  A common problem in health research is that we have a large database with
many variables measured on a large number of individuals. We are interested in
measuring additional variables on a subsample; these measurements may be newly
available, or expensive, or simply not considered when the data were first
collected. The intended use for the new measurements is to fit a regression
model generalisable to the whole cohort (and to its source population). This is
a two-phase sampling problem; it differs from some other two-phase sampling
problems in the richness of the phase I data and in the goal of regression
modelling. In particular, an important special case is measurement-error
models, where a variable strongly correlated with the phase II measurements is
available at phase I. We will explain how influence functions have been useful
as a unifying concept for extending classical results to this setting, and
describe the steps from designing for a simple weighted estimator at known
parameter values through adaptive multiwave designs and the use of prior
information. We will conclude with some comments on the information gap between
design-based and model-based estimators in this setting.
