Using Data Augmentation to Facilitate Conduct of Phase I-II Clinical Trials with Delayed Outcomes

A practical impediment in adaptive clinical trials is that outcomes must be observed soon enough to apply decision rules to choose treatments for new patients. For example, if outcomes take up to six weeks to evaluate and the accrual rate is one patient per week, on average three new patients will be accrued while waiting to evaluate the outcomes of the previous three patients. The question is how to treat the new patients. This logistical problem persists throughout the trial. Various ad hoc practical solutions are used, none entirely satisfactory. We focus on this problem in phase I-II clinical trials that use binary toxicity and efficacy, defined in terms of event times, to choose doses adaptively for successive cohorts. We propose a general approach to this problem that treats late-onset outcomes as missing data, uses data augmentation to impute missing outcomes from posterior predictive distributions computed from partial follow-up times and complete outcome data, and applies the design's decision rules using the completed data. We illustrate the method with two cancer trials conducted using a phase I-II design based on efficacy-toxicity trade-offs, including a computer stimulation study.