Capturerecapture method

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Capture-recapture method

• Preben Aavitsland

Based on presentations given by Jean-Claude
Desenclos, Thomas Grein, Tony Nardone, Anne
Gallay, Natasha Crowcroft
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What is it?

• Capture-recapture methods are used for counting
  the total number of individuals in a population
  using two or more incomplete lists of those
  individuals
• Originially used in wildlife (birds, polar bears,
  wild salmon) counting
• Capture gt tag gt recapture gt calculate

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Uses in epidemiology

• Estimate prevalence or incidence from incomplete
  sources
• Simplify prevalence surveys
• Evaluate completeness of a surveillance system
  (Epiet objective!)
• Can be used for any condition

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Principles

• Two or more sources (lists, registries,
  observations, samples) of cases with a given
  disease or state
• Sources considered independent capture samples
  from the same source (total) population
• Cases can be matched by unique identifiers
• Estimate total number in the source population
  (captured and uncaptured) from the numbers of
  captured in each capture

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Two-source model
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Two-source model
N?
Y1
Source Y
Z1
Source Z
b
a
c
x?
N a b c x
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Two-source analysis
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With independent sources

• pYZ pYnot Z
• a/(ab) c/(cx)
• c(ab) a(cx)
• bc ax
• x bc / a

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Estimations

• Unobserved cell x bc / a
• Total population N abc(bc/a) N (ab)
  (ac) / a
• N Y1 Z1 / a
• Sensitivity of Y Ysn Y1/N (ac)/N
• Sensitivity of Z Zsn Z1/N (ab)/N

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Confidence interval

• N Y1 Z1 / a
• VarN Y1 Z1 b c / a3
• 95 ci N 1.96 vVarN
• (Of course, adjusts only for sampling
  fluctuations, not for violations of assumptions
  of the method.)

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Assumptions

• The population is closed
• No change during the investigation
• Individuals captured on both occasions can be
  matched
• No loss of tags
• For each sample, each individual has the same
  chance of being included
• Same catchability
• Capture in the second sample is independent of
  capture in the first
• The two samples are independent, pYZ pY pZ

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Assumptions may not hold

• The population is closed ? Usually possible
• Individuals captured on both occasions can be
  matched ? OK if good recording systems
• For each sample, each individual has the same
  chance of being included ? Rarely true
• Capture in the second sample is independent of
  capture in the first ? Rarely true

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Closed population

• Nobody enters or leaves the population during the
  study period
• No immigration, emigration, death
• Open population
• Individuals captured in first sample cannot be
  captured in second
• Probability of recapture ? ? a ? ?
  overestimates N

N Y1 Z1 a
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True cases

• All cases in any source are true cases
• False positive cases
• Positive predictive value (PPV) lt 1
• Overestimation of Y1 or Z1 ? overestimates N
• Correction
• Take random sample of positive samples and verify
• Estimate PPV and adjust PPV Y1 Z1

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True matches

• Matches and only matches are identified
• Ideally, unique identifier available (social
  security number, name, etc)
• Combination of criteria Name initials, age,
  sex...
• True matches missed
• a ? ? overestimates N
• Wrong matches created
• a ? ? underestimates N

N Y1 Z1 a
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Equal catchability

• For each source, probability of capture is the
  same for all cases
• Probability may differ between sources - ok
• Some people have low probability of capture by
  any source
• Drug users, homeless, severely ill
• Not counted ? underestimates N

N Y1 Z1 a
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Accounting for variable catchability

• Identify and exclude population outside of all
  sources
• or
• Stratify by factor introducing variable
  catchability
• Calculate estimates by strata
• Sum N by strata

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Sources are independent(most important condition)

• Being in one source does not influence the
  probability of being in the other source

OR gt 1 (positive dependence) d lt d ?
underestimates N OR lt 1 (negative dependence) d
gt d ? overestimates N
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Example

• Estimation of number of IVDU in Bangkok in 1991
  (Maestro 1994)
• Two sources used
• Methadone programme (April May 1991)
• Police arrests (June September 1991)
• Methadone ? Need for drugs ? ? Probability of
  being arrested ? negative dependence,
  overestimation of N

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Still useful

• There will always be dependence
• We can predict the direction
• So we know whether our estimate is a lower or
  upper boundary
• And this may be what we need
• NB Confidence intervals does not solve the
  problem of dependency!!

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Evaluation of source dependence

• Two sources
• Qualitative analysis of the notification process
  in each source
• No statistical method to allow for dependence for
  two sources
• More than two sources
• Wittes method
• Log-linear modelling

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Wittes method

• Evaluate dependence between sources
• Compare two-source estimates of N
• If estimates different ?
• Test of independence
• Calculate odds ratios between cell counts of two
  sources within a third source
• If OR ? 1 ? dependence
• Merge dependent sources
• Repeat calculation of estimates with merged source

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Test of independence
A
B
a
b
f
c
d
e
OR cg/de
g
C
OR 1 ? independence OR gt 1 ? positive
dependence ? underestimation of N OR lt 1 ?
negative dependence ? overestimation of N
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Example Legionellosis in France
NS Notification system NRL National Reference
Laboratory HL Hospital Laboratories
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Example Legionellosis in France

• Two-source estimates
• Tests of independence (Wittes)
• Merge NS/NLR into one source

NS/NRL 389 cases NS/HL 615 cases HL/NRL
715 cases
NS?NRL / HL 528 495561 cases
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Conclusion

• If conditions are met
• Great potentital to estimate population size by
  using incomplete sources
• Cheaper than exhaustive registers or full
  counting
• Two sources
• Impossible to quantify extent of dependence
• Multiple sources
• Log-linear modelling method of choice
• Can adjust for dependence and variable
  catchability

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How many participants are there?

• Capture Source Preben
• Recapture Source Arnold
• Estimations ?
• Assumptions hold? ?

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Estimations

• Unobserved cell x bc / a
• Total population N abc(bc/a)
• N Preb1 Arn1 / a
• Sensitivity of Preb Prebsn Preb1/N (ac)/N
• Sensitivity of Arn Arnsn Arn1/N (ab)/N

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Confidence interval

• N Preb1 Arn1 / a
• VarN Preb1 Arn1 b c / a3
• 95 ci N 1.96 vVarN
• (Of course, adjusts only for sampling
  fluctuations, not for violations of assumptions
  of the method.)

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Assumptions hold?

• The population is closed
• Individuals captured on both occasions can be
  matched
• For each sample, each individual has the same
  chance of being included
• Capture in the second sample is independent of
  capture in the first

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Recommended reading

• Wittes JT, Colton T and Sidel VW.
  Capture-recapture models for assessing the
  completeness of case ascertainment using multiple
  information sources. J Chronic Dis 19742725-36.
• Hook EB, Regal RR. Capture-recapture methods in
  epidemiology. Methods and limitations. Epidemiol
  Rev 1995 17 243-264
• International Working Group for Disease
  Monitoring and Forecasting. Capture-recapture and
  multiple-record systems estimation I History and
  theoretical development. Am J Epidemiol
  19951421047-58
• International Working Group for Disease
  Monitoring and Forecasting. Capture-recapture and
  multiple-record systems estimation II
  Applications in human diseases. Am J Epidemiol
  19951421059-68

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Some examples from field epidemiology

• Legionnaires disease. Nardone et al Epidemiol
  Infect 2003131647-54
• Malaria. Klein and Bosman. Euro Surveill 2005
  10 244-6
• Measles. Van den Hof et al Pediatr Inf Dis J
  2002 211146-50
• Acute flaccid paralysis. Whitfield Bull WHO
  200280846-851
• Pertussis deaths. Crowcroft et al Arch Dis Child
  200286336-8
• Intussception after rotavirus vaccination.
  Verstraeten et al Am J Epidemiol
  20011541006-1012
• Tuberculosis. Tocque et al Commun Dis Public
  Health 20014141-3
• Salmonella outbreaks. Gallay et al Am J Epidemiol
  2000 152171-7
• AIDS. Bernillon et al Int J Epidemiol
  200029168-174
• Meningitis. Faustini et al. Eur J Epidemiol
  200016843-8