  Cluster randomized trials (CRTs) often enroll large numbers of participants,
but due to logistical and fiscal challenges, only a subset of participants may
be selected for measurement of certain outcomes, and those sampled may,
purposely or not, be unrepresentative of all participants. Missing data also
present a challenge: if sampled individuals with measured outcomes are
dissimilar from those with missing outcomes, unadjusted estimates of
arm-specific outcomes and the intervention effect may be biased. Further, CRTs
often enroll and randomize few clusters by necessity, limiting statistical
power and raising concerns about finite sample performance. Motivated by a
sub-study of the SEARCH community randomized trial on the incidence of TB
infection, we demonstrate interlocking methods to handle these challenges.
First, we extend Two-Stage targeted minimum loss-based estimation (TMLE) to
account for three sources of missingness: (1) sampling for the sub-study; (2)
measurement of baseline status among those sampled, and (3) measurement of
final status among those in the incidence cohort (i.e., persons known to be at
risk at baseline). Second, we critically evaluate the assumptions under which
sub-units of the cluster can be considered the conditionally independent unit,
improving precision and statistical power but also causing the CRT to behave
more like an observational study. Our application to the SEARCH highlights the
impact of different assumptions on measurement and dependence as well as the
real-life gains of our approach for bias reduction and efficiency improvement.
