searo –csr early warning and surveillance system module principles of capture- recapture
DESCRIPTION
SEARO –CSR Early Warning and Surveillance System Module 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 Estimate total population size by applying rule of three: Estimate total population size by applying rule of three: Outline Applications 2-source Method Applicability ExampleTRANSCRIPT
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
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
Objectives of this lecture
To present the main 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
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
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
1. Take sample
Outline
Applications
2-source Method
Applicability
Example
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
2. Tag captures
x
xx
x
x
x
x
Outline
Applications
2-source Method
Applicability
Example
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
3. Release captures
Outline
Applications
2-source Method
Applicability
Example
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
4. Take second sample
# recaptures in sample 2# sample 2
# captures in sample 1# total population
Outline
Applications
2-source Method
Applicability
Example
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
Use of CR in humans
Demography• CR has been applied to estimate the size of
human populations.
Outline
Applications
2-source Method
Applicability
Example
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Example of the use of
capture-recapture
Outline
Applications
2-source Method
Applicability
Example
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
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
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
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
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
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
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
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
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
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
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
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
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
Two-source estimates
Two-source estimates
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
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
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
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
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
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
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
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
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.