A case study of an adaptive design for a clinical trial with 2 doses and 2 endpoints in a rare disease area

Patient recruitment is challenging in rare disease clinical trials. To save time and resources, an inferential seamless phase II/III clinical trial design is considered for a clinical trial in a rare disease area. In particular, 2 doses compared to a placebo control are evaluated at phase II (ie, stage I). Based on the results of a phase II intermediate endpoint, additional patients may be enrolled into the 2 doses and control, 1 selected dose and control, or none of the 3 treatment arms at stage II. All patients including those of unselected dose (s) will be followed for the measurements of the phase III (ie, stage II) primary and secondary endpoints and incorporated in the final analysis. Under a reasonable condition, the type I error rate will be controlled at the nominal level if the same nominal level is applied for testing a dose effect based on either only the data of patients of stage I (in case the dose is not selected for stage II) or data of patients of stages I and II combined. A graphical testing procedure is also introduced for multiplicity adjustments to account for the 2 doses and 2 endpoints for the overall type I error rate control. Moreover, an imputation approach is proposed for conditional power calculation at stage I for a sample size adaptive design. Simulations are carried out under different parameter configurations to compare the performances of various approaches. The trial example is further used to illustrate the applications of the methods.