On linkage bias-correction for estimators using iterated bootstraps

TL;DR

This paper introduces a bootstrap-based method to correct linkage bias in estimators derived from linked datasets, along with a test to evaluate the benefit of increasing bootstrap iterations, demonstrated through simulated and real data.

Contribution

It proposes a novel bootstrap-based approach for linkage bias correction and a test to determine the optimal number of bootstrap iterations for improved accuracy.

Findings

The bootstrap bias-corrected estimators effectively reduce linkage bias.

The test helps identify when additional bootstrap iterations no longer improve accuracy.

Application to real and simulated data validates the methodology.

Abstract

By amalgamating data from disparate sources, the resulting integrated dataset becomes a valuable resource for statistical analysis. In probabilistic record linkage, the effectiveness of such integration relies on the availability of linkage variables free from errors. Where this is lacking, the linked data set would suffer from linkage errors and the resultant analyses, linkage bias. This paper proposes a methodology leveraging the bootstrap technique to devise linkage bias-corrected estimators. Additionally, it introduces a test to assess whether increasing the number of bootstrap iterations meaningfully reduces linkage bias or merely inflates variance without further improving accuracy. An application of these methodologies is demonstrated through the analysis of a simulated dataset featuring hormone information, along with a dataset obtained from linking two data sets from the Australian Bureau of Statistics' labour mobility surveys.