Meta-analysis of two studies with random effects?

Abstract

A meta-analysis (MA) combines similar studies resulting in a larger number of subjects to improve the degree of belief in the significance declared. Its major purpose is to increase the number of observations and the associated statistical power, thereby increasing the precision for the estimates of the effect size as it relates to an association or an intervention. As commonly known, there are discrepancies between MAs and the large randomized clinical trials. The conclusions drawn are subject to bias because they are affected by the small size of clinical studies. However, large randomized clinical trials are the most reliable way of obtaining reproducible results; in other words, we expect the same results if we repeated the experiment. On the other hand, large trials do not guarantee that the protocol or the conclusions were appropriate. Although it is intuitive to believe an MA of similar trials is more likely to result in valid conclusions, studies show this is not always the case. By the same argument, adding studies with diverse protocols makes an MA less reliable. Because an MA is a summation, its reliability depends on the combined trials. Inclusion/exclusion criteria, conclusions, reliability of the results, and applicability for the conclusions affect the bias. Hence, we cannot declare that MA represents the final and accurate viewpoint on an area of research. Several statistical methods similar to what have been used to perform analyses on individual subject data have been modified to improve the reliability of MA.