  In epidemiological studies, the capture-recapture (CRC) method is a powerful
tool that can be used to estimate the number of diseased cases or potentially
disease prevalence based on data from overlapping surveillance systems.
Estimators derived from log-linear models are widely applied by epidemiologists
when analyzing CRC data. The popularity of the log-linear model framework is
largely associated with its accessibility and the fact that interaction terms
can allow for certain types of dependency among data streams. In this work, we
shed new light on significant pitfalls associated with the log-linear model
framework in the context of CRC using real data examples and simulation
studies. First, we demonstrate that the log-linear model paradigm is highly
exclusionary. That is, it can exclude, by design, many possible estimates that
are potentially consistent with the observed data. Second, we clarify the ways
in which regularly used model selection metrics (e.g., information criteria)
are fundamentally deceiving in the effort to select a best model in this
setting. By focusing attention on these important cautionary points and on the
fundamental untestable dependency assumption made when fitting a log-linear
model to CRC data, we hope to improve the quality of and transparency
associated with subsequent surveillance-based CRC estimates of case counts.
