Data fusion using weakly aligned sources

We introduce a new data fusion method that utilizes multiple data sources to estimate a smooth, finite-dimensional parameter. Most existing methods only make use of fully aligned data sources that share common conditional distributions of one or more variables of interest. However, in many settings, the scarcity of fully aligned sources can make existing methods require unduly large sample sizes to be useful. Our approach enables the incorporation of weakly aligned data sources that are not perfectly aligned, provided their degree of misalignment is known up to finite-dimensional parameters. {We quantify the additional efficiency gains achieved through the integration of these weakly aligned sources. We characterize the semiparametric efficiency bound and provide a general means to construct estimators achieving these efficiency gains.} We illustrate our results by fusing data from two harmonized HIV monoclonal antibody prevention efficacy trials to study how a neutralizing antibody biomarker associates with HIV genotype.