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

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