Estimation of conditional power in the presence of auxiliary data

Conditional power (CP) is a commonly used tool to inform interim decision-making in clinical trials, but the conventional approach using only primary endpoint data to calculate CP may not perform well when the primary endpoint requires a long follow-up period, or the treatment effect size changes during the trial. Several methods have been proposed to use additional short term auxiliary data observed at the interim analysis to improve the CP estimation in these situations, however, they may rely on strong assumptions, have limited applications, or use ad hoc choices of information fraction. In this paper we propose a general framework where the true CP formula is first derived in the presence of auxiliary data, and CP estimation is obtained by substituting the unknown parameters with consistent estimators. We conducted extensive simulations to examine the performance of both proposed and conventional approaches using the true CP as the benchmark. As the proposed approach is based on the true underlying CP, the simulations confirmed its superiority over the conventional approach in terms of efficiency and accuracy, especially if observed auxiliary data reflect the change of treatment effect size. The simulations also indicate that the magnitude of improvement in CP estimation is associated with the correlation between auxiliary and primary endpoints and/or the magnitude of the effect size change during the trial.