Bayesian optimal adaptive designs for delayed-response dose-finding studies

Bayesian adaptive design has been broadly recognized as a method of improving the efficiency of determining dose-response relationships in clinical trials, thus leading to reliable dose selection for phase III clinical trials. However, in some disease areas such as diabetes and obesity, patients may need to be studied for several weeks or months for a drug effect to emerge. These delayed-response studies provide challenges for using traditional adaptive design methods. Many current methods for analyzing the data at the time of the interim analysis only use the last observation from patients who have completed the study. Data for those patients who have not completed the study are often ignored or imputed via last observation carried forward (LOCF) or other imputation method. Therefore, data collected at intermediate timepoints are not fully used for decision making. These approaches are useful for studies where the final responses can be quickly observed. However, in delayed-response studies, where longitudinal data are normally collected for each patient, using all available information instead of just endpoint values is critical to improving efficiency. Fu and Manner (2010) proposed an integrated two-component prediction (ITP) model for delayed-response adaptive design. In this paper, we extend their ITP model to incorporate a dose-response model in it and propose an ITP Emax model. Furthermore, we derive a method to find the minimum effective dose (MED) for our newly proposed model by using an optimal design theorem. By using the proposed method, a better understanding of the dose-response relationship and the MED was achieved more efficiently. Potential sample size reduction is also discussed in this paper.