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El. knyga: Capture-Recapture Methods for the Social and Medical Sciences

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Capture-recapture methods have been used in biology and ecology for more than 100 years. However, it is only recently that these methods have become popular in the social and medical sciences to estimate the size of elusive populations such as illegal immigrants, illicit drug users, or people with a drinking problem. Capture-Recapture Methods for the Social and Medical Sciences brings together important developments which allow the application of these methods. It has contributions from more than 40 researchers, and is divided into eight parts, including topics such as ratio regression models, capture-recapture meta-analysis, extensions of single and multiple source models, latent variable models and Bayesian approaches.

The book is suitable for everyone who is interested in applying capture-recapture methods in the social and medical sciences. Furthermore, it is also of interest to those working with capture-recapture methods in biology and ecology, as there are some important developments covered in the book that also apply to these classical application areas.

Recenzijos

"This is a timely, important book on the use of capture-recapture methods for social and medical data. Several books have been written on capture-recapture methods for ecology, over many years, and one focussing on social and medical applications has been long overdue. This book illustrates the power of appropriate capture-recapture analyses in areas other than ecology. Several of the book chapters describe new methods, and suggest avenues for future research. The relevance of the methods described is evident, with applications to studies of the prevalence of scrapie, and estimating numbers of injecting drug users, of immigrants, and of victims of domestic violence, etc. Time and again we see the power of Statistics in providing answers to really important questions. I enjoyed reading this book enormously. A great attraction is the wide range of motivating examples, complete with data, which include several from ecology. The way that methods are regularly illustrated on both real and simulated data is engrossing. Models are clearly described and accessible. The book should be required reading, for years to come, for any university course on Applied Statistical Modeling, as well as being a vital reference for research. I am sure that this book will be much read, and make a major impact." From the Foreword by Byron J. T. Morgan

"Capture-Recapture Methods for the Social and Medical Sciences is a much-needed text focussing on social science applications and methods of capturerecapture modelling. Theory within the field of analysis of capturerecapture data has developed in a disparate fashion between areas of applications, and many texts have focused on the presentation of ecological applications. This book does an excellent job of approaching the field from a different perspective, whilst still retaining how ecological applications fit into the developments. The book has been written by over 40 contributors, each an expert in their own area, which means that the theory presented is cutting-edge but has been presented in an accessible style...I will certainly be recommending this book to my collaborators and research students, as it provides a unique perspective, which is lacking in other capture-recapture books currently available on the market. Although this is a text that most likely will be dipped in and out of for reference to a particular topic, the book could be read cover-to-cover and anyone completing this can be sure of being up to date on the latest modelling approaches for capturerecapture data in the social sciences." -Rachel S. McCrea, Univeristy of Kent

"Capture-Recapture Methods for the Social and Medical Sciences, edited by Böhning, van der Heijden, and Bunge is the first book explicitly centered on applications of capture-recapture methods to human populations and medical problems...The most interesting aspect of this book is the example applications. Most of them are taken from outside the classical setting of estimating animal abundance, and illustrate well the applicability of CR methods to diverse domains in social science and medicine...Capture-Recapture Methods for the Social and Medical Sciences deserves praise for being the first of its class. It is a good catalog of single-list CR methods, and contains some limited information about multi-list methods. This book can be useful for raising awareness among applied researchers of the applicability of capture-recapture methods for estimating human populations." -Daniel Manrique-Vallier, The American Statistician, Volume 34, 2020

Foreword xvii
Byron J.T. Morgan
Preface xix
List of Figures xxi
List of Tables xxv
Contributors xxxi
I Introduction 1(18)
1 Basic concepts of capture-recapture
3(16)
Dankinar Bohning
John Bunge
Peter G.M. van der Heijden
1.1 Introduction and background
4(1)
1.2 Data sets
4(6)
1.2.1 Golf tees in St. Andrews
4(1)
1.2.2 Homeless population of the city of Utrecht
5(1)
1.2.3 McKendrick's Cholera data
6(1)
1.2.4 Matthews's data on estimating the Dystrophin density in the human muscle
6(1)
1.2.5 Del Rio Vilas's data on Scrapie surveillance in Great Britain 2005
6(1)
1.2.6 Hser's data on estimating hidden intravenous drug users in Los Angeles 1989
7(1)
1.2.7 Methamphetamine drug use in Bangkok 2001
7(1)
1.2.8 Chun's data on estimating hidden software errors for the AT&Ts 5ESS switch
7(1)
1.2.9 Estimating the size of the female grizzly bear population in the Greater Yellowstone Ecosystem
8(1)
1.2.10 Spinner dolphins around Moorea Island
8(1)
1.2.11 Microbial diversity in the Gotland Deep
8(1)
1.2.12 Illegal immigrants in the Netherlands
9(1)
1.2.13 Shakespeare's unused words
10(1)
1.3 Estimating population size under homogeneity
10(2)
1.4 Simple estimates under heterogeneity
12(1)
1.5 Examples and applications
13(1)
1.6 Heterogeneity of sources or occasions
14(2)
1.6.1 Darroch's estimator and Lincoln-Petersen
15(1)
1.7 Glossary
16(3)
II Ratio Regression Models 19(60)
2 Ratio regression and capture-recapture
21(18)
Marco Ago
Dankmar Bohning
Irene Rocchetti
2.1 Introduction
21(2)
2.2 Individual and aggregated data
23(2)
2.3 Real data examples
25(1)
2.3.1 Fixed number of sources: The bowel cancer data
25(1)
2.3.2 Unknown number of sources: The Shakespeare data
26(1)
2.4 The ratio plot
26(6)
2.4.1 The Katz family
29(1)
2.4.2 Power series
30(1)
2.4.3 Mixed power series
31(1)
2.4.4 A specific case: The Beta-binomial distribution
31(1)
2.5 The regression approach
32(3)
2.6 Applications
35(2)
2.6.1 The bowel cancer data
35(1)
2.6.2 The Shakespeare data
36(1)
2.7 Discussion
37(2)
3 The Conway-Maxwell-Poisson distribution and capture-recapture count data
39(16)
Antonello Maruotti
Orasa Anan
3.1 Introduction
39(1)
3.2 The Conway-Maxwell-Poisson distribution and capture-recapture count data
40(2)
3.2.1 Preliminaries
40(1)
3.2.2 The CMP distribution
41(1)
3.3 Model inference
42(4)
3.3.1 The ratio plot
42(1)
3.3.2 The ratio regression
43(3)
3.4 Variance estimation
46(3)
3.4.1 Approaches based upon resample techniques
46(1)
3.4.2 An approximation-based approach
47(1)
3.4.3 Comparing confidence intervals
48(1)
3.5 Applications
49(2)
3.5.1 Snowshoe hares
50(1)
3.5.2 Colorectal polyps
50(1)
3.5.3 Root data
51(1)
3.5.4 Taxicab data in Edinburgh
51(1)
3.6 Discussion
51(4)
4 The geometric distribution, the ratio plot under the null and the burden of dengue fever in Chiang Mai province
55(6)
Dankmar Bohning
Veerasak Punyapornwithaya
4.1 Introduction
55(1)
4.2 The case study on dengue fever
55(1)
4.3 Geometric distribution
56(1)
4.4 Ratio plot
57(2)
4.5 Ratio plot under the null
59(1)
4.6 Application to estimate the burden of dengue fever
60(1)
5 A ratio regression approach to estimate the size of the Salmonella- infected flock population using validation information
61(18)
Carla Azevedo
Dankmar Bohning
Mark Arnold
5.1 Introduction and background
61(2)
5.2 Case study
63(2)
5.2.1 Salmonella data
64(1)
5.3 Ratio plot and ratio regression
65(5)
5.4 Ratio regression using validation information
70(2)
5.4.1 Application to the case study
72(1)
5.5 Simulation study
72(3)
5.6 The inflated model
75(2)
5.6.1 Simulation study on zero-inflated data
75(2)
5.7 Discussion and conclusions
77(2)
III Meta-Analysis in Capture-Recapture 79(28)
6 On meta-analysis in capture-recapture
81(6)
John Bunge
6.1 Introduction and background
81(2)
6.2 Analysis of grizzly bear data
83(1)
6.3 Comments and future directions
84(3)
7 A case study on maritime accidents using meta-analysis in capture-recapture
87(12)
Dankmar Bohning
John Bunge
7.1 Introduction
87(1)
7.2 The case study on maritime accidents
88(2)
7.3 Meta-anal34is essentials
90(1)
7.4 Analysis of maritime accident data
91(1)
7.5 Comments and future directions
91(4)
7.6 Software
95(4)
8 A meta-analytic generalization of the Lincoln-Petersen estimator for mark-and-resight studies
99(8)
Dankmar Bohning
Mehmet Orman
Timur Kase
John Bunge
8.1 What are mark-and-resight studies?
99(1)
8.2 A case study on stray dogs in South Bhutan
100(1)
8.3 Meta-analysis and mark-resight studies
101(1)
8.4 A Mantel-Haenszel estimator for mark-resight studies
102(2)
8.5 Some simulation work
104(2)
8.6 Concluding remarks
106(1)
IV Extensions of Single Source Models 107(104)
9 Estimating the population size via the empirical probability generating function
109(12)
John Bunge
Sarah Sernaker
9.1 Introduction and background
109(1)
9.2 Implementation of the empirical pgf method
110(4)
9.2.1 Initial values for 0 search
111(1)
9.2.2 Error estimation for N
112(1)
9.2.3 Goodness of fit for the empirical pgf procedure
113(1)
9.3 The Kemp distributions
114(2)
9.3.1 Approximate maximum likelihood estimates
115(1)
9.4 Simulations, data analyses, and discussion
116(5)
10 Convex estimation
121(20)
Cecile Durot
Jade Giguelay
Sylvie Huet
Francois Koladjo
Stephane Robin
10.1 Introduction
121(2)
10.1.1 Motivation
121(1)
10.1.2 Convex abundance distribution
122(1)
10.2 Testing the convexity of p+
123(4)
10.2.1 The statistical test
124(1)
10.2.2 Simulation study
124(3)
10.3 Estimating the number N of species
127(2)
10.3.1 Identifiability of N
127(1)
10.3.2 Estimating p+
128(1)
10.3.3 Estimating N
129(1)
10.4 Confidence intervals and standard errors
129(2)
10.4.1 Estimator based on empirical frequencies
129(1)
10.4.2 Estimator based on the constraint LSE
129(2)
10.5 Case studies
131(3)
10.6 Appendix
134(7)
10.6.1 Testing convexity of a discrete distribution
134(3)
10.6.2 Confidence intervals and standard errors
137(4)
11 Non-parametric estimation of the population size using the empirical probability generating function
141(14)
Pedro Puig
11.1 Introduction
141(1)
11.2 The LC-class: A large family of count distributions
142(2)
11.2.1 Compound-Poisson distributions belong to the LC-class
142(1)
11.2.2 Mixed-Poisson distributions belong to the LC-class
143(1)
11.2.3 Other distributions belonging (and not belonging) to the LC-class
143(1)
11.3 Some lower bounds of po for the LC-class
144(2)
11.3.1 Example: A two-component Mixed-Poisson distribution
145(1)
11.3.2 Example: A Hermite distribution
145(1)
11.4 Estimating a lower bound of the population size
146(2)
11.5 Examples of application
148(4)
11.5.1 McKendrick's Cholera data
149(1)
11.5.2 Abundance of grizzly bears in 1998 and 1999
150(1)
11.5.3 Biodosimetry data
150(2)
11.6 Discussion
152(3)
12 Extending the truncated Poisson regression model to a time-at-risk model
155(8)
Maarten J.L.F. Cruyff
Thomas F. Husken
Peter G.M. van der Heijden
12.1 Introduction
155(1)
12.2 The models
156(3)
12.2.1 The ZTPR
156(1)
12.2.2 The two-stage ZTPR
157(1)
12.2.3 The time-at-risk ZTPR
157(2)
12.3 Simulation study
159(1)
12.4 The application
160(2)
12.5 Discussion
162(1)
13 Extensions of the Chao estimator for covariate information: Poisson case
163(28)
Alberto Vidal-Diez
Dankmar Bohning
13.1 Introduction
163(1)
13.2 Generalised Chao estimator K counts and no covariates
164(2)
13.3 Generalised Chao estimator Poisson case with covariates
166(5)
13.3.1 Two counts
166(1)
13.3.2 Generalised Chao estimator Poisson case: K counts and covariates
167(2)
13.3.3 Variance estimator for NGc with K non-truncated counts and covariates
169(2)
13.4 Simulations
171(11)
13.4.1 Simulation 1: Including unexplained heterogeneity
172(6)
13.4.2 Simulation 2: Model with misclassification
178(1)
13.4.3 Simulation 3: Data generated from a negative binomial distribution
178(4)
13.5 Case study: Carcass submission from animal farms in Great Britain
182(5)
13.6 Software
187(4)
14 Population size estimation for one-inflated count data based upon the geometric distribution
191(20)
Panicha Kaskasamkul
Dankmar Bohning
14.1 Introduction and background
191(2)
14.2 The geometric model with truncation
193(1)
14.3 One-truncated geometric model
194(3)
14.3.1 One-truncated Turing estimator
195(1)
14.3.2 One-truncated maximum likelihood estimator
196(1)
14.4 Zero-truncated one-inflated geometric model
197(4)
14.4.1 Zero-truncated one-inflated maximum likelihood estimator
198(3)
14.5 Simulation study
201(3)
14.6 Real data examples
204(5)
14.6.1 Scrapie-infected holdings
206(1)
14.6.2 Domestic violence incidents in the Netherlands
207(1)
14.6.3 Illegal immigrants in the Netherlands
208(1)
14.7 Conclusion
209(2)
V Multiple Sources 211(64)
15 Dual and multiple system estimation: Fully observed and incomplete co- variates
213(16)
Peter G.M. van der Heijden
Maarten Cruyff
Joe Whittaker
Bart F.M. Bakker
Paul A. Smith
15.1 Introduction
213(2)
15.2 The population of people with Middle Eastern nationality staying in the Netherlands
215(2)
15.3 Fully observed covariates
217(6)
15.3.1 Two registers
217(3)
15.3.2 Three registers
220(1)
15.3.3 Active and passive covariates
221(1)
15.3.4 Example
222(1)
15.4 Incomplete covariates
223(3)
15.4.1 Active and passive covariates revisited
224(1)
15.4.2 Example revisited
225(1)
15.5 Conclusion
226(3)
16 Population size estimation in CRC models with continuous covariates
229(8)
Eugene Zwane
16.1 Introduction and background
229(1)
16.2 Modeling observed heterogeneity
230(3)
16.2.1 Notation
231(1)
16.2.2 Classical log-linear model
231(1)
16.2.3 Multinomial logit model
232(1)
16.2.4 Model selection
232(1)
16.2.5 Multi-model approach
233(1)
16.2.6 Bootstrap variance and confidence interval estimation
233(1)
16.3 Data set
233(1)
16.4 Results
234(1)
16.5 Conclusion
235(2)
17 Trimmed dual system estimation
237(22)
Li-Chun Zhang
John Dunne
17.1 Introduction
237(3)
17.1.1 Census coverage adjustments
238(1)
17.1.2 Replacing census with administrative sources
239(1)
17.2 Theory
240(8)
17.2.1 Ideal DSE given erroneous enumeration
240(1)
17.2.2 Trimmed DSE
241(2)
17.2.3 Stopping rules
243(2)
17.2.4 Discussion: Erroneous enumeration in both lists
245(1)
17.2.5 Discussion: Record linkage errors
246(2)
17.3 Emerging census opportunity: Ireland
248(11)
17.3.1 Background
248(1)
17.3.2 Overview of data sources
248(1)
17.3.3 Underlying assumptions and population concepts
249(3)
17.3.4 Application of TDSE
252(3)
17.3.5 Comparisons with census figures
255(1)
17.3.6 Discussion of future works
256(3)
18 Estimation of non-registered usual residents in the Netherlands
259(16)
Bart F.M. Bakker
Peter G.M. van der Heijden
Susanna C. Gerritse
18.1 Introduction
259(2)
18.2 Previous findings
261(1)
18.3 Meeting the assumptions of the capture-recapture method
262(2)
18.4 The residence duration
264(4)
18.5 Capture-recapture estimates
268(4)
18.6 Conclusion
272(3)
VI Latent Variable Models 275(86)
19 Population size estimation using a categorical latent variable
277(14)
Elena Stanghellini
Maria Giovanna Ranalli
19.1 Introduction and background
277(2)
19.2 Notation
279(1)
19.3 Concentration graphical models
280(1)
19.4 Capture-recapture estimation with graphical log-linear models with observed covariates
281(1)
19.5 Extended Latent Class models
282(1)
19.6 Identification of Extended Latent Class models
283(1)
19.7 Confidence intervals
284(1)
19.8 Example of models under unobserved heterogeneity
285(4)
19.8.1 Congenital Anomaly data
285(1)
19.8.2 Bacterial Meningitis data
286(3)
19.9 Discussion
289(2)
20 Latent class: Rasch models and marginal extensions
291(14)
Francesco Bartolucci
Antonio Forcina
20.1 Introduction and background
291(1)
20.2 Latent class: Rasch models and their extensions
292(5)
20.2.1 The basic latent class model
292(1)
20.2.2 The Rasch model
293(1)
20.2.3 Extensions based on marginal log-linear parametrisations
294(2)
20.2.4 Modelling the effect of covariates
296(1)
20.3 Likelihood inference
297(2)
20.3.1 Estimation of the model parameters
297(1)
20.3.2 Estimation of the population size
298(1)
20.4 Applications
299(4)
20.4.1 Greal Copper Butterfly
299(2)
20.4.2 Bacterial meningitis
301(2)
20.5 Appendix: Matrices used in the marginal parametrisation
303(2)
21 Performance of hierarchical log-linear models for a heterogeneous population with three lists
305(10)
Zhiyuan Ma
Chang Xuan Mao
Yitong Yang
21.1 Introduction
305(1)
21.2 Hierarchical log-linear models
306(2)
21.3 Performance given Rasch mixtures
308(2)
21.4 Simulation
310(1)
21.5 Example
310(2)
21.6 Discussion
312(1)
21.7 Appendix: Proofs of the three theorems
312(3)
22 A multidimensional Rasch model for multiple system estimation
315(26)
Elvira Pelle
David J. Hessen
Peter G.M. van der Heijden
22.1 Introduction
315(1)
22.2 Data set
316(2)
22.3 Estimating population size under the log-linear multidimensional Rasch model
318(9)
22.3.1 Notation and basic assumptions
318(1)
22.3.2 Methodology
318(5)
22.3.3 Model with a stratifying variable
323(2)
22.3.4 Assumption of measurement invariance
325(1)
22.3.5 Generalisation
326(1)
22.4 MR model and standard log-linear model
327(2)
22.5 EM algorithm to estimate missing entries
329(2)
22.6 Application to real data
331(6)
22.7 Appendix
337(4)
23 Extending the Lincoln-Petersen estimator when both sources are counts
341(20)
Rattana Lerdsuwansri
Dankmar Bohning
23.1 Introduction
341(2)
23.2 Discrete mixtures of bivariate, conditional independent Poisson distributions
343(2)
23.3 Maximum likelihood estimation for bivariate zero-truncated Poisson mixtures
345(2)
23.4 Unconditional MLE via a profile mixture likelihood
347(5)
23.4.1 Profile likelihood of the homogeneous Poisson model
348(1)
23.4.2 Profile mixture likelihood of the heterogeneous Poisson model
349(3)
23.5 Confidence interval estimation for population size N based upon the profile mixture likelihood
352(2)
23.6 A simulation study
354(1)
23.7 Real data example
355(2)
23.8 Concluding remarks
357(4)
VII Bayesian Approaches 361(26)
24 Objective Bayes estimation of the population size using Kemp distributions
363(8)
Kathryn Barger
John Bunge
24.1 Introduction and background
363(1)
24.2 The Kemp family of distributions
364(1)
24.3 The likelihood function
365(2)
24.3.1 On maximum likelihood estimation
366(1)
24.4 Objective Bayes procedures
367(1)
24.5 Data analyses
368(3)
25 Bayesian population size estimation with censored counts
371(16)
Danilo Alunni Fegatelli
Alessio Farcomeni
Luca Tardella
25.1 Introduction
371(1)
25.2 Scotland Drug Injectors data set
372(2)
25.3 Mathematical set-up
374(2)
25.3.1 Log-linear models for possibly truncated counts
374(1)
25.3.1.1 Unobserved heterogeneity
375(1)
25.4 Priors and model choice
376(4)
25.4.1 Prior choices for the population size
377(1)
25.4.1.1 Induced priors
377(2)
25.4.2 Prior choices for the other parameters
379(1)
25.4.3 Model choice
380(1)
25.5 Bayesian inference
380(2)
25.6 Data analysis
382(1)
25.7 Conclusions
383(1)
25.8 Appendix A: Induced gamma-type priors on N
383(4)
VIII Miscellaneous Topics 387(10)
26 Uncertainty assessment in capture-recapture studies and the choice of sampling effort
389(8)
Dankmar Bohning
John Bunge
Peter G.M. van der Heijden
26.1 Introduction and background
389(1)
26.2 Computing variances using conditional moments
390(1)
26.3 Application to log-linear models
391(1)
26.4 Bootstrap for capture-recapture
392(1)
26.5 Choice of sampling effort
393(1)
26.6 Lincoln-Petersen estimation and sampling effort
394(3)
References 397(20)
Index 417
Dankmar Böhning is Professor of Medical Statistics and Director of the Southampton Statistical Sciences Research Institute at the University of Southampton. His interests are in capture-recapture modelling, meta-analysis and research synthesis as well as mixed modelling.

John Bunge is Professor of Statistics in the Department of Statistical Science of Cornell University. His interests are capture-recapture modelling, microbiome statistics, and nonclassical probability distribution theory.

Peter. G.M. van der Heijden is Professor of Social Statistics at the University of Utrecht and at the University of Southampton. His interests are capture-recapture modelling for the Social Sciences and Official Statistics.
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