Estimating population counts with capture-recapture models in the context of erroneous records in linked administrative data

In the absence of a traditional census and a comprehensive population register (as it is the case in the UK), administrative data sources, i.e. health, school or tax records, can offer an alternative to estimate the size of residence population. However, such data sources are designed to capture information only from specific populations which imposes a challenge to the estimation. A suitable method to overcome the challenge is to link administrative data sources that collect information from different but overlapping populations and use capture-recapture models to estimate the population counts. There are various assumptions required to obtain unbiased estimates by using capture-recapture models. In practice, especially the assumptions on 'homogeneous inclusion probabilities' and ‘no over coverage' are often not met. This paper proposes a two-step procedure for estimating population counts with capture-recapture models that account for heterogeneity of inclusion probabilities and the over coverage in the data sources. We apply our methodology to the linked Patient Register and Customer Information System dataset which violates both of the aforementioned assumptions. The Patient Register includes people who are registered with a National Health Service General Practitioner doctor. In 2011, the Patient Register overestimated the size of England and Wales population by 4.3% (over coverage) and its sex ratio was different than the 2011 Census estimates (heterogeneous of inclusion probabilities). The Customer Information System dataset provides information on all individuals who have ever had a national insurance number and children whose parents have made a child benefit claim relating to them. In 2011, it over estimated the size of England and Wales population by 9.5% and its age and sex structure was different than the 2011 Census estimates. Applying our approach, we estimate population counts of the South East region of England by age, sex and local authority, and compare them with census estimates using percentage difference maps.