  Motivated by a clinical trial conducted by Janssen Pharmaceuticals in which a
flexible dosing regimen is compared to placebo, we evaluate how switchers in
the treatment arm (i.e., patients who were switched to the higher dose) would
have fared had they been kept on the low dose. This in order to understand
whether flexible dosing is potentially beneficial for them. Simply comparing
these patients' responses with those of patients who stayed on the low dose is
unsatisfactory because the latter patients are usually in a better health
condition. Because the available information in the considered trial is too
scarce to enable a reliable adjustment, we will instead transport data from a
fixed dosing trial that has been conducted concurrently on the same target,
albeit not in an identical patient population. In particular, we will propose
an estimator which relies on an outcome model and a propensity score model for
the association between study and patient characteristics. The proposed
estimator is asymptotically unbiased if at least one of both models is
correctly specified, and efficient (under the model defined by the restrictions
on the propensity score) when both models are correctly specified. We show that
the proposed method for using results from an external study is generically
applicable in studies where a classical confounding adjustment is not possible
due to positivity violation (e.g., studies where switching takes place in a
deterministic manner). Monte Carlo simulations and application to the
motivating study demonstrate adequate performance.
