1. Challenges in data linkage: error and bias
 Katie Harron
October 2014
UCL Institute of Child Health

2. The linkage problem Match status Match Non-match Link status Link
Match status
Match
(pair from same individual)
Non-match
(pair from different individuals)
Link status
Link
Identified match
False match
Non-link
Missed match
Identified non-match 2

3. Deterministic linkage in Hospital Episode Statistics (HES)
Few false-matches 1
Sex
Date of Birth
NHS Number 2
Postcode
Local Patient Identifier within Provider 3
More missed-matches
What kind of linkage is this?
Which patients might be missed?

4. Quality of unique identifiers
166,406 records of admissions to paediatric intensive care (PICANet)
85,137 non-matches
81,269 matches
46 (0.1%)
same NHS number
3,207 (4%)
different NHS numbers
Hagger-Johnson et al. Causes and consequences of data linkage errors: False and missed matches following linkage of hospital data (under review)

5. Deterministic linkage with pseudonymisation at source
Courtesy of Peter Jones, ONS Beyond 2011 programme

6. Probabilistic linkage
Highest weight is retained
pair 1
pair 2
pair 3
Low match High match
weight weight
Primary File
Ronald Fisher
Linking File
Ronald Fisher
Linking File
Karl Pearson
Linking File
Carl Gauss

7. Probabilistic linkage
Highest weight is retained
pair 3
Low match High match
weight weight
P(γ=1 | M) = m-probability = sensitivity
the probability of agreement given the records from same subject
 P(γ=1 | U) = u-probability= 1-specificity
the probability of agreement given the records from different subjects
Log ratio = w = log2 (m/u) if identifiers agree
log2 [(1-m)/(1-u)] if identifiers disagree
Match weight = W = ∑wi

8. Probabilistic linkage
Matches
agreement on NHS number
Non-matches
agreement on sex
Low match High match
weight weight
disagreement on date of birth
agree on some ids
disagree on some ids
Chance (same date of birth)
Recording errors
Missing data

9. Matches Non-matches Two thresholds Missed matches False matches Links
Low match High match
weight weight
Links
Links
Two thresholds

10. Evaluating linkage quality
Small amounts of linkage error can result in substantially biased results
The impact of linkage error on results is rarely reported
Linkage error affects different types of analysis in different ways

11. Why it’s important to evaluate linkage error
Schmidlin et al (2013) Impact of unlinked deaths and coding changes on mortality trends in the Swiss National Cohort. BMC Med Inform Decis Mak 13 (1):1

12. Why it’s important to evaluate linkage error
Hobbs, G. & Vignoles, A., Is free school meal status a valid proxy for socio-economic status (in schools research)? Centre for the Economics of Education; London School of Economics and Political Science.

13. Why it’s important to evaluate linkage error
Highly sensitive
Highly specific
Lariscy (2011). Differential Record Linkage by Hispanic Ethnicity and Age in Linked Mortality Studies: Implications for the Epidemiologic Paradox. J Aging Health 23(8):

14. Why it’s important to evaluate linkage error
Ford et al Characteristics of unmatched maternal and baby records in linked birth records and hospital discharge data. Paediatric and Perinatal Epidemiology 20(4):

15. Evaluating linkage quality
i) Sensitivity analysis using different linkage criteria
ii) Subset of gold-standard data to quantify linkage bias
Highly sensitive
Highly specific
iii) Comparisons of linked and unlinked data
iv) Imputation for uncertain links

16. Imputation for linkage
Primary file
Linking file
Variable of interest
Record 1
Exact match
high
Record 2
low
Record 3
Prior-informed imputation
high
low
Record 4
Match weight=10
med
Match weight=1
low
Record n
Match weight=5
Match weight=4
high
Match weight=3
med
high
Goldstein et al Stat Med 2012;31(28):
Harron et al BMC Med Res Method 2014;14(1):36

17. Implications for data providers
i) Sensitivity analysis using different thresholds
Availability of all candidate records (linked and unlinked)
ii) Subset of gold-standard data to quantify linkage bias
iii) Comparisons of linked and unlinked data
Subset of data where true match status is known (gold-standard)
iv) Imputation for uncertain links
Harron et al Opening the black box of record linkage. J Epidemiol Commun H 66(12):1198

18. Summary
Data linkage is a powerful tool for enhancing administrative data
Linkage error has important effects on analyses
Results vary according to choice of thresholds and methods
Taking error into account is possible without releasing identifiable data
Communication between linkers and data users is vital

19. Acknowledgements and funding
Harvey Goldstein, Ruth Gilbert, Gareth Hagger-Johnson and Angie Wade,
UCL Institute of Child Health
Berit Muller-Pebody,
Public Health England
Roger Parslow, Tom Fleming, Lee Norman and the PICANet team,
University of Leeds
This work was supported by funding from the National Institute for Health Research Health Technology Assessment (NIHR HTA) programme (project number 08/13/47). The views and opinions expressed therein are those of the authors and do not necessarily reflect those of the HTA programme, NIHR, NHS or the Department of Health. The authors state no conflicts of interest.