Sensitivity and Uncertainty Analysis for Two-Stream Capture-Recapture in Epidemiological Surveillance Open Access

Chen, Jiandong (Spring 2020)

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The capture-recapture approach is a well-studied paradigm for estimating wildlife population sizes, based on tag and release strategies. Statistical methods associated with this approach are also used in epidemiological studies to estimate total numbers (N) of cases or deaths from multiple registries. Using simulated data and DRS data on death obtained from a Population Change Survey conducted by the National Statistical Office in Malawi between 1970 to 1972 as examples, sensitivity and uncertainty analyses are proposed and incorporated to provide a more defensible picture of variability in estimates of homogeneous population size when the assumption of list independence fails in the two-capture scenario. In this report, maximum likelihood estimators (MLEs) for population size (N) and the variance of these MLEs are formulated upon fixing the values of key non-identifiable parameters. A discussion is made of the placement of the Lincoln-Petersen (LP) estimate and the estimator of Chao (1987) on the proposed sensitivity analysis plots, and the proposed uncertainty analyses are demonstrated and evaluated through simulations based on two prior assumptions for a key parameter upon which estimation hinges. Some features of the proposed MLEs are also highlighted in this report.

Table of Contents

Table of Contents

1. Introduction

2. Methods

2.1 Preliminaries

2.2 Maximum likelihood estimators (MLEs) and variance based on known ψ=p2|1

2.3 Maximum likelihood estimators (MLEs) and variance based on known ϕ=p2|1p2|1

2.4 Clarification for the formulas of MLEs based on ψ and ϕ

2.5 Sensitivity Analysis

2.6 Uncertainty Analysis

3. Results

4. Discussion

5. Tables and Figures

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