Gao S, Hui SL, Hall KS, Hendrie HC. Estimating disease prevalence from two-phase surveys with non-response at the second phase. Stat Med 2000;19(16):2101-2114.

In this paper we compare several methods for estimating population disease prevalence from data collected by two-phase sampling when there is non-response at the second phase. The traditional weighting type estimator requires the missing completely at random assumption and may yield biased estimates if the assumption does not hold. We review two approaches and propose one new approach to adjust for non-response assuming that the non-response depends on a set of covariates collected at the first phase: an adjusted weighting type estimator using estimated response probability from a response model; and a regression type estimator combining the adjusted weighting type estimator and the modelling type estimator. The estimators are illustrated using data from an Alzheimer's disease study in two population.