Interval estimation for Poisson capture-recapture models in epidemiological studies

Capture-recapture studies in epidemiology are frequently undertaken to adjust underlying rates for underreporting. This contrasts with applications in ecology, in which the aim is to estimate population size. In consequence, the Poisson model provides a more appropriate framework than the multinomial in some epidemiological applications. A method for constructing profile Poisson likelihood interval estimates using log-linear modelling, avoiding the need for constrained optimization, is described for several relevant parameters, including the unobserved disease rate, the total disease rate, and the case ascertainment probability. Asymptotic properties of these estimates are studied and contrasted with those derived from the multinomial model. The method is illustrated with a published data set on spina bifida