SEARO –CSR Early Warning and Surveillance System Module Principles of Capture- Recapture

E P I D E M I C A L E R T A N D R E S P O N S E SEARO –CSR Early Warning and Surveillance System Module

Principles of Capture-Recapture


Objectives of this lecture

To present the main principles of capture-recapture


Capture-recapture methods (CRM)

CR procedures: Take a random sample of an animal

population Tag and release captured animals Take second random sample,

count previously caught animals

population total #1 sample in captures #

2 sample #2 sample in recaptures #

Estimate total population size by applying rule of three:

Outline

Applications

2-source Method

Applicability

Example


1. Take sample

Outline

Applications

2-source Method

Applicability

Example


2. Tag captures

x

xx

x

x

x

x

Outline

Applications

2-source Method

Applicability

Example


3. Release captures

Outline

Applications

2-source Method

Applicability

Example


4. Take second sample

# recaptures in sample 2# sample 2

# captures in sample 1# total population

Outline

Applications

2-source Method

Applicability

Example


Use of CR in humans

Demography• CR has been applied to estimate the size of

human populations.

Outline

Applications

2-source Method

Applicability

Example


Use of CR in humans Epidemiology

Principle:• list of a given disease (sources)• sources considered random captured

samples from the population

• Individuals appearing in more than one source identified through unique identifier

• estimation of total number of individuals missed by sources

Outline

Applications

2-source Method

Applicability

Example


Applications of CR in epidemiology

Evaluating sensitivity, exhaustivity

of a surveillance source

Refining incidence and prevalence estimates from surveillance systems or population surveys

Outline

Applications

2-source Method

Applicability

Example


Two-source CR

Source A

Source B

x12 x11 x21

x22?

1 included in source2 not included in source

Outline

Applications

2-source Method

Applicability

Example


Estimated conditionally to the number of cases observed in other cells

Two-source CRM

22

22

x

x

N

x x x

obs

122111

Source A + -

+ X11 X21 N2

Sour

ce B

- X12 X22

N1 N

Outline

Applications

2-source Method

Applicability

Example


Estimation Method If the sources are independent:

P(A+ if B+) = P(A+ if B-)

1 xxxx OR

21 12

22 11

11

21 1222

xxx x

11

2 1

xNN N

N

11

21 12 2 1 N

Var 1.96 N 95%CIx

xxNN Var3

Outline

Applications

2-source Method

Applicability

Example


Sensitivity of sources:

If numbers in cells are small, then probability that x11= 0 exists (we add 1)

Estimation Method

NN B Sens

NN A Sens

2

1

1x1) (N1)(N N

11

2 1

2) (x)(xxx 1)1)(N(N Var

11111

21 12 2 1 N

2

- 1

Outline

Applications

2-source Method

Applicability

Example


Conditions needed

1. Same study period and area2. Closed population3. True cases4. True matches5. Equal catchability6. Sources are independent

Outline

Applications

2-source Method

Applicability

Example


1. Same study period and area

Cases occur during the study period and in study area

If different period of capture: Probability of recapture x11

overestimation of N11

2 1

xNN N

Outline

Applications

2-source Method

Applicability

Example


2. 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 x11 overestimation of N

11

2 1

xNN N

Outline

Applications

2-source Method

Applicability

Example


3. True cases

All cases in any source are true cases

False positive cases

Positive predictive value (PPV) < 1

Overestimation of N1 or N2

overestimation of N 11

2 1

xNN N

Outline

Applications

2-source Method

Applicability

Example


4. True matches Matches and only matches are identified

True matches missed

x11

overestimation of N

Wrong matches created

x11

underestimation of N

11

2 1

xNN N

Outline

Applications

2-source Method

Applicability

Example


5. Equal catchability For a given source, probability of

capture should be the same for all cases• Often not true for epidemiological

datasets• Low or no probability of capture by any

source (eg. IVDU, homeless) Disregarded in estimate underestimation of N

Outline

Applications

2-source Method

Applicability

Example


Accounting for variable catchability Stratify by factor introducing variable catchability Calculate estimates by strata

Stratum 1

Stratum 2

N = Ni = N1 + N2

Source A + -

+ X11 X21 B1 Source B

- X12 X22 A1 N1

11

1 11 x

BA N

11

2 22 x

BA N

Outline

Applications

2-source Method

Applicability

Example


6. Sources are independent (+++)

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

Source A + -

+ X11 X21 N2 Source B

- X12 X22 N1 N

OR > 1 (positive dependence) => N is underestimated

OR < 1 (negative dependence) => N is overestimated

2121

2211

XXXX OR

Outline

Applications

2-source Method

Applicability

Example


An example on source-dependenceEstimation of number of IVDU

in Bangkok in 1991 (Maestro 1994)

Two sources were used: Methadone (April – Mai 1991) Police arrests (June – September 1991)

Methadone Need for drugs Probability of being arrested

Negative dependence Overestimation of N

Outline

Applications

2-source Method

Applicability

Example


Evaluation of sources dependence

If two sources: Qualitative analysis of the

notification process in each source.

If multiple (>2) sources: a. Wittes method or b. Log-linear modelling

Outline

Applications

2-source Method

Applicability

Example


Example of the use of

capture-recapture

Outline

Applications

2-source Method

Applicability

Example


Evaluation of Legionella notification system, France, 1995

1995: surveillance revision in France Evaluation of legionnaires´diseases

defined as a priority

Evaluate sensitivity of system using CR

Outline

Applications

2-source Method

Applicability

Example


Three sources were available1. Notification system (NS)

2. National Reference Laboratory (NRL) Confirmation of diagnosis, typing of

strains >200 diagnoses per year

3. Hospital Laboratories (HL) Survey among all hospital bacteriology

laboratories, N=432

Outline

Applications

2-source Method

Applicability

Example


Sources

• What are your thoughts on the sources in terms of:

1. Same study period and area2. Closed population3. True cases4. True matches5. Equal catchability6. Sources are independent


Distribution of case reports by source

NS Notification systemNRL Nat. Reference LabHL Hospital Labs

Outline

Applications

2-source Method

Applicability

Example

10

NS, n=50

HL, n=357

190

59

138

18

11

11

10

NS, n=50

NRL, n=226

HL, n=357

190

59

138

18

11

11


Two-source estimates

Two-source estimates:

Merge NS/NLR into one source

NS/NRL 389 casesNS/HL 615 casesHL/NRL 517cases

NS/NRL inside HL: OR 2.3 [1.0-5.7] NS/HL inside NRL: OR 0.7 [0.3-1.8] NRL/HL inside NS: OR 1.5 [0.4-5.4]

Positive dependence

NSNRL / HL 528 [495–561] cases

Estimate NS/NRL = cases in NS x cases in NRL recaptures in NRL from NS

= 50 x 226 = 389

18+11

Outline

Applications

2-source Method

Applicability

Example


Test of independence

a b

cd e

f

g

A B

C OR = cg/de

OR = 1 independenceOR > 1 positive dependence underestimation of NOR < 1 negative dependence overrestimation of N

Outline

Applications

2-source Method

Applicability

Example

Source A + -

+ c e N 2

Sour

ce B

- d g

N 1 N




Tests of independence (Wittes)

NS/NRL 389 casesNS/HL 615 casesHL/NRL 517 cases

NS/NRL inside HL: OR 2.3 [1.0-5.7] NS/HL inside NRL: OR 0.7 [0.3-1.8] NRL/HL inside NS: OR 1.5 [0.4-5.4]

Positive dependence

NSNRL / HL 528 [495–561] cases

Outline

Applications

2-source Method

Applicability

Example

Merge NS/NLR into one source


Sensitivity existing legionelosis notification

sources• Estimated total number of cases:

N = 528 • Cases notified by NS:

N1 = 50• Cases notified by NRL:

N2 =226• Cases notified by both sources combined =

247

• Sensitivity NS = 50/528 = 9%• Sensitivity NRL = 226/528 = 43%• Sensitivity both combined = 247/528 = 47%

Outline

Applications

2-source Method

Applicability

Example

Need to reinforce

the existing surveillance

system


11

2 1

xNN N

N

11

21 12 2 1 N

Var 1.96 N 95%CIx

xxNN Var3

Outline

Applications

2-source Method

Applicability

Example


Conclusions on CR: Use the technique when appropriate, but be careful! Not the solution to all problems

Conditions for application seldom met in surveillance systems

Complementary technique Two sources

Impossible to quantify extent of dependence Requires a third source

Multiple sources Log-linear modelling method of choice Can adjust for dependence and variable catchability


References Wittes JT, Colton T and Sidel VW. Capture-recapture models for assessing the completeness of case

ascertainment using multiple information sources. J Chronic diseases 1974;27:25-36. Hook EB, Regal RR. Capture-recapture methods in epidemiology. Methods and limitations.

Epidemiologic Rev 1995; 17(2): 243-264. Hook EB, Regal RR. Recommendations for presentation and evaluation of capture-recapture estimates

in epidemiology. J Clin Epidemiol 1999;917-2 Gallay A, Nardone A. La méthode capture-recapture appliquée a l´épidemiologie : principes, limites et

applications. Revue epidemiologie sante publique 2002;219-32. Desenclos JC, Hubert B. Limitations to the universal use of capture-recapture methods. Int J Epidemiol

1994;1322-3. Infuso A, Hubert B, Etienne J. Underreporting of legionnaires disease in France : the case for more active

surveillance.Euro Surveill. 1998 May;3(5):48-50. Nardone A, Decludt B, Jarraud S, Etienne J, Hubert B, Infuso A, Desenclos JC. Repeat capture-recapture

studies as part of the evaluation of the surveillance of Legionnaires' disease in France. Gallay A, Vaillant V, Bouvet P, Grimont P, Desenclos JC. How many foodborne outbreaks of Salmonella

infection occurred in France in 1995? Application of the capture-recapture method to three surveillance systems. American Journal of Epidemiology. 2000;171-7.

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SEARO –CSR Early Warning and Surveillance System Module Principles of Capture- Recapture