Use of hierarchical models for meta-analysis: experience in the metabolic ward studies of diet and blood cholesterol.
Frost C., Clarke R., Beacon H.
Overviews that combine single effect estimates from published studies generally use a summary statistic approach where the effect of interest is first estimated within each study and then averaged across studies in an appropriately weighted manner. Combining multiple regression coefficients from publications is more problematic, particularly when there are differences in study design and inconsistent reporting of effect sizes and standard errors. This paper describes the use of a hierarchical model in such circumstances. Its use is illustrated in a meta-analysis of the metabolic ward studies that have investigated the effect of changes in intake of various dietary lipids on blood cholesterol. These studies all reported average blood cholesterol for groups of individuals who were studied on one or more diets. Thirty-one studies had randomized cross-over designs, 12 had matched parallel group designs, 12 had non-randomized Latin square designs and 16 had other uncontrolled designs. The hierarchical model allowed the different types of comparison (within-group between-diet, between matched group) that were made in the various studies to each contribute to the overall estimates in an appropriately weighted manner by distinguishing between-study variation, within-study between-matched-group variation and within-group between-diet variation. The hierarchical models do not require consistent specification of effect sizes and standard errors and hence have particular utility in combining results from published studies where the relationships between a dependent variable and two or more predictors have been investigated using heterogeneous methods of analysis.