  Shared controls in platform trials comprise concurrent and non-concurrent
controls. For a given experimental arm, non-concurrent controls refer to data
from patients allocated to the control arm before the arm enters the trial. The
use of non-concurrent controls in the analysis is attractive because it may
increase the trial's power of testing treatment differences while decreasing
the sample size. However, since arms are added sequentially in the trial,
randomization occurs at different times, which can introduce bias in the
estimates due to time trends. In this article, we present methods to
incorporate non-concurrent control data in treatment-control comparisons,
allowing for time trends. We focus mainly on frequentist approaches that model
the time trend and Bayesian strategies that limit the borrowing level depending
on the heterogeneity between concurrent and non-concurrent controls. We examine
the impact of time trends, overlap between experimental treatment arms and
entry times of arms in the trial on the operating characteristics of treatment
effect estimators for each method under different patterns for the time trends.
We argue under which conditions the methods lead to type 1 error control and
discuss the gain in power compared to trials only using concurrent controls by
means of a simulation study in which methods are compared.
