A generalized BLUE approach for combining location and scale information in a meta-analysis

In systematic reviews and meta-analyses, one is interested in combining information from a variety of sources in order to obtain unbiased and efficient pooled estimates of the mean treatment effect compared to a control group along with the corresponding standard errors and confidence intervals, particularly when the source data is unavailable. However, in many studies the mean and standard deviation are not reported in lieu of other descriptive measures such as the median and quartiles. In this note we provide a theoretically optimal best linear unbiased estimator (BLUE) strategy for combining different types of summary information in order to pool results and estimate the overall treatment effect and the corresponding confidence intervals. Our approach is less biased and much more flexible than past attempts at solving this problem and can accommodate combining a variety of summary information across studies. We show that confidence intervals based on our methods have the appropriate coverage probabilities. Our proposed methods are theoretically justified and verified by simulation studies. The BLUE method is illustrated via a real data application.