  The primary analysis in two-arm clinical trials usually involves inference on
a scalar treatment effect parameter; e.g., depending on the outcome, the
difference of treatment-specific means, risk difference, risk ratio, or odds
ratio. Most clinical trials are monitored for the possibility of early
stopping. Because ordinarily the outcome on any given subject can be
ascertained only after some time lag, at the time of an interim analysis, among
the subjects already enrolled, the outcome is known for only a subset and is
effectively censored for those who have not been enrolled sufficiently long for
it to be observed. Typically, the interim analysis is based only on the data
from subjects for whom the outcome has been ascertained. A goal of an interim
analysis is to stop the trial as soon as the evidence is strong enough to do
so, suggesting that the analysis ideally should make the most efficient use of
all available data, thus including information on censoring as well as other
baseline and time-dependent covariates in a principled way. A general group
sequential framework is proposed for clinical trials with a time-lagged
outcome. Treatment effect estimators that take account of censoring and
incorporate covariate information at an interim analysis are derived using
semiparametric theory and are demonstrated to lead to stronger evidence for
early stopping than standard approaches. The associated test statistics are
shown to have the independent increments structure, so that standard software
can be used to obtain stopping boundaries.
