers that describe these concepts in more detail. I will update this post once I have a chance to search for them.
Related threads on Cross Validated that may be helpful: