  While randomized controlled trials (RCTs) are the gold standard for
estimating treatment effects in medical research, there is increasing use of
and interest in using real-world data for drug development. One such use case
is the construction of external control arms for evaluation of efficacy in
single-arm trials, particularly in cases where randomization is either
infeasible or unethical. However, it is well known that treated patients in
non-randomized studies may not be comparable to control patients -- on either
measured or unmeasured variables -- and that the underlying population
differences between the two groups may result in biased treatment effect
estimates as well as increased variability in estimation. To address these
challenges for analyses of time-to-event outcomes, we developed a meta-analytic
framework that uses historical reference studies to adjust a log hazard ratio
estimate in a new external control study for its additional bias and
variability. The set of historical studies is formed by constructing external
control arms for historical RCTs, and a meta-analysis compares the trial
controls to the external control arms. Importantly, a prospective external
control study can be performed independently of the meta-analysis using
standard causal inference techniques for observational data. We illustrate our
approach with a simulation study and an empirical example based on reference
studies for advanced non-small cell lung cancer. In our empirical analysis,
external control patients had lower survival than trial controls (hazard ratio:
0.907), but our methodology is able to correct for this bias. An implementation
of our approach is available in the R package ecmeta.
