Linkage of administrative data is an important tool for service evaluation and research, as individual-level information can be combined in a relatively cost-effective and timely manner compared with conventional data collection models. Most administrative data sources were not developed with linkage in mind, posing unique challenges for identifying the same individual in different sources [1]. Typographical errors, missing values and identifiers that change over time can prevent records from matching and lead to linkage error (false-matches and missed-matches) [2, 3]. Even low error rates can lead to biased results, particularly when records from particular types of individuals or organisations are less likely to link successfully than others. Such ‘differential’ linkage can lead to a form of bias in analysis, for example when specific groups of records are misclassified or excluded from the linked dataset [4–8].

For linkage of data sources that do not contain a reliable unique identifier, probabilistic methods are commonly used [9, 10]. Probabilistic linkage makes use of variables such as sex, date of birth and postcode to create a match weight for classifying records as matches or non-matches. Match weights are traditionally based on the Fellegi-Sunter approach using conditional probabilities derived from estimated rates of errors in identifiers: the probability that identifiers agree given records belong to the same subject (m-probability), and the probability that identifiers agree given records belong to different subjects (u-probability) [11, 12]. Conditional probabilities can be derived from ‘training’ data, i.e. a sub-sample of data where the true match status for each record pair is known (supervised matching) [13]. If no training data are available, probabilities are typically estimated using statistical methods, such as the expectation-maximisation (EM) algorithm [14].

There are several problems associated with the calculation of probabilistic match weights using the traditional approach. Firstly, match weights are calculated assuming that identifier errors occur randomly within a dataset, and that the probability of an identifier error is unrelated to any other characteristic (age, ethnicity etc.) [11]. However, this assumption is often invalid: data quality is often associated with individual-level characteristics and can also vary on an organisational level [15]. These associations are typically ignored, unless these characteristics are incorporated into a blocking scheme with match weights being produced separately for each block. Secondly, match weights are typically calculated by summing the logarithms of m- and u-probability ratios across identifiers. This requires the assumption that identifier errors are independent (i.e. agreement on year of birth is independent of agreement on forename) - an assumption that often fails and can lead to misclassification of record pairs [16].

One approach to overcome these problems is to estimate match weights jointly over a set of identifiers (the agreement pattern), thus overcoming the need for independence between identifiers. It is also possible to calculate match weights allowing dependence on individual- and/or organisational-level covariates. Although characteristics of the identifying variables, such as the frequency of common or rare surnames, are often incorporated into match weight calculation, this has not been the case for individual characteristics that are not used for matching (e.g. ethnicity) or at an organisational level (e.g. by hospital). The present study aims first to provide empirical evidence on the associations between identifier error rates and individual characteristics in a national administrative data source (Hospital Episode Statistics; HES). Quality of identifier recording in HES is likely to be representative of other administrative sources, i.e. those where identifiers are input using a range of IT systems, and so information on identifier error rates will be relevant to linkage of other large administrative data sources. Secondly, we develop methods to estimate match weights without relying on the independence assumption, and incorporating individual or organisational-level attributes, and evaluate these weights as alternatives to traditional probabilistic match weights.

Our study provides empirical evidence on variation in identifier error rates by individual characteristics in a widely-used and extensive administrative data source. This information will be valuable for other researchers assessing the feasibility of linkage with administrative data sources, particularly where no training data are available, as the identifier error rates observed in HES will provide an appropriate starting point for estimating m- and u-probabilities in other similar datasets. We provide methods for incorporating dependence between identifiers, and variation in identifier errors by individual and organisational-level characteristics, into match weight calculation. Our simulation study demonstrated that match weights incorporating individual characteristics or organisational variation were effective at reducing bias associated with errors in linkage, particularly when errors are distributed non-randomly.

Results from our simulation study support a large body of literature showing that substantial bias can be introduced into results of analyses based on data containing linkage errors [22–25]. This is particularly important when error is non-random, i.e. dependent on individual-level characteristics, and when there are a large number of missed-matches (e.g. with linkage requiring exact matching of identifiers). Evidence from previous studies highlights that the most vulnerable groups are those most likely to be affected by linkage error [2, 26]. In our study, readmission rates estimated using linkage with traditional match weights were underestimated, due to low sensitivity when fixing the false-match rate at 1%. In practice, false-match rates are often lower than 1%, corresponding with a lower sensitivity (where false-matches are avoided, to the expense of missed-matches) and a greater risk of under-estimated readmission rates [15, 27]. Bias was greatest for Mixed, Asian, or Black ethnic groups, meaning that relative comparisons by ethnicity would be biased using match weights derived by the traditional method. However, we show that attribute- or organisational-specific match weights, incorporating information on variation in identifier errors, can substantially reduce bias associated with linkage error. Additional methods for handling linkage error, such as incorporating match weights into analysis in a multiple imputation framework, could be used to reduce bias further [23, 28].

Incorporating information on individual or organisational characteristics, or dependence between identifiers, into match weight estimation is a relatively simple process, given a large enough sample from which to estimate the relevant parameters. In practice, detailed information on identifier error rates is not always available and parameters are often derived from a sample of data. Where a large enough sample on which to base estimates of error rates is not available, it would be possible to incorporate characteristics into latent class models such as the Expectation-Maximisation (EM) algorithm, which can be used to estimate conditional probabilities for the traditional Fellegi-Sunter approach [14, 29]. The value of incorporating information on record attributes is likely to be most evident in linkage of large-scale administrative datasets, particularly where records are grouped, for example by organisation or region. However, our study used a relatively simple design of linkage within one longitudinal dataset, and further evaluation is required to understand performance and practicalities of the method in large, complex linkages involving multiple files.

There is limited evidence on how the failure of the assumption of independence affects linkage quality over and above the calculation of match weights. Tromp et al. (2008) found that dependence between highly correlated identifiers (such as expected birth and actual date of birth) had a negative impact on match weights and that this resulted in an incorrect ranking of record pairs ordered by match weight [16]. Similarly, Herzog et al. (2010) found that match weights assigned to non-dependent identifiers were too low in the presence of dependent identifiers [30]. Methods for accounting for dependence between identifiers have also been shown to improve the quality of linkage [31]. Others believe that the impact of dependence between identifiers is small, and that the failure of the independence assumption can be ignored [32, 33]. In our study, ordering of record pairs based on weights incorporating dependence between identifiers was the same as with traditional match weights, mainly due to a lack of strong dependence between errors in sex, postcode and date of birth observed in HES. However, incorporating dependence into match weights may become more important in data where obvious dependencies do exist, although handling dependence between a large number of identifiers may become impractical.

A major strength of this study was the use of a large, generalizable administrative data source that is frequently linked with other datasets and used for commissioning and monitoring of the NHS in England and for research. Our study demonstrates the usefulness of the PDS as a reference dataset. There is a lack of published information available on PDS but it holds potential for developing a better understanding of the mechanisms underlying identifier errors, for improving data linkage methods, and for validating identifiers in HES [34]. However, our study was limited by the assumption that agreement on NHS number between HES and PDS indicated that records belonged to the same individual. In reality, NHS number is not always a reliable identifier for linkage [20]. If well-completed NHS number is indicative of good data quality more generally, we may have underestimated identifier error rates through our study design. In addition, we based our extract on date of birth, and so excluded all records where date of birth was missing. We also used a one year study period, and therefore would not have captured changes in postcode over time. Inspection of PDS reveals that 55% of children have at least two postcodes in their first year of life and 69% have at least two postcodes by age 5/6 (19% have four or more different postcodes by this age). In our simulation study, we fixed our threshold at a false-match rate of 1%. In practice, choice of appropriate thresholds can be difficult, and is typically chosen based on a sample of manually-reviewed records, or using synthetic data [35].

Incorporating information on individual characteristics or organisational variation into match weight calculation can reduce bias associated with errors in linkage, particularly when errors are distributed non-randomly. Continued improvement of linkage methods will allow more efficient exploitation of administrative data sources, reduce bias associated with linkage of imperfect identifiers and improve the reliability and transparency of analysis based on linked data. This will improve the ability of those working in government and health policy, who frequently use research data generated from administrative data sources to inform health policy, to make informed decisions on patient care and health systems. Evaluation of services for specific age or ethnic groups can be important for policy, but as our study shows, results for specific groups can be biased if associated linkage error is not addressed. Careful consideration should be given to the trade-off between bespoke linkage strategies for each study (that prioritise the quality of linkage) versus routine linkage systems that maximise efficiency and security. In order for data users to understand the limitations of linked data sources, it is vital that information on linkage quality and error rates are made available on release of linked data. Data providers need to improve transparency about data processing before during and after linkage.