Capture-recapture, epidemiology, and list mismatches: two lists

In recent years, capture-recapture methods for closed populations have been extensively applied to epidemiology. For example, suppose we have several incomplete lists of diabetics and we wish to estimate the total number of diabetics by estimating the number missing from all the lists. A major problem is that the information about individuals on the lists may have been given incorrectly or the information may have been typed incorrectly so that some list matches are missed. Using the concept of tag loss borrowed from animal population studies, we consider methods for estimating both the probabilities of making list errors and the population size for just two independent lists. The effect of heterogeneity on the errors is examined. The methods are applied to a large data set of diabetic persons consisting of a list obtained from a survey and a list obtained from doctors' records. It was found that the error rates were high and that ignoring the errors led to a gross overestimate of the total number of diabetic persons.