Health surveys typically have stratified multistage clustered designs in which individuals are sampled with differing probabilities. The sampling design is taken into account in a classical survey analysis by using sample-weighted estimators and variance estimators calculated at the primary-sampling-unit level. In this paper we investigate the possibility of modelling the sampling design using fixed and random effects to redefine target parameters, improve estimators of standard target parameters and improve standard variance estimators. References in which this type of additional modelling was used in health surveys are given. The problem of estimating population variance components is discussed in some detail, with an application involving estimation of between- and within-family variance components in the Hispanic Health and Nutrition Examination Survey.