  We discuss generalizability analyses under a partially nested trial design,
where part of the trial is nested within a cohort of trial-eligible
individuals, while the rest of the trial is not nested. This design arises, for
example, when only some centers participating in a trial are able to collect
data on non-randomized individuals, or when data on non-randomized individuals
cannot be collected for the full duration of the trial. Our work is motivated
by the Necrotizing Enterocolitis Surgery Trial (NEST) that compared initial
laparotomy versus peritoneal drain for infants with necrotizing enterocolitis
or spontaneous intestinal perforation. During the first phase of the study,
data were collected from randomized individuals as well as consenting
non-randomized individuals; during the second phase of the study, however, data
were only collected from randomized individuals, resulting in a partially
nested trial design. We propose methods for generalizability analyses with
partially nested trial designs. We describe identification conditions and
propose estimators for causal estimands in the target population of all
trial-eligible individuals, both randomized and non-randomized, in the part of
the data where the trial is nested, while using trial information spanning both
parts. We evaluate the estimators in a simulation study.
