Logistic analysis of studies with two-stage sampling: a comparison of four approaches

This paper discusses the analysis of two-stage studies where covariates are missing or measured with error at the first stage of sampling and are validated at the second stage in a subsample. Four recently developed approaches, the weighted pseudo-likelihood method of Flanders and Greenland (1991), the pseudo-conditional likelihood methods of Breslow and Cain (1988) and Schill et al. (1993) and the maximum likelihood estimate obtained via the EM-algorithm (Wacholder and Weinberg, 1994) are reviewed, and some connections between them are established. It is shown that, with respect to odds ratio estimation, case-control designs can be analysed as if first-stage sampling had been prospective. The procedures are numerically compared with respect to asymptotic relative efficiency in a missing value setting.