  We develop a method for hybrid analyses that uses external controls to
augment internal control arms in randomized controlled trials (RCT) where the
degree of borrowing is determined based on similarity between RCT and external
control patients to account for systematic differences (e.g. unmeasured
confounders). The method represents a novel extension of the power prior where
discounting weights are computed separately for each external control based on
compatibility with the randomized control data. The discounting weights are
determined using the predictive distribution for the external controls derived
via the posterior distribution for time-to-event parameters estimated from the
RCT. This method is applied using a proportional hazards regression model with
piecewise constant baseline hazard. A simulation study and a real-data example
are presented based on a completed trial in non-small cell lung cancer. It is
shown that the case weighted adaptive power prior provides robust inference
under various forms of incompatibility between the external controls and RCT
population.
