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Interval estimation for Poisson capture–recapture models in epidemiology
Author(s) -
Farrington C. P.
Publication year - 2002
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1223
Subject(s) - poisson distribution , multinomial distribution , mark and recapture , statistics , poisson regression , interval (graph theory) , count data , econometrics , interval estimation , population , generalized linear model , confidence interval , computer science , mathematics , demography , combinatorics , sociology
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. Copyright © 2002 John Wiley & Sons, Ltd.