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In some meta-analytic data constellations, only the quantity of interest and sample size are available from the published reports. In addition, for some individual studies, this partial information is available for only one of two treatment groups. These are typically excluded from the meta-analysis, whereas in fact, it would be preferable to include such studies. This paper proposes an approach for estimating the parameter of interest when study-specific variance is not included in the study information and potentially only one arm information is presented. The approach we propose allows the full set of individual studies to be analyzed. The joint likelihoods included missing case modeling is used to estimate the mean difference and variance using a fixed effect model. In simulations, we evaluate the performance of the estimators in terms of bias and standard deviation, and compare the results with those from an existing method but using only studies in which information is available in both treatment arms. The coverage probability is also computed to investigate the efficiency of the confidence intervals. Our estimators derived under the homogeneity model show better performance than the existing method when estimating the mean difference and related variance. They are also useful for estimating the mean difference parameter under several heterogeneity scenarios: baseline heterogeneity but no effect heterogeneity, as well as under baseline heterogeneity jointly with effect heterogeneity across studies. We apply our method to a meta-analysis of clinical study data and demonstrate its practicality.

Statistical inference on mixed one- and two-armed studies in meta-analysis without study-specific variance