On the design of closed recapture experiments

Abstract

We propose a method to plan the number of occasions of recapture experiments for population size estimation. We do so by fixing the smallest number of capture occasions so that the expected length of the profile confidence interval is less than or equal to a fixed threshold. In some cases, we solve the optimization problem in closed form. For more complex models we use numerical optimization. We detail models assuming homogeneous, time-varying, subject-specific capture probabilities, behavioral response to capture, and combining behavioral response with subject-specific effects. The principle we propose can be extended to plan any other model specification. We formally show the validity of the approach by proving distributional convergence. We illustrate with simulations and challenging examples in epidemiology and ecology. We report that in many cases adding as few as two sampling occasions may substantially reduce the length of confidence intervals.

Fully General Chao and Zelterman Estimators with Application to a Whale Shark Population

“…An open issue is how to fix S in advance for Chao, GC, Zelterman and GZ estimators, to balance study length and precision of the estimates. For more classical models this was considered for instance in Alunni Fegatelli and Farcomeni (2016).…”

A likelihood ratio test for completed sampling in population size estimation studies

“…The population includes Gulf War (1990War ( -1991 veterans, who are known to be at higher risk of ALS, probably due to exposure to certain risk factors. The data have been revisited also in Alunni Fegatelli and Farcomeni (2016). The main issue is ascertainment bias: Are there militaries with the disease that have not been diagnosed?…”

“…This is of interest in several areas. For planning of the experiment, if the test is rejected researchers might decide to proceed with further sampling (see also Alunni Fegatelli and Farcomeni, 2016). In epidemiology, subjects might be of interest for further assessment, and neglecting to sample some of them might put them at risk; for example, some people with a disease might not be diagnosed and treated.…”