The University of Southampton
University of Southampton Institutional Repository

Extending the Lincoln-Petersen estimator for multiple identifications in one source

Extending the Lincoln-Petersen estimator for multiple identifications in one source
Extending the Lincoln-Petersen estimator for multiple identifications in one source
The Lincoln–Petersen estimator is one of the most popular estimators used in capture–recapture studies. It was developed for a sampling situation in which two sources independently identify members of a target population. For each of the two sources, it is determined if a unit of the target population is identified or not. This leads to a 2?×?2 table with frequencies f11,f10,f01,f00 indicating the number of units identified by both sources, by the first but not the second source, by the second but not the first source and not identified by any of the two sources, respectively. However, f00 is unobserved so that the 2?×?2 table is incomplete and the Lincoln–Petersen estimator provides an estimate for f00. In this paper, we consider a generalization of this situation for which one source provides not only a binary identification outcome but also a count outcome of how many times a unit has been identified. Using a truncated Poisson count model, truncating multiple identifications larger than two, we propose a maximum likelihood estimator of the Poisson parameter and, ultimately, of the population size. This estimator shows benefits, in comparison with Lincoln–Petersen's, in terms of bias and efficiency. It is possible to test the homogeneity assumption that is not testable in the Lincoln–Petersen framework. The approach is applied to surveillance data on syphilis from Izmir, Turkey.
lincoln–petersen estimator, EM algorithm, trinomially truncated estimator, robust estimation
0277-6715
4237-4249
Kose, T.
28c75502-b97a-4a93-a4f3-364505135df0
Orman, M.
7e785c9c-a3ff-491a-9a7c-d3e4deaf1c68
Ikiz, F.
719667c5-d4eb-45df-9f34-8468cf10a728
Baksh, M.F.
fb3f4020-4e9b-4ebe-8a1f-e2aa401ae6a3
Gallagher, J.
6b9b8d95-c9f6-4bc1-9fb6-cf93f8ad33bf
Boehning, D.
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Kose, T.
28c75502-b97a-4a93-a4f3-364505135df0
Orman, M.
7e785c9c-a3ff-491a-9a7c-d3e4deaf1c68
Ikiz, F.
719667c5-d4eb-45df-9f34-8468cf10a728
Baksh, M.F.
fb3f4020-4e9b-4ebe-8a1f-e2aa401ae6a3
Gallagher, J.
6b9b8d95-c9f6-4bc1-9fb6-cf93f8ad33bf
Boehning, D.
1df635d4-e3dc-44d0-b61d-5fd11f6434e1

Kose, T., Orman, M., Ikiz, F., Baksh, M.F., Gallagher, J. and Boehning, D. (2014) Extending the Lincoln-Petersen estimator for multiple identifications in one source. Statistics in Medicine, 33 (24), 4237-4249. (doi:10.1002/sim.6208). (PMID:24833434)

Record type: Article

Abstract

The Lincoln–Petersen estimator is one of the most popular estimators used in capture–recapture studies. It was developed for a sampling situation in which two sources independently identify members of a target population. For each of the two sources, it is determined if a unit of the target population is identified or not. This leads to a 2?×?2 table with frequencies f11,f10,f01,f00 indicating the number of units identified by both sources, by the first but not the second source, by the second but not the first source and not identified by any of the two sources, respectively. However, f00 is unobserved so that the 2?×?2 table is incomplete and the Lincoln–Petersen estimator provides an estimate for f00. In this paper, we consider a generalization of this situation for which one source provides not only a binary identification outcome but also a count outcome of how many times a unit has been identified. Using a truncated Poisson count model, truncating multiple identifications larger than two, we propose a maximum likelihood estimator of the Poisson parameter and, ultimately, of the population size. This estimator shows benefits, in comparison with Lincoln–Petersen's, in terms of bias and efficiency. It is possible to test the homogeneity assumption that is not testable in the Lincoln–Petersen framework. The approach is applied to surveillance data on syphilis from Izmir, Turkey.

Full text not available from this repository.

More information

Accepted/In Press date: 23 April 2014
e-pub ahead of print date: 15 May 2014
Published date: 30 October 2014
Keywords: lincoln–petersen estimator, EM algorithm, trinomially truncated estimator, robust estimation
Organisations: Primary Care & Population Sciences

Identifiers

Local EPrints ID: 373498
URI: https://eprints.soton.ac.uk/id/eprint/373498
ISSN: 0277-6715
PURE UUID: d901b5ef-ffd9-42b1-a9ae-7aa4b337c5c8
ORCID for D. Boehning: ORCID iD orcid.org/0000-0003-0638-7106

Catalogue record

Date deposited: 20 Jan 2015 15:08
Last modified: 14 Oct 2019 18:57

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×