A multiple-record systems estimation method that takes observed and unobserved heterogeneity into account

We present a model to estimate the size of an unknown population from a number of lists that applies when the assumptions of (a) homogeneity of capture probabilities of individuals and (b) marginal independence of lists are violated. This situation typically occurs in epidemiological studies, where the heterogeneity of individuals is severe and researchers cannot control the independence between sources of ascertainment. We discuss the situation when categorical covariates are available and the interest is not only in the total undercount, but also in the undercount within each stratum resulting from the cross-classification of the covariates. We also present several techniques for determining confidence intervals of the undercount within each stratum using the profile log likelihood, thereby extending the work of Cormack (1992, Biometrics48, 567-576).