Rob van Hest Capture-recapture Methods in Surveillance - RePub ...

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Methodology of capture-recapture analysis developed for capture-recapture analysis by Fienberg. 3 With three registers there are eight possible combinations of these registers in which cases do or do not appear. The general model uses eight parameters, the common parameter (the logarithm of the number expected to be in all lists), three ‘main effects’ parameters (the log odds ratios against appearing in each list for cases who appear in the others), three ‘two-way interactions’ or second order effect parameters (the log odds ratios between pairs of lists for cases who appear in the other), and a ‘three-way’ interaction parameter. For three registers, A with i levels, B with j levels, C with k levels, the natural logarithm (ln or loge) of expected frequency F ijk for cell ijk, ln F ijk, can be denoted as A B C AB AC BC ABC lnFijk = θ + λi + λ j + λk + λij + λik + λ jk + λijk whereθ is the common parameter , λ A , λ B , and λ C are the main effect parameters, λ AB , λ AC and λ BC are the second order effect (two-way interaction) parameters and λ ABC is the highest order effect (three-way interaction) parameter. The value of this last three-way interaction parameter can not be tested from the study data and is assumed to be zero. Assumptions about the other parameters can be tested, although these tests may not be very powerful for small samples. Three types of log-linear models can be recognised. Firstly, the ‘independent model’ which assumes that all registers are independent. Secondly, models that are equivalent to two independent registers or two independent subsets of registers. Finally, a ‘saturated’ model that incorporates all possible interactions, including possible three-way interaction. To assess how the various log-linear models fit the data (model fitting) the log likelihood-ratio test, also known as G 2 or deviance, is used, denoted as (2.4) G 2 = -2∑Obs j ln[Obs j /Exp ji] (2.5) where Obs j is the observed number of individuals in each cell j, and Exp ji is the expected number of individuals in each cell j under model i. The lower the value of G 2 the better is the fit of the model. In the log-linear estimation procedure after model fitting follows model selection, i.e. to identify the models that are clearly wrong and select from a number of acceptable models the most appropriate. For model selection, apart from previous knowledge and expectations about dependencies between registers and heterogeneity of the population, formal procedures based upon likelihood-ratio tests, known as information criteria, can be used. One of these procedures is Akaike’s Information Criterion (AIC) 24 which can be expressed as AIC = G 2 – 2 [df] (2.6) The first term, G 2 , is a measure of how well the model fits the data and the second term, 2 [df], is a penalty for the addition of parameters (and hence model complexity). Another information criterion is the Bayesian Information Criterion (BIC) 25 which can be expressed as BIC = G 2 – [ln Nobs] [df] (2.7) where Nobs is the total number of observed individuals. Relative to the AIC, the BIC penalises complex models more heavily. In general, in the log-linear capture-recapture estimation procedure the least complex, i.e. the least saturated (in other words the most 27
Chapter 2 parsimonious) model, whose fit appears adequate, is preferred. 11 Since the G 2 of the saturated model is zero and has no degrees of freedom left, the AIC and BIC are also zero and models with a negative AIC and BIC are preferred although this does not necessarily mean that the estimate is correct. When the saturated model is selected by any criterion the investigator should be particularly cautious about using the associated outcome. 7,26 However, when external considerations do not justify the presumption of plausible interactions of sources in the simpler models, some advocate the saturated model. 27 The confidence interval around log-linear estimates can be constructed based on likelihood-ratio statistics. 28,29 However, any confidence interval only adjusts for sampling fluctuation but it does not adjust for any uncertainty as to whether the underlying assumptions are violated. 27 With an increasing number of registers, the number of possible capture-recapture models rapidly increases. Programs for the analysis of loglinear models exist in most large statistical computer packages, such as S+, SAS and SPSS, and some have been specially developed for capture-recapture analysis, e.g. GLIM, 30 MARK 31 and CARE. 32 2.1.5 Truncated models As an alternative to the more conventional two-source and log-linear multiple-source capture-recapture analysis, so-called truncated models have been employed, assuming a specific distribution of the observed data, e.g. Poisson, binomial or a mixture of different distributions. 7 Truncated models, such as Zelterman’s truncated Poisson mixture model and Chao’s heterogeneity and bias-corrected homogeneity models 33-35 can be applied to frequency counts of observations of cases in a single register or multiple registers, with the aim to estimate the number of unobserved persons in the (truncated) zero-frequency class, based upon information of the lower frequency classes. These models have been used in genetic epidemiology 36 and social sciences, e.g. to estimate the size of hidden populations of illicit drug users and homeless persons. 37-40 The simple estimators do not need statistical packages, Zelterman’s model supposedly allows for greater flexibility and applicability on real life data and the Zelterman and Chao models are arguably more robust to violation of the homogeneity assumption because they are partly based upon the lower frequency classes, assumed to have more resemblance to the zero frequency class. Despite obvious violation of other underlying assumptions, especially the independent registers assumption in case of multiple sources or the constant individual probability of re-observation assumption in case of a single source 39,40 , truncated models have performed well when compared to log-linear capture-recapture estimates. 41 An overview of a range of truncated models is given elsewhere. 42 28
Page 1 and 2: Capture-recapture Methods in Survei
Page 3 and 4: Colofon Capture-recapture methods i
Page 5 and 6: Promotiecommissie Promotor: Prof.dr
Page 8: Contents Page 1 Introduction 9 2 Me
Page 11 and 12: Chapter 1 1.1 Assessing completenes
Page 13 and 14: Chapter 1 94% among AIDS patients w
Page 15 and 16: Table 1.1 Objectives, methods, data
Page 17 and 18: Researchers Objective Method Data-s
Page 19 and 20: Chapter 1 source capture-recapture
Page 21 and 22: Chapter 1 32. Bradley BL, Kerr KM,
Page 24 and 25: 2 Methodology of capture-recapture
Page 26 and 27: Methodology of capture-recapture an
Page 36: Methodology of capture-recapture an
Page 39 and 40: Chapter 3 3.1 Application of captur
Page 41 and 42: Table 3.1 Published capture-recaptu
Page 43 and 44: Disease Authors Objective Method Da
Page 49 and 50: Chapter 3 3.3 References 1. Hook EB
Page 51 and 52: Chapter 3 52. Reintjes R, Termorshu
Page 53 and 54: Chapter 4 Abstract The aim of this
Page 55 and 56: Chapter 4 Methods Nearly all Dutch
Page 57 and 58: Chapter 4 Table 4.2 The number of m
Page 59 and 60: Chapter 4 diagnosis. Other patients
Page 61 and 62: Chapter 4 stratify the population i
Page 63 and 64: Chapter 4 25. Lambeth, Southwark an
Page 65 and 66: Chapter 5 Abstract To estimate inci
Page 67 and 68: Chapter 5 patients. Capture-recaptu
Page 69 and 70: Chapter 5 Figure 5.1 Four regions o
Page 71 and 72: Chapter 5 Hospital records From 385
Page 73 and 74: Chapter 5 Table 5.1 Epidemiological
Page 75 and 76: Table 5.2 Number and proportion of
Page 77 and 78: Chapter 5 cautious about the associ
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Chapter 5 Incidence of community-ac
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Chapter 6 Abstract The aim of this
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Chapter 6 3. Hospitalised patients
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Chapter 6 Record-linkage of all 537
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Chapter 6 Figure 6.1 Schematic view
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Chapter 6 Table 6.2 Total and strat
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Chapter 6 administrative discrepanc
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Chapter 6 the patients, and complet
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7 Undetected burden of tuberculosis
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Introduction Underreporting of tube
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Underreporting of tuberculosis in t
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Table 7.1 Total and subset numbers
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Table 7.2 Capture-recapture estimat
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Chapter 8 Abstract In 1999 the Enha
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Chapter 8 bacteriological confirmat
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Chapter 8 Results Table 8.1 shows t
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Table 8.3 Annual and overall observ
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Table 8.4 Annual and overall estima
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Chapter 8 interaction however, i.e.
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Chapter 8 shows that observed under
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9 Estimating the coverage of tuberc
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Introduction Estimating targeted mo
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Estimating targeted mobile tubercul
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References Estimating targeted mobi
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10 Estimating infectious diseases i
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Introduction Estimating infectious
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Estimating infectious disease incid
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Study Disease and number of patient
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4. Gallay A, Vaillant V, Bouvet P,
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Table 10.3 Comparison of the variou
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Discussion Estimating infectious di
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Chapter 11 The aim of this thesis i
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Chapter 11 overestimation of the nu
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Chapter 11 clinicians to the Public
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Chapter 11 operation with the chest
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Chapter 11 of the proportion of fal
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Chapter 11 Question 3: What is the
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Chapter 11 11.2 Some findings of th
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Chapter 11 • To improve timelines
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Summary Summary Surveillance is an
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Summary linkage of notification and
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Samenvatting Samenvatting Surveilla
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Samenvatting subgroepen binnen de b
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Acknowledgements Acknowledgements W
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Curriculum vitae Rob van Hest was b
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Publications This thesis Van Hest N
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