Relative efficiency of using summary versus individual data in random-effects meta-analysis.

Meta-analysis is a statistical methodology for combining information from diverse sources so that a more reliable and efficient conclusion can be reached. It can be conducted by either synthesizing study-level summary statistics or drawing inference from an overarching model for individual participant data (IPD) if available. The latter is often viewed as the "gold standard." For random-effects models, however, it remains not fully understood whether the use of IPD indeed gains efficiency over summary statistics. In this paper, we examine the relative efficiency of the two methods under a general likelihood inference setting. We show theoretically and numerically that summary-statistics-based analysis is at most as efficient as IPD analysis, provided that the random effects follow the Gaussian distribution, and maximum likelihood estimation is used to obtain summary statistics. More specifically, (i) the two methods are equivalent in an asymptotic sense; and (ii) summary-statistics-based inference can incur an appreciable loss of efficiency if the sample sizes are not sufficiently large. Our results are established under the assumption that the between-study heterogeneity parameter remains constant regardless of the sample sizes, which is different from a previous study. Our findings are confirmed by the analyses of simulated data sets and a real-world study of alcohol interventions.