Outcome-adaptive randomization for a delayed outcome with a short-term predictor: imputation-based designs

Delay in the outcome variable is challenging for outcome-adaptive randomization, as it creates a lag between the number of subjects accrued and the information known at the time of the analysis. Motivated by a real-life pediatric ulcerative colitis trial, we consider a case where a short-term predictor is available for the delayed outcome. When a short-term predictor is not considered, studies have shown that the asymptotic properties of many outcome-adaptive randomization designs are little affected unless the lag is unreasonably large relative to the accrual process. These theoretical results assumed independent identical delays, however, whereas delays in the presence of a short-term predictor may only be conditionally homogeneous. We consider delayed outcomes as missing and propose mitigating the delay effect by imputing them. We apply this approach to the doubly adaptive biased coin design (DBCD) for motivating pediatric ulcerative colitis trial. We provide theoretical results that if the delays, although non-homogeneous, are reasonably short relative to the accrual process similarly as in the iid delay case, the lag is also asymptotically ignorable in the sense that a standard DBCD that utilizes only observed outcomes attains target allocation ratios in the limit. Empirical studies, however, indicate that imputation-based DBCDs performed more reliably in finite samples with smaller root mean square errors. The empirical studies assumed a common clinical setting where a delayed outcome is positively correlated with a short-term predictor similarly between treatment arm groups. We varied the strength of the correlation and considered fast and slow accrual settings.