Multi-arm response-adaptive designs for circular responses

A multi-arm response-adaptive allocation design is developed for circular treatment outcomes. Several exact and asymptotic properties of the design are studied. Stage-wise treatment selection procedures based on the proposed response-adaptive design are also suggested to exclude the worse performing treatment(s) at earlier stages. Detailed simulation study is carried out to evaluate the proposed selection procedures. The applicability of the proposed methodologies is illustrated through a real clinical trial data on cataract surgery.     

Variance-penalized response-adaptive randomization with mismeasurement

We consider response-adaptive design of clinical trials under a variance-penalized criterion in the presence of mismeasurement. An explicit expression for the variance-penalized criterion with misclassified dichotomous responses is derived for response-adaptive designs and some properties are discussed. A new target proportion of treatment allocation is proposed under the criterion and related simulation results are presented.     

Multiple-objective response-adaptive repeated measurement designs for clinical trials

In a response-adaptive design, we review and update the trial on the basis of outcomes in order to achieve a specific goal. Response-adaptive designs for clinical trials are usually constructed to achieve a single objective. In this paper, we develop a new adaptive allocation rule to improve current strategies for building response-adaptive designs to construct multiple-objective repeated measurement designs. This new rule is designed to increase estimation precision and treatment benefit by assigning more patients to a better treatment sequence. We demonstrate that designs constructed under the new proposed allocation rule can be nearly as efficient as fixed optimal designs in terms of the mean squared error, while leading to improved patient care.     

An optimal allocation for response-adaptive designs

A new allocation proportion is derived by using differential equation methods for response-adaptive designs. This new allocation is compared with the balanced and the Neyman allocations and the optimal allocation proposed by Rosenberger, Stallard, Ivanova, Harper and Ricks (RSIHR) from an ethical point of view and statistical power performance. The new allocation has the ethical advantages of allocating more than 50% of patients to the better treatment. It also allocates higher proportion of patients to the better treatment than the RSIHR optimal allocation for success probabilities larger than 0.5. The statistical power under the proposed allocation is compared with these under the balanced, the Neyman and Rosenberger's optimal allocations through simulation. The simulation results indicate that the statistical power under the proposed allocation proportion is similar as to those under the balanced, the Neyman and the RSIHR allocations.     

Multi-treatment covariate-adjusted adaptive design under informative censoring

In the present work, we find a set of reliability functionals to fix up an allocation strategy among K(≥2) treatments when the response distributions, conditionally dependent on some continuous prognostic variable, are exponential with unknown linear regression functions as the means of the respective conditional distributions. Targeting such reliability functionals, we propose a covariate-adjusted response-adaptive randomization procedure for the multi-treatment single-period clinical trial under the Koziol–Green model for informative censoring. We compare the proposed procedure with its competitive covariate-eliminated procedure.     

Longitudinal covariate-adjusted response-adaptive randomized designs

Clinical trials often involve longitudinal data set which has two important characteristics: repeated and correlated measurements and time-varying covariates. In this paper, we propose a general framework of longitudinal covariate-adjusted response-adaptive (LCARA) randomization procedures. We study their properties under widely satisfied conditions. This design skews the allocation probabilities which depend on both patients' first observed covariates and sequentially estimated parameters based on the accrued longitudinal responses and covariates. The asymptotic properties of estimators for the unknown parameters and allocation proportions are established. The special case of binary treatment and continuous responses is studied in detail. Simulation studies and an analysis of the National Cooperative Gallstone Study (NCGS) data are carried out to illustrate the advantages of the proposed LCARA randomization procedure.     

A numerical study for comparing two response-adaptive designs for continuous treatment effects

We study two sequential, response-adaptive randomized designs for clinical trials; one has been proposed in Bandyopadhyay and Biswas (Biometrika 88: 409–419, 2001) and in Biswas and Basu (Sankhya Ser B 63:27–42, 2001), the other stems from the randomly reinforced urn introduced and studied in Muliere et al. (J Stat Plan Inference 136:1853–1874, 2006a). Both designs can be used in clinical trials where the response from each patient is a continuous variable. Comparison is conducted through numerical studies and along a new guideline for the evaluation of a response-adaptive design.     

A new response-adaptive design for continuous treatment responses for phase III clinical trials

A new response-adaptive design, applicable for general class of continuous response distributions, is proposed. The allocation design is studied both theoretically and numerically and compared with some existing procedures. The applicability of the proposed procedure is also illustrated using real life data sets.     

Adaptive Crossover Design for Normal Responses

In a response-adaptive design, we review and update the trial on the basis of outcomes in order to achive a specific goal. In clinical trials our goal is to allocate a larger number of patients to the better treatment. In the present paper, we use a response adaptive design in a two-treatment two-period crossover trial where the treatment responses are continuous. We provide probability measures to choose between the possible treatment combinations AA, AB, BA, or BB. The goal is to use the better treatment combination a larger number of times. We calculate the allocation proportions to the possible treatment combinations and their standard errors. We also derive some asymptotic results and provide solutions on related inferential problems. The proposed procedure is compared with a possible competitor. Finally, we use a data set to illustrate the applicability of our proposed design.     

Response-adaptive designs for continuous outcomes

In this paper, we propose two new response-adaptive designs to use in a trial comparing treatments with continuous outcomes. Both designs assign more subjects to the better treatment on average. The new designs are compared with existing procedures and the equal allocation. The power of the treatment comparison is assessed.     

Response-adaptive randomization for survival trials: the parametric approach

Summary.  Few references deal with response-adaptive randomization procedures for survival outcomes and those that do either dichotomize the outcomes or use a non-parametric approach. In this paper, the optimal allocation approach and a parametric response-adaptive randomization procedure are used under exponential and Weibull distributions. The optimal allocation proportions are derived for both distributions and the doubly adaptive biased coin design is applied to target the optimal allocations. The asymptotic variance of the procedure is obtained for the exponential distribution. The effect of intrinsic delay of survival outcomes is treated. These findings are based on rigorous theory but are also verified by simulation. It is shown that using a doubly adaptive biased coin design to target the optimal allocation proportion results in more patients being randomized to the better performing treatment without loss of power. We illustrate our procedure by redesigning a clinical trial.     

Optimal and lead-in adaptive allocation for binary outcomes: A comparison of Bayesian methods

We compare posterior and predictive estimators and probabilities in response-adaptive randomization designs for two- and three-group clinical trials with binary outcomes. Adaptation based upon posterior estimates are discussed, as are two predictive probability algorithms: one using the traditional definition, the other using a skeptical distribution. Optimal and natural lead-in designs are covered. Simulation studies show that efficacy comparisons lead to more adaptation than center comparisons, though at some power loss, skeptically predictive efficacy comparisons and natural lead-in approaches lead to less adaptation but offer reduced allocation variability. Though nuanced, these results help clarify the power-adaptation trade-off in adaptive randomization.     

A statistical multivariable optimization method using improved orthogonal algorithm based on large data

Multivariable optimization under large data environment concerns with how to reliably obtain a set of optimization results from a mass of data that influence the object function complexly. This is an important issue in statistical calculation because the complexity between variable parameters leads to repeated statistical calculation analysis and a significant amount of data waste. A statistical multivariable optimization method using improved orthogonal algorithm based on large data is proposed. Considering the optimization problem with multi-parameters under large data environment, a multi-parameter optimization model used for improved orthogonal algorithm is established based on large data. Furthermore, an extensive simulation study on temperature field distribution of anti-/de-icing component was conducted to verify the validity of the statistical calculation analysis optimization method. The optimized temperature field distribution meets the anti-/de-icing requirements through numerical simulation. Simulation results show that the optimization effect is more evident and accurate than the non-optimized temperature distribution with the optimized results of the proposed method. Results verify the effectiveness of the proposed method.     

An urn model to construct an efficient test procedure for response adaptive designs

We study the statistical performance of different tests for comparing the mean effect of two treatments. Given a reference classical test \({\mathcal {T}}_0\), we determine which sample size and proportion allocation guarantee to a test \({\mathcal {T}}\), based on response-adaptive design, to be better than \({\mathcal {T}}_0\), in terms of (a) higher power and (b) fewer subjects assigned to the inferior treatment. The adoption of a response-adaptive design to implement the random allocation procedure is necessary to ensure that both (a) and (b) are satisfied. In particular, we propose to use a Modified Randomly Reinforced Urn design and we show how to perform the model parameters selection for the purpose of this paper. Then, the opportunity of relaxing some assumptions on treatment response distributions is presented. Results of simulation studies on the test performance are reported and a real case study is analyzed.     

Sequential estimation for covariate-adjusted response-adaptive designs

In clinical trials, a covariate-adjusted response-adaptive (CARA) design allows a subject newly entering a trial a better chance of being allocated to a superior treatment regimen based on cumulative information from previous subjects, and adjusts the allocation according to individual covariate information. Since this design allocates subjects sequentially, it is natural to apply a sequential method for estimating the treatment effect in order to make the data analysis more efficient. In this paper, we study the sequential estimation of treatment effect for a general CARA design. A stopping criterion is proposed such that the estimates satisfy a prescribed precision when the sampling is stopped. The properties of estimates and stopping time are obtained under the proposed stopping rule. In addition, we show that the asymptotic properties of the allocation function, under the proposed stopping rule, are the same as those obtained in the non-sequential/fixed sample size counterpart. We then illustrate the performance of the proposed procedure with some simulation results using logistic models. The properties, such as the coverage probability of treatment effect, correct allocation proportion and average sample size, for diverse combinations of initial sample sizes and tuning parameters in the utility function are discussed.     

A theoretical analysis of the power of biased coin designs

Outlining some recently obtained results of Hu and Rosenberger [2003. Optimality, variability, power: evaluating response-adaptive randomization procedures for treatment comparisons. J. Amer. Statist. Assoc. 98, 671–678] and Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835] on the relationship between sequential randomized designs and the power of the usual statistical procedures for testing the equivalence of two competing treatments, the aim of this paper is to provide theoretical proofs of the numerical results of Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835]. Furthermore, we prove that the Adjustable Biased Coin Design [Baldi Antognini A., Giovagnoli, A., 2004. A new “biased coin design” for the sequential allocation of two treatments. J. Roy. Statist. Soc. Ser. C 53, 651–664] is uniformly more powerful than the other “coin” designs proposed in the literature for any sample size.     

New two-stage sampling designs based on neoteric ranked set sampling

Neoteric ranked set sampling (NRSS) is a recently developed sampling plan, derived from the well-known ranked set sampling (RSS) scheme. It has already been proved that NRSS provides more efficient estimators for population mean and variance compared to RSS and other sampling designs based on ranked sets. In this work, we propose and evaluate the performance of some two-stage sampling designs based on NRSS. Five different sampling schemes are proposed. Through an extensive Monte Carlo simulation study, we verified that all proposed sampling designs outperform RSS, NRSS, and the original double RSS design, producing estimators for the population mean with a lower mean square error. Furthermore, as with NRSS, two-stage NRSS estimators present some bias for asymmetric distributions. We complement the study with a discussion on the relative performance of the proposed estimators. Moreover, an additional simulation based on data of the diameter and height of pine trees is presented.     

On Multi-Treatment Adaptive Allocation Design for Dichotomous Response

The use of ridit, as a probability score, is a very common practice to compare discrete random variables in discrete data analysis. In the present work we formulate ridit reliability functionals for some comparison of K independent binary random variables. We use such functionals to provide a generalized response-adaptive design (GRAD) on K(≥ +2) treatment-arms for dichotomous response variables. We exhibit some properties of the proposed design and compare it with some of the existing competitors by computing its various performance measures. We also provide a discussion towards a possible modification of the GRAD in the presence of covariates.     

A signature enrichment design with Bayesian adaptive randomization

Clinical trials in the era of precision cancer medicine aim to identify and validate biomarker signatures which can guide the assignment of individually optimal treatments to patients. In this article, we propose a group sequential randomized phase II design, which updates the biomarker signature as the trial goes on, utilizes enrichment strategies for patient selection, and uses Bayesian response-adaptive randomization for treatment assignment. To evaluate the performance of the new design, in addition to the commonly considered criteria of Type I error and power, we propose four new criteria measuring the benefits and losses for individuals both inside and outside of the clinical trial. Compared with designs with equal randomization, the proposed design gives trial participants a better chance to receive their personalized optimal treatments and thus results in a higher response rate on the trial. This design increases the chance to discover a successful new drug by an adaptive enrichment strategy, i.e. identification and selective enrollment of a subset of patients who are sensitive to the experimental therapies. Simulation studies demonstrate these advantages of the proposed design. It is illustrated by an example based on an actual clinical trial in non-small-cell lung cancer.     

A new ranked set sample estimator of variance

Summary. We develop an unbiased estimator of the variance of a population based on a ranked set sample. We show that this new estimator is better than estimating the variance based on a simple random sample and more efficient than the estimator based on a ranked set sample proposed by Stokes. Also, a test to determine the effectiveness of the judgment ordering process is proposed.