Estimating Omissions From Searches

The mark-recapture method was devised by Petersen in 1896 to estimate the number of fish migrating into the Limfjord, and independently by Lincoln in 1930 to estimate waterfowl abundance. The technique can be applied to any search for a finite number of items by two or more people or agents, allowing the number of searched-for items to be estimated. This ubiquitous problem appears in fields from ecology and epidemiology, through to mathematics, social sciences, and computing. Here, we exactly calculate the moments of the hypergeometric distribution associated with this longstanding problem, confirming that widely used estimates conjectured in 1951 are often too small. Our Bayesian approach highlights how different search strategies will modify the estimates. The estimates are applied to several examples. For some published applications, substantial errors are found to result from using the Chapman or Lincoln–Petersen estimates. Supplementary materials for this article are available online.

[1]  Andrew Booth,et al.  How much searching is enough? Comprehensive versus optimal retrieval for technology assessments , 2010, International Journal of Technology Assessment in Health Care.

[2]  Derrick A Bennett,et al.  Capture-recapture is a potentially useful method for assessing publication bias. , 2004, Journal of clinical epidemiology.

[3]  C. Becker,et al.  Endometrial alterations in endometriosis: a systematic review of putative biomarkers. , 2011, Human reproduction update.

[4]  George A. F. Seber,et al.  The Effects of Trap Response on Tag Recapture Estimates , 1970 .

[5]  D. Sackett,et al.  Evidence based medicine: what it is and what it isn't , 1996, BMJ.

[6]  J. Higgins,et al.  Cochrane Handbook for Systematic Reviews of Interventions, Version 5.1.0. The Cochrane Collaboration , 2013 .

[7]  J. Ioannidis,et al.  The PRISMA Statement for Reporting Systematic Reviews and Meta-Analyses of Studies That Evaluate Health Care Interventions: Explanation and Elaboration , 2009, Annals of Internal Medicine [serial online].

[8]  D. G. Chapman.  Some properties of the hypergeometric distribution with applications to zoölogical somple censuses , 1951 .

[9]  Akbar Fotouhi,et al.  Capture-recapture method for assessing publication bias , 2010, Journal of research in medical sciences : the official journal of Isfahan University of Medical Sciences.

[10]  R R Regal,et al.  Capture-recapture methods in epidemiology: methods and limitations. , 1995, Epidemiologic reviews.

[11]  T. J. Gaskell,et al.  A BAYESIAN MODIFICATION OF THE LINCOLN INDEX , 1972 .

[12]  Phil Edwards,et al.  Identification of randomized controlled trials in systematic reviews: accuracy and reliability of screening records , 2002, Statistics in medicine.

[13]  A. Chao,et al.  The Petersen–Lincoln Estimator and its Extension to Estimate the Size of a Shared Population , 2008, Biometrical journal. Biometrische Zeitschrift.

[14]  E. Sutherland.  Ecological Census Techniques - 2nd Edition , 2006 .

[15]  R. García-Pelayo.  A Bayesian, combinatorial approach to capture-recapture. , 2006, Theoretical population biology.

[16]  G. Arfken.  Mathematical Methods for Physicists , 1967 .

[17]  J. Ioannidis,et al.  The PRISMA statement for reporting systematic reviews and meta-analyses of studies that evaluate healthcare interventions: explanation and elaboration , 2009, BMJ : British Medical Journal.

[18]  F. C. Lincoln.  Calculating waterfowl abundance on the basis of banding returns , 1930 .

[19]  J. Wittes,et al.  331. Note: On the Bias and Estimated Variance of Chapman's Two-Sample Capture-Recapture Population Estimate , 1972 .

[20]  M. Airey,et al.  Use of the capture-recapture technique to evaluate the completeness of systematic literature searches , 1996, BMJ.

[21]  Sutherland.  Ecological Census Techniques , 2006 .

[22]  K Ann McKibbon,et al.  The capture-mark-recapture technique can be used as a stopping rule when searching in systematic reviews. , 2009, Journal of clinical epidemiology.

[23]  J. Higgins.  Cochrane handbook for systematic reviews of interventions. Version 5.1.0 [updated March 2011]. The Cochrane Collaboration , 2011 .