On some pitfalls of the log-linear modeling framework for capture-recapture studies in disease surveillance

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.