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.

Proof of Theorem 3.1 Without loss of generality, we set ϵ ′ = ϵ in this proof. Let ϵ > 0, and choose E 1 = E 1 (ϵ), N = N (ϵ) and K = K(ϵ) as in condition (b). Let H n = {D n ≥ ϵ/N 2 }, and use condition (c) to choose n * = n * (ϵ) large enough so that(1)We shall use the coupling method to prove thatfor any fixed 'target time' M ≥ max(K, n * ) + N , where L(X M ) denotes the distribution of X M . The remainder of the proof follows the proof of Theorem 1 of Roberts and Rosenthal

Classic item response models assume that all items with the same difficulty have the same response probability among all respondents with the same ability. These assumptions, however, may very well be violated in practice, and it is not straightforward to assess whether these assumptions are violated, because neither the abilities of respondents nor the difficulties of items are observed. An example is an educational assessment where unobserved heterogeneity is present, arising from unobserved variables such as cultural background and upbringing of students, the quality of mentorship and other forms of emotional and professional support received by students, and other unobserved variables that may affect response probabilities. To address such violations of assumptions, we introduce a novel latent space model which assumes that both items and respondents are embedded in an unobserved metric space, with the probability of a correct response decreasing as a function of the distance between the respondent’s and the item’s position in the latent space. The resulting latent space approach provides an interaction map that represents interactions of respondents and items, and helps derive insightful diagnostic information on items as well as respondents. In practice, such interaction maps enable teachers to detect students from underrepresented groups who need more support than other students. We provide empirical evidence to demonstrate the usefulness of the proposed latent space approach, along with simulation results.

Early-phase dose-finding clinical trials are often subject to the issue of lateonset outcomes. In phase I/II clinical trials, the issue becomes more intractable because toxicity and efficacy can be competing risk outcomes such that the occurrence of the first outcome will terminate the other one. In this paper, we propose a novel Bayesian adaptive phase I/II clinical trial design to address the issue of late-onset competing risk outcomes. We use the continuation-ratio model to characterize the trinomial response outcomes and the cause-specific hazard rate method to model the competing-risk survival outcomes. We treat the late-onset outcomes as missing data and develop a Bayesian data augmentation method to impute the missing data from the observations. We also propose an adaptive dose-finding algorithm to allocate patients and identify the optimal biological dose during the trial. Simulation studies show that the proposed design yields desirable operating characteristics.

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