Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

(1976). Survival Distributions: Reliability Applications in the Biomedical Sciences. Technometrics: Vol. 18, No. 4, pp. 501-501.

Survival Distributions: Reliability Applications in the Biomedical Sciences

Analysis of Binary Data.

67A Designed extension of studies based on conditional power

Outcome-adaptive randomization is one of the possible elements of an adaptive trial design in which the ratio of patients randomly assigned to the experimental treatment arm versus the control treatment arm changes from 1:1 over time to randomly assigning a higher proportion of patients to the arm that is doing better. Outcome-adaptive randomization has intuitive appeal in that, on average, a higher proportion of patients will be treated on the better treatment arm (if there is one). In both the randomized phase II and phase III settings with a short-term binary outcome, we compare outcome-adaptive randomization with designs that use 1:1 and 2:1 fixed-ratio randomizations (in the latter, twice as many patients are randomly assigned to the experimental treatment arm). The comparisons are done in terms of required sample sizes, the numbers and proportions of patients having an inferior outcome, and we restrict attention to the situation in which one treatment arm is a control treatment (rather than the less common situation of two experimental treatments without a control treatment). With no differential patient accrual rates because of the trial design, we find no benefits to outcome-adaptive randomization over 1:1 randomization, and we recommend the latter. If it is thought that the patient accrual rates will be substantially higher because of the possibility of a higher proportion of patients being randomly assigned to the experimental treatment (because the trial will be more attractive to patients and clinicians), we recommend using a fixed 2:1 randomization instead of an outcome-adaptive randomization.

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Outcome-Adaptive Randomization: Is It Useful?

SUMMARY Adaptive designs are often used in clinical trials to force balance in sequential allocation of patients between two or more competitive treatments. Sometimes, from ethical considerations, the goal may be to allocate a larger number of patients to the better treatment in the course of the trial. In the present paper we consider patients who are heterogeneous with respect to some prognostic factors and assume that the response from each patient is a continuous variable. We consider a normal linear model and provide an allocation design with due attention to the prognostic factors. The loss of efficiency incurred by using a balanced design is also indicated. Issues of inference based on adaptive allocation are also discussed. Finally a guideline is provided for the appropriate choice of the design parameters.

https://www.jstor.org/stable/pdfplus/2673489.pdf

Adaptive designs for normal responses with prognostic factors

In the present work, we develop a two-stage allocation rule for binary response using the log-odds ratio within the Bayesian framework allowing the current allocation to depend on the covariate value of the current subject. We study, both numerically and theoretically, several exact and limiting properties of this design. The applicability of the proposed methodology is illustrated by using some data set. We compare this rule with some of the existing rules by computing various performance measures.

A covariate adjusted two-stage allocation design for binary responses in randomized clinical trials.

A randomized two-stage adaptive Bayesian design is proposed and studied for allocation and comparison in a phase III clinical trial with survival time as treatment response. Several exact and limiting properties of the design and the follow-up inference are studied, both numerically and theoretically, and are compared with a single-stage randomized procedure. The applicability of the proposed methodology is illustrated by using some real data.

A Bayesian adaptive design for two-stage clinical trials with survival data

In the context of comparing two treatments in clinical trials, randomized play-the-winner rule is used with a goal to treat more patients by the better treatment. On its basis some decision rules are proposed taking delayed response into account. Some exact and asymptotic results of the decision rules are studied. Minimax decison rule is also obtained.

Delayed Response in Randomized Play-The-Winner Rule; A Decision Theoretic Outlook

In the present work, we introduce a partial sequential sampling scheme to develop a sequential rank-based nonparametric test for the identity of two unknown univariate continuous distribution functions against one-sided shift in location occurring at an unknown time point. Our work is motivated by Wolfe (1977) as well as Orban and Wolfe (1980). We provide detailed discussion on asymptotic studies related to the proposed test. We compare the proposed test with a usual rank-based test. Some simulation studies are also presented.

Uttam Bandyopadhyay

Papers

Adaptive designs for normal responses with prognostic factors

A covariate adjusted two-stage allocation design for binary responses in randomized clinical trials.

A Bayesian adaptive design for two-stage clinical trials with survival data

Delayed Response in Randomized Play-The-Winner Rule; A Decision Theoretic Outlook

Nonparametric Partial Sequential Test for Location Shift at an Unknown Time Point