Increasing efficiency for estimating treatment-biomarker interactions with historical data

Detecting a treatment-biomarker interaction, which is a task better suited for large sample sizes, in a phase II trial, which has a small sample size, is challenging. In this paper, we investigate how two plausibly available sources of historical data may contain partial information to help estimate the treatment-biomarker interaction parameter in a randomized phase II study. The parameter is not identified in either historical dataset alone; nonetheless, both can provide some information about the parameter and, consequently, increase the precision of its estimate. To illustrate the potential for gains in efficiency and implications for the design of the study, we consider Gaussian outcomes and biomarker data and calculate the asymptotic variance using the expected Fisher information matrix. We quantify the gain in efficiency both through a numerical study and, in a simplified setting, insights derived from an algebraic development of the problem. We find that a non-negligible gain in precision is possible, even if the historical and prospective data do not arise from identical underlying models.