  To use historical controls for indirect comparison with single-arm trials,
the population difference between data sources should be adjusted to reduce
confounding bias. The adjustment is more difficult for time-to-event data with
a cure fraction. We propose different adjustment approaches based on pseudo
observations and calibration weighting by entropy balancing. We show a simple
way to obtain the pseudo observations for the cure rate and propose a simple
weighted estimator based on them. Estimation of the survival function in
presence of a cure fraction is also considered. Simulations are conducted to
examine the proposed approaches. An application to a breast cancer study is
presented.
