Statistical Quality Control By M Mahajan Pdf.rar
Honorato Winkel
Adaptive designs offer added flexibility in the execution of clinical trials, including the possibilities of allocating more patients to the treatments that turned out more successful, and early stopping due to either declared success or futility. Commonly applied adaptive designs, such as group sequential methods, are based on the frequentist paradigm and on ideas from statistical significance testing. Interim checks during the trial will have the effect of inflating the Type 1 error rate, or, if this rate is controlled and kept fixed, lowering the power.
These classical approaches in the design and execution of clinical trials have been challenged from both foundational and practical perspectives. Important early contributions include, e.g., Thompson [11], Flhler et al. [12], Berry [13], Spiegelhalter et al. [14], Berger and Berry [15], Spiegelhalter et al. [16] and Thall and Simon [17]; for a brief historical account and a large number of references, see Grieve [18]. Comprehensive expositions of the topic are provided in the monographs Spiegelhalter et al. [19], Berry et al. [20] and Yuan et al. [21].
The key argument here is the change of focus: instead of guarding against false positives in a series of trials in long term, the main aim is to utilize the full information potential in the observed data from the ongoing trial itself. Then, looking into the data in interim analyses is not viewed as something incurring a cost, but rather, as providing an opportunity to act more wisely. The foundational arguments enabling this change are provided by the adoption of the likelihood principle, e.g., Berger and Wolpert [22].
In practice, this also implies a change of the inferential paradigm, from frequentist into Bayesian. In Bayesian inference, the conditional (posterior) distribution for unknown model parameters is being updated based on the available data, via updates of the corresponding likelihood. In a clinical trial, it is even possible to continuously monitor the outcome data as they are observed, and thereby utilize such data in a fully adaptive fashion during the execution of the trial. The advantages of this approach are summarized neatly in the short review paper Berry [23], in Berry [24], Lee and Chu [25], and more recently, in Yin et al. [26], Ruberg et al. [27] and Giovagnoli [28]. Importantly, the posterior probabilities provide intuitively meaningful and directly interpretable answers to questions concerning the mutual comparison of different treatments, given the available evidence, and do so without needing reference to concepts such as sampling distribution of a test statistic under given hypothetical circumstances.
MAMS designs, on the other hand, aim at selecting the best treatments, or even the single best if there is one, of several that are tested in a multi-arm trial. This is often done indirectly by applying pre-specified stopping boundaries, to determine whether a considered treatment should be dropped. Recent contributions to such designs include Wason and Jaki [37], Wason and Trippa [38], Jacob et al. [39], Wathen and Thall [32], Yu et al. [40], Ryan et al. [33] and Ryan et al. [35].
Unfortunately, general results on optimal strategies are largely lacking and their application in practice often infeasible because of computational complexity; however, see Press [41] and Yu et al. [40]. Recently, simulation based approximations have been used for applying Bayesian decision theory in the clinical trials context, e.g., Mller et al. [42], Yuan et al. [21], Alban et al. [43] and Bassi et al. [36].
Here we consider adaptive designs mainly from the perspective of multi-arm phase II clinical trials, in which one or more experimental treatments are compared to a control. However, the same ideas can be applied, essentially without change, in confirmatory phase III trials, where usually only a single experimental treatment is compared to a control, but the planned size of the trial is larger. In both situations, treatment allocation of individual trial participants is assumed to take place according to a fixed block randomization, albeit with an important twist: The performance of each treatment arm is assessed after every measured outcome in terms of the posterior distribution of a corresponding model parameter. Different treatments arms are then compared to each other according to pre-defined criteria. If a treatment arm is found to be inferior in such a comparison to the others, it can be closed off either temporarily or permanently from further accrual.
We consider first, in The case of Bernoulli outcomes section, the simple situation in which the outcomes are binary, and they can be observed soon after the treatment has been delivered. In namerefsection:no:3 section, the approach is extended to cover situations in which either binary outcomes are measured after a fixed time lag from the treatment, or the data consist of time-to-event measurements, with the possibility of right censoring. This section includes also some notes on vaccine efficacy trials. The paper concludes with a discussion in Discussion section. A Supplement accompanied with the main text reports results from extensive simulation experiments, which follow closely the settings of two examples in Villar et al. [30] but apply the adaptive methods introduced in The case of Bernoulli outcomes section. The presentation is to a large extent comparative and expository. As a companion to this paper, we provide an implementation of the proposed method in the form of a freely available R package called barts, Marttila et al. [44], that facilitates the simulation of clinical trials with adaptive treatment allocation and selection.
Allocation of the participants to the different treatment arms is now assumed to follow this list, but with the possibility of skipping a treatment arm in case it has been determined to be in the dormant state for the considered value of n. This leads to a balanced design in the sense that, as long as no treatment arms have been skipped by the time of considering list index n, the numbers of participants allocated to different treatments can differ from each other by at most 1, and they are equal when n is a multiple of K+1.
The distinction between active and dormant states is that no trial participants are allocated, at a value n of the list index, to a treatment arm r(n) if it is in the dormant state. Generally speaking, treatments whose performance in the trial has been poor, in a relative sense to the others, are more likely to be transferred into the dormant sate. However, with more data, there may later turn out to be sufficient evidence for such a trial arm to be returned back to the active state.
While application of BARTA may at least temporarily inactivate some less successful treatment arms and thereby close them off from further accrual, this closure need not be final. As long as a treatment arm is in the dormant state, and given that the priors for different treatments have been assumed to be independent, the posterior for the corresponding parameter θk remains fixed. In contrast, with the accrual of participants to active treatment arms still continuing, the posteriors for their parameters can be expected to become less and less dispersed. As a consequence, returns from dormant to active state tend to become increasingly rare.
Note also that, in BARTA, all currently active treatment arms in a block are considered symmetrically, with exactly one patient allocated to each active treatment; after this has been done, the algorithm proceeds to considering the next permutation of the K+1 treatments, etc. Unless this is not regulated differently by the prior, fully balanced block randomization of all K+1 treatments, reminiscent to a burn-in, is applied during the early part of the trial, until there is one arm that is made dormant.
To compare, most AR-designs suggested in the literature update the randomization probabilities only at the times of a few pre-planned interim analyses, whereas in the prototype version of BARTA, the posterior probabilities for determining the activity states are computed after every new measured outcome. If such a continuous monitoring scheme is difficult to employ in practice, for example, for logistic reasons, it can in principle be replaced by any more appropriate non-informative stopping rule. However, the results in Viele et al. [35] suggest that, in AR designs, more frequent checks and updates are advantageous from the perspective of several different performance measures, and the same is likely to hold for BARTA as well.
With this in mind, we complement BARTA with an optional possibility to conclusively terminate the accrual of additional participants to the less successful treatment arms. The consequent algorithm BARTS (for Bayesian adaptive rule for treatment selection), is provided in the form of a pseudocode in Section A of the Supplement. The treatment allocation procedure is identical to that in BARTA, and makes a treatment arm dormant if its performance, according to pre-specified criteria, is assessed to be poor when compared to the current best. BARTS does the same, but will actually drop a treatment arm permanently if such judgement holds with respect to an even stricter criterion. BARTS can therefore be said to be an adaptation of corresponding ideas and definitions in, e.g., Thall and Wathen [47], Berry et al. [20], Xie et al. [48], Jacob et al. [39] and Wathen and Thall [32]. In the commonly adopted terminology of adaptive designs, it can be said to combine elements from different versions of AR and MAMS designs.
After every new observed outcome, the algorithm of BARTS determines the current state of each treatment arm, choosing between the three possible options: active, dormant, or dropped. All moves between these states are possible except that the dropped state is absorbing: once a treatment arm has been dropped, it will stay. If an arm is in dormant state, it is at least momentarily closed from further patient accrual.
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