Adaptive Designs to Maximize Power in Clinical Trials with Multiple Treatments
TL;DR: In this article, a clinical trial with three competing treatments and study designs that allocate subjects sequentially in order to maximize the power of relevant tests is considered, and two different criteria are considered: the first is to find the best treatment and the second is to order all three.
Abstract: We consider a clinical trial with three competing treatments and study designs that allocate subjects sequentially in order to maximize the power of relevant tests. Two different criteria are considered: the first is to find the best treatment and the second is to order all three. The power converges to one in an exponential rate and we find the optimal allocation that maximizes this rate by large deviation theory. For the first criterion the optimal allocation has the plausible property that it assigns a small fraction of subjects to the inferior treatment. The optimal allocation depends heavily on the unknown parameters and, therefore, in order to implement it, a sequential adaptive scheme is considered. At each stage of the trial the parameters are estimated and the next subject is allocated according to the estimated optimal allocation. We study the asymptotic properties of this design by large deviations theory and the small sample behavior by simulations. Our results demonstrate that, unlik...
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TL;DR: The present paper gives an overview of optimal designs for various important problems that arise in different stages of clinical drug development, including phase I dose–toxicity studies; phase I/II studies that consider early efficacy and toxicity outcomes simultaneously; phase II dose–response studies driven by multiple comparisons, modeling techniques, or their combination.
Abstract: Optimization of clinical trial designs can help investigators achieve higher quality results for the given resource constraints. The present paper gives an overview of optimal designs for various important problems that arise in different stages of clinical drug development, including phase I dose–toxicity studies; phase I/II studies that consider early efficacy and toxicity outcomes simultaneously; phase II dose–response studies driven by multiple comparisons (MCP), modeling techniques (Mod), or their combination (MCP–Mod); phase III randomized controlled multi-arm multi-objective clinical trials to test difference among several treatment groups; and population pharmacokinetics–pharmacodynamics experiments. We find that modern literature is very rich with optimal design methodologies that can be utilized by clinical researchers to improve efficiency of drug development.
13 citations
TL;DR: A response-adaptive procedure based on an optimal target proportion is developed and the associated limiting results are derived and the proposed procedure is compared with the existing competitors.
Abstract: An optimal target proportion is derived balancing between the needs of clinician and statistician considering a general criterion and binary treatment outcome. A response-adaptive procedure based o...
3 citations
Cites background or methods from "Adaptive Designs to Maximize Power ..."
...Azriel and Feigin (2014) optimal allocation (Azriel CO): This is related to probability of correct order, maximizing the large deviations rate of power for detecting the correct order among the available treatments....
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...Another formulation of optimal allocation for binary response trials with multiple treatments can be found in Azriel and Feigin (2014)....
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...For our purpose, we consider t = 3 treatments, ψk = qk and the following competitors: Azriel and Feigin (2014) optimal allocation (Azriel CS): This is related to probability of correct selection, which maximizes the large deviations rate of power for detecting the best treatment correctly....
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TL;DR: In this paper, it was shown that Efron's biased coin design provides more power than a perfect simple randomization for a large enough sample size, and the exponential rate at which the power converges to one, under different designs, using large deviations theory.
1 citations
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"Adaptive Designs to Maximize Power ..." refers methods in this paper
...A similar design was considered by Thompson (1933) for two samples....
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Book•
01 Jan 1977
TL;DR: In this paper, the authors present a review of basic probability theory and its application in statistical models, goals, and performance criteria, as well as several non-decision theoretic criteria.
Abstract: (NOTE: Each chapter concludes with Problems and Complements, Notes, and References.) 1. Statistical Models, Goals, and Performance Criteria. Data, Models, Parameters, and Statistics. Bayesian Models. The Decision Theoretic Framework. Prediction. Sufficiency. Exponential Families. 2. Methods of Estimation. Basic Heuristics of Estimation. Minimum Contrast Estimates and Estimating Equations. Maximum Likelihood in Multiparameter Exponential Families. Algorithmic Issues. 3. Measures of Performance. Introduction. Bayes Procedures. Minimax Procedures. Unbiased Estimation and Risk Inequalities. Nondecision Theoretic Criteria. 4. Testing and Confidence Regions. Introduction. Choosing a Test Statistic: The Neyman-Pearson Lemma. Uniformly Most Powerful Tests and Monotone Likelihood Ratio Models. Confidence Bounds, Intervals and Regions. The Duality between Confidence Regions and Tests. Uniformly Most Accurate Confidence Bounds. Frequentist and Bayesian Formulations. Prediction Intervals. Likelihood Ratio Procedures. 5. Asymptotic Approximations. Introduction: The Meaning and Uses of Asymptotics. Consistency. First- and Higher-Order Asymptotics: The Delta Method with Applications. Asymptotic Theory in One Dimension. Asymptotic Behavior and Optimality of the Posterior Distribution. 6. Inference in the Multiparameter Case. Inference for Gaussian Linear Models. Asymptotic Estimation Theory in p Dimensions. Large Sample Tests and Confidence Regions. Large Sample Methods for Discrete Data. Generalized Linear Models. Robustness Properties and Semiparametric Models. Appendix A: A Review of Basic Probability Theory. The Basic Model. Elementary Properties of Probability Models. Discrete Probability Models. Conditional Probability and Independence. Compound Experiments. Bernoulli and Multinomial Trials, Sampling with and without Replacement. Probabilities on Euclidean Space. Random Variables and Vectors: Transformations. Independence of Random Variables and Vectors. The Expectation of a Random Variable. Moments. Moment and Cumulant Generating Functions. Some Classical Discrete and Continuous Distributions. Modes of Convergence of Random Variables and Limit Theorems. Further Limit Theorems and Inequalities. Poisson Process. Appendix B: Additional Topics in Probability and Analysis. Conditioning by a Random Variable or Vector. Distribution Theory for Transformations of Random Vectors. Distribution Theory for Samples from a Normal Population. The Bivariate Normal Distribution. Moments of Random Vectors and Matrices. The Multivariate Normal Distribution. Convergence for Random Vectors: Op and Op Notation. Multivariate Calculus. Convexity and Inequalities. Topics in Matrix Theory and Elementary Hilbert Space Theory. Appendix C: Tables. The Standard Normal Distribution. Auxiliary Table of the Standard Normal Distribution. t Distribution Critical Values. X 2 Distribution Critical Values. F Distribution Critical Values. Index.
1,630 citations
Book Chapter•
01 Jan 2009
1,432 citations
01 Jan 2010
TL;DR: The official goal of the ICH is to harmonize inconsistent technical regulatory standards across different regions and countries in order to avoid costly, wasteful, and duplicative testing in pharmaceutical development.
Abstract: The International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use (ICH) is a combined industry and government organization. It is centrally involved in constructing and setting international technical standards for the testing, development, and monitoring of pharmaceuticals, especially in the fields of drug quality, safety, and efficacy. There are two types of memberships: full membership with voting rights; and membership that permits only 'observer' status without voting rights. The ICH Steering Committee (SC) was established in 1990 and determines the policies and procedures for ICH, selects the topics for harmonization and monitors the progress of harmonization initiatives. The core financial support for ICH is, and has been, provided by the international pharmaceutical industry trade associations. The official goal of the ICH is to harmonize inconsistent technical regulatory standards across different regions and countries in order to avoid costly, wasteful, and duplicative testing in pharmaceutical development. Keywords: drug regulatory authorities; ICH; ICH Steering Committee (SC); international pharmaceutical industry
1,137 citations