  We consider studies where multiple measures on an outcome variable are
collected over time, but some subjects drop out before the end of follow up.
Analyses of such data often proceed under either a 'last observation carried
forward' or 'missing at random' assumption. We consider two alternative
strategies for identification; the first is closely related to the
difference-in-differences methodology in the causal inference literature. The
second enables correction for violations of the parallel trend assumption, so
long as one has access to a valid 'bespoke instrumental variable'. These are
compared with existing approaches, first conceptually and then in an analysis
of data from the Framingham Heart Study.
