Efficient integration of aggregate data and individual participant data in one-way mixed models

Often both aggregate data (AD) studies and individual participant data (IPD) studies are available for specific treatments. Combining these two sources of data could improve the overall meta-analytic estimates of treatment effects. Moreover, often for some studies with AD, the associated IPD maybe available, albeit at some extra effort or cost to the analyst. We propose a method for combining treatment effects across trials when the response is from the exponential family of distribution and hence a generalized linear model structure can be used. We consider the case when treatment effects are fixed and common across studies. Using the proposed combination method, we study the relative efficiency of analyzing all IPD studies vs combining various percentages of AD and IPD studies. For many different models, design constraints under which the AD estimators are the IPD estimators, and hence fully efficient, are known. For such models, we advocate a selection procedure that chooses AD studies over IPD studies in a manner that force least departure from design constraints and hence ensures an efficient combined AD and IPD estimator.