Bootstrap inference using estimating equations and data that are linked with complex probabilistic algorithms

Probabilistic record linkage is the act of bringing together records that are believed to belong to the same unit (e.g., person or business) from two or more files. It is a common way to enhance dimensions such as time and breadth or depth of detail. Probabilistic record linkage is not an error-free process and link records that do not belong to the same unit. Naively treating such a linked file as if it is linked without errors can lead to biased inferences. This paper develops a method of making inference with estimating equations when records are linked using algorithms that are widely used in practice. Previous methods for dealing with this problem cannot accommodate such linking algorithms. This paper develops a parametric bootstrap approach to inference in which each bootstrap replicate involves applying the said linking algorithm. This paper demonstrates the effectiveness of the method in simulations and in real applications.