  Cluster randomized trials with measurements at baseline can improve power
over post-test only designs by using difference in difference designs. However,
subjects may be lost to follow-up between the baseline and follow-up periods.
While equations for sample size and variance have been developed assuming no
loss to follow-up ("cohort") and completely different subjects at baseline and
follow-up ("cross-sectional") difference in difference designs, equations have
yet to be developed when some subjects are observed in both periods ("mixture"
designs). We present a general equation for calculating the variance in
difference in difference designs and derive special cases assuming loss to
follow-up with replacement of lost subjects and assuming loss to follow-up with
no replacement but retaining the baseline measurements of all subjects.
Relative efficiency plots, plots of variance against subject autocorrelation,
and plots of variance by follow-up rate and subject autocorrelation are used to
compare cohort, cross-sectional, and mixture approaches. Results indicate that
when loss to follow-up to uncommon, mixture designs are almost as efficient as
cohort designs with a given initial sample size. When loss to follow-up is
common, mixture designs with full replacement maintain efficiency relative to
cohort designs. Finally, our results provide guidance on whether to replace
lost subjects during trial design and analysis.
