Exact two-stage designs for phase II activity trials with rank-based endpoints
TL;DR: This work presents exact two-stage Mann-Whitney designs in the context of two-arm randomized clinical trials and presents tables of decision rules under a variety of assumed realities for use in trial planning.
About: This article is published in Contemporary Clinical Trials.The article was published on 2012-03-01. It has received 18 citations till now. The article focuses on the topics: Optimal design & Context (language use).
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TL;DR: An efficient intelligent process, the branch-and-bound algorithm, is used in extensively searching for the optimal adaptive design with the smallest expected sample size under the null, while the type I and II error rates are maintained and the aforementioned monotonicity characteristic is respected.
Abstract: Simon's optimal two-stage design has been widely used in early phase clinical trials for Oncology and AIDS studies with binary endpoints. With this approach, the second-stage sample size is fixed when the trial passes the first stage with sufficient activity. Adaptive designs, such as those due to Banerjee and Tsiatis (2006) and Englert and Kieser (2013), are flexible in the sense that the second-stage sample size depends on the response from the first stage, and these designs are often seen to reduce the expected sample size under the null hypothesis as compared with Simon's approach. An unappealing trait of the existing designs is that they are not associated with a second-stage sample size, which is a non-increasing function of the first-stage response rate. In this paper, an efficient intelligent process, the branch-and-bound algorithm, is used in extensively searching for the optimal adaptive design with the smallest expected sample size under the null, while the type I and II error rates are maintained and the aforementioned monotonicity characteristic is respected. The proposed optimal design is observed to have smaller expected sample sizes compared to Simon's optimal design, and the maximum total sample size of the proposed adaptive design is very close to that from Simon's method. The proposed optimal adaptive two-stage design is recommended for use in practice to improve the flexibility and efficiency of early phase therapeutic development.
65 citations
TL;DR: This work presents exact two-stage designs based on Barnard's exact test for differences in proportions and compares the designs to those proposed by Kepner (2010) and Jung (2010).
Abstract: In areas such as oncology, two-stage designs are often preferred as compared to one-stage designs due to the ability to stop the trial early when faced with evidence of lack of sufficient efficacy and the associated sample size savings. We present exact two-stage designs based on Barnard's exact test for differences in proportions and compare the designs to those proposed by Kepner ( 2010 ) and Jung ( 2010 ). In addition, we present tables of decision rules under a variety of assumed realities for use in trial planning. The procedure is recommended for use due to the substantial sample size savings experienced.
28 citations
TL;DR: A modified nonparametric Baumgartner-Weiβ-Schindler test is proposed and its use in testing for trends among K binomial populations is investigated and it is shown that the E+ M approach has higher power than the conditional approach in the unbalanced case.
21 citations
TL;DR: An extensive power comparison shows that the new test is generally more powerful than others under various conditions, including the same type of distribution, and mixed distributions.
Abstract: We propose a new nonparametric test for ordered alternative problem based on the rank difference between two observations from different groups. These groups are assumed to be independent from each other. The exact mean and variance of the test statistic under the null distribution are derived, and its asymptotic distribution is proven to be normal. Furthermore, an extensive power comparison between the new test and other commonly used tests shows that the new test is generally more powerful than others under various conditions, including the same type of distribution, and mixed distributions. A real example from an anti-hypertensive drug trial is provided to illustrate the application of the tests. The new test is therefore recommended for use in practice due to easy calculation and substantial power gain.
21 citations
Cites methods from "Exact two-stage designs for phase I..."
...An extension of the new test in exact testing framework [23,24,25,26] and for repeated data from randomized block designs are also interesting....
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TL;DR: The simulation results show the score testing procedure usually produces satisfactory type I error control and has reasonable power, and the three test procedures get closer when sample size becomes larger.
Abstract: In ophthalmologic studies, measurements obtained from both eyes of an individual are often highly correlated. Ignoring the correlation could lead to incorrect inferences. An asymptotic method was proposed by Tang and others (2008) for testing equality of proportions between two groups under Rosner's model. In this article, we investigate three testing procedures for general g ≥ 2 groups. Our simulation results show the score testing procedure usually produces satisfactory type I error control and has reasonable power. The three test procedures get closer when sample size becomes larger. Examples from ophthalmologic studies are used to illustrate our proposed methods.
21 citations
Cites background from "Exact two-stage designs for phase I..."
...A randomized clinical trial is a good choice to eliminate many of the biases and to avoid ethical problems that may arise from comparing treatments [3] [4]....
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References
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TL;DR: A model by which a combined assessment of all existing lesions, characterized by target lesions and nontarget lesions, is used to extrapolate an overall response to treatment is proposed, which is largely validated by the Response Evaluation Criteria in Solid Tumors Group and integrated into the present guidelines.
Abstract: Anticancer cytotoxic agents go through a process by which their antitumor activity-on the basis of the amount of tumor shrinkage they could generate-has been investigated. In the late 1970s, the International Union Against Cancer and the World Health Organization introduced specific criteria for the codification of tumor response evaluation. In 1994, several organizations involved in clinical research combined forces to tackle the review of these criteria on the basis of the experience and knowledge acquired since then. After several years of intensive discussions, a new set of guidelines is ready that will supersede the former criteria. In parallel to this initiative, one of the participating groups developed a model by which response rates could be derived from unidimensional measurement of tumor lesions instead of the usual bidimensional approach. This new concept has been largely validated by the Response Evaluation Criteria in Solid Tumors Group and integrated into the present guidelines. This special article also provides some philosophic background to clarify the various purposes of response evaluation. It proposes a model by which a combined assessment of all existing lesions, characterized by target lesions (to be measured) and nontarget lesions, is used to extrapolate an overall response to treatment. Methods of assessing tumor lesions are better codified, briefly within the guidelines and in more detail in Appendix I. All other aspects of response evaluation have been discussed, reviewed, and amended whenever appropriate.
14,926 citations
TL;DR: The comparison of two treatments generally falls into one of the following two categories: (a) a number of replications for each of the two treatments, which are unpaired, or (b) we may have a series of paired comparisons, some of which may be positive and some negative as mentioned in this paper.
Abstract: The comparison of two treatments generally falls into one of the following two categories: (a) we may have a number of replications for each of the two treatments, which are unpaired, or (b) we may have a number of paired comparisons leading to a series of differences, some of which may be positive and some negative. The appropriate methods for testing the significance of the differences of the means in these two cases are described in most of the textbooks on statistical methods.
12,871 citations
TL;DR: In this paper, the authors show that the limit distribution is normal if n, n$ go to infinity in any arbitrary manner, where n = m = 8 and n = n = 8.
Abstract: Let $x$ and $y$ be two random variables with continuous cumulative distribution functions $f$ and $g$. A statistic $U$ depending on the relative ranks of the $x$'s and $y$'s is proposed for testing the hypothesis $f = g$. Wilcoxon proposed an equivalent test in the Biometrics Bulletin, December, 1945, but gave only a few points of the distribution of his statistic. Under the hypothesis $f = g$ the probability of obtaining a given $U$ in a sample of $n x's$ and $m y's$ is the solution of a certain recurrence relation involving $n$ and $m$. Using this recurrence relation tables have been computed giving the probability of $U$ for samples up to $n = m = 8$. At this point the distribution is almost normal. From the recurrence relation explicit expressions for the mean, variance, and fourth moment are obtained. The 2rth moment is shown to have a certain form which enabled us to prove that the limit distribution is normal if $m, n$ go to infinity in any arbitrary manner. The test is shown to be consistent with respect to the class of alternatives $f(x) > g(x)$ for every $x$.
11,055 citations
"Exact two-stage designs for phase I..." refers methods in this paper
...They pointed out that the distribution of Um,n is almost normal distributed for large values of m and n. Kurt Hornik [21] recently developed a function for computing the distribution of the Mann–Whitney statistic for given sample sizes for the statistical software R based on the algorithm presented by Mann and Whitney....
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...Mann and Whitney [20] presented the two-sample one-stage rank-sum test which is widely used in many areas of application, including randomized phase II activity trials, and its statistical properties are well studied....
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...Mann and Whitney computed the null distribution of the test statistics based on sample sizes m and n, denoted Um,n, for sample sizes up to m=n=8 by using the recurrence relation tables....
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...Under null hypothesis, Mann and Whitney [20] showed the mean and variance of Um,n to be, E Um;n ¼ mn 2 and Var Um;n ¼ mn mþ nþ 1ð Þ 12 ; respectively....
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...Under null hypothesis, Mann and Whitney [20] showed the mean and variance of Um,n to be,...
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Book•
01 Mar 1973
TL;DR: An ideal text for an upper-level undergraduate or first-year graduate course, Nonparametric Statistical Methods, Second Edition is also an invaluable source for professionals who want to keep abreast of the latest developments within this dynamic branch of modern statistics.
Abstract: This Second Edition of Myles Hollander and Douglas A. Wolfe's successful Nonparametric Statistical Methods meets the needs of a new generation of users, with completely up-to-date coverage of this important statistical area. Like its predecessor, the revised edition, along with its companion ftp site, aims to equip readers with the conceptual and technical skills necessary to select and apply the appropriate procedures for a given situation. An extensive array of examples drawn from actual experiments illustrates clearly how to use nonparametric approaches to handle one- or two-sample location and dispersion problems, dichotomous data, and one-way and two-way layout problems. An ideal text for an upper-level undergraduate or first-year graduate course, Nonparametric Statistical Methods, Second Edition is also an invaluable source for professionals who want to keep abreast of the latest developments within this dynamic branch of modern statistics.
7,240 citations
"Exact two-stage designs for phase I..." refers methods in this paper
...For the one-stage Mann–Whitney test, Hollander and Wolfe [29] showed that the variance of the Mann–Whitney statistic becomes smaller in the presence of ties....
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Book•
01 Jan 1977
TL;DR: In this article, the Chi-square test of homogeneity of proportions is used to compare the proportions of different groups of individuals in a population to a single variable, and the Wilcoxon Signed-Rank Test is used for the comparison of different proportions.
Abstract: PART I: INTRODUCTION 1. WHAT IS STATISTICS? Introduction / Why Study Statistics? / Some Current Applications of Statistics / What Do Statisticians Do? / Quality and Process Improvement / A Note to the Student / Summary / Supplementary Exercises PART II: COLLECTING THE DATA 2. USING SURVEYS AND SCIENTIFIC STUDIES TO COLLECT DATA Introduction / Surveys / Scientific Studies / Observational Studies / Data Management: Preparing Data for Summarization and Analysis / Summary PART III: SUMMARIZING DATA 3. DATA DESCRIPTION Introduction / Describing Data on a Single Variable: Graphical Methods / Describing Data on a Single Variable: Measures of Central Tendency / Describing Data on a Single Variable: Measures of Variability / The Box Plot / Summarizing Data from More Than One Variable / Calculators, Computers, and Software Systems / Summary / Key Formulas / Supplementary Exercises PART IV: TOOLS AND CONCEPTS 4. PROBABILITY AND PROBABILITY DISTRIBUTIONS How Probability Can Be Used in Making Inferences / Finding the Probability of an Event / Basic Event Relations and Probability Laws / Conditional Probability and Independence / Bayes's Formula / Variables: Discrete and Continuous / Probability Distributions for Discrete Random Variables / A Useful Discrete Random Variable: The Binomial / Probability Distributions for Continuous Random Variables / A Useful Continuous Random Variable: The Normal Distribution / Random Sampling / Sampling Distributions / Normal Approximation to the Binomial / Summary / Key Formulas / Supplementary Exercises PART V: ANALYZING DATA: CENTRAL VALUES, VARIANCES, AND PROPORTIONS 5. INFERENCES ON A POPULATION CENTRAL VALUE Introduction and Case Study / Estimation of / Choosing the Sample Size for Estimating / A Statistical Test for / Choosing the Sample Size for Testing / The Level of Significance of a Statistical Test / Inferences about for Normal Population, s Unknown / Inferences about the Population Median / Summary / Key Formulas / Supplementary Exercises 6. COMPARING TWO POPULATION CENTRAL VALUES Introduction and Case Study / Inferences about 1 - 2: Independent Samples / A Nonparametric Alternative: The Wilcoxon Rank Sum Test / Inferences about 1 - 2: Paired Data / A Nonparametric Alternative: The Wilcoxon Signed-Rank Test / Choosing Sample Sizes for Inferences about 1 - 2 / Summary / Key Formulas / Supplementary Exercises 7. INFERENCES ABOUT POPULATION VARIANCES Introduction and Case Study / Estimation and Tests for a Population Variance / Estimation and Tests for Comparing Two Population Variances / Tests for Comparing k > 2 Population Variances / Summary / Key Formulas / Supplementary Exercises 8. INFERENCES ABOUT POPULATION CENTRAL VALUES Introduction and Case Study / A Statistical Test About More Than Two Population Variances / Checking on the Assumptions / Alternative When Assumptions are Violated: Transformations / A Nonparametric Alternative: The Kruskal-Wallis Test / Summary / Key Formulas / Supplementary Exercises 9. MULTIPLE COMPARISONS Introduction and Case Study / Planned Comparisons Among Treatments: Linear Contrasts / Which Error Rate Is Controlled / Multiple Comparisons with the Best Treatment / Comparison of Treatments to a Control / Pairwise Comparison on All Treatments / Summary / Key Formulas / Supplementary Exercises 10. CATEGORICAL DATA Introduction and Case Study / Inferences about a Population Proportion p / Comparing Two Population Proportions p1 - p2 / Probability Distributions for Discrete Random Variables / The Multinomial Experiment and Chi-Square Goodness-of-Fit Test / The Chi-Square Test of Homogeneity of Proportions / The Chi-Square Test of Independence of Two Nominal Level Variables / Fisher's Exact Test, a Permutation Test / Measures of Association / Combining Sets of Contingency Tables / Summary / Key Formulas / Supplementary Exercises PART VI: ANALYZING DATA: REGRESSION METHODS, MODEL BUILDING 11. SIMPLE LINEAR REGRESSION AND CORRELATION Linear Regression and the Method of Least Squares / Transformations to Linearize Data / Correlation / A Look Ahead: Multiple Regression / Summary of Key Formulas. Supplementary Exercises. 12. INFERENCES RELATED TO LINEAR REGRESSION AND CORRELATION Introduction and Case Study / Diagnostics for Detecting Violations of Model Conditions / Inferences about the Intercept and Slope of the Regression Line / Inferences about the Population Mean for a Specified Value of the Explanatory Variable / Predictions and Prediction Intervals / Examining Lack of Fit in the Model / The Inverse Regression Problem (Calibration): Predicting Values for x for a Specified Value of y / Summary / Key Formulas / Supplementary Exercises 13. MULTIPLE REGRESSION AND THE GENERAL LINEAR MODEL Introduction and Case Study / The General Linear Model / Least Squares Estimates of Parameters in the General Linear Model / Inferences about the Parameters in the General Linear Model / Inferences about the Population Mean and Predictions from the General Linear Model / Comparing the Slope of Several Regression Lines / Logistic Regression / Matrix Formulation of the General Linear Model / Summary / Key Formulas / Supplementary Exercises 14. BUILDING REGRESSION MODELS WITH DIAGNOSTICS Introduction and Case Study / Selecting the Variables (Step 1) / Model Formulation (Step 2) / Checking Model Conditions (Step 3) / Summary / Key Formulas / Supplementary Exercises PART VII: ANALYZING DATA: DESIGN OF EXPERIMENTS AND ANOVA 15. DESIGN CONCEPTS FOR EXPERIMENTS AND STUDIES Experiments, Treatments, Experimental Units, Blocking, Randomization, and Measurement Units / How Many Replications? / Studies for Comparing Means versus Studies for Comparing Variances / Summary / Key Formulas / Supplementary Exercises 16. ANALYSIS OF VARIANCE FOR STANDARD DESIGNS Introduction and Case Study / Completely Randomized Design with Single Factor / Randomized Block Design / Latin Square Design / Factorial Experiments in a Completely Randomized Design / The Estimation of Treatment Differences and Planned Comparisons in the Treatment Means / Checking Model Conditions / Alternative Analyses: Transformation and Friedman's Rank-Based Test / Summary / Key Formulas / Supplementary Exercises 17. ANALYSIS OF COVARIANCE Introduction and Case Study / A Completely Randomized Design with One Covariate / The Extrapolation Problem / Multiple Covariates and More Complicated Designs / Summary / Key Formulas / Supplementary Exercises 18. ANALYSIS OF VARIANCE FOR SOME UNBALANCED DESIGNS Introduction and Case Study / A Randomized Block Design with One or More Missing Observations / A Latin Square Design with Missing Data / Incomplete Block Designs / Summary / Key Formulas / Supplementary Exercises 19. ANALYSIS OF VARIANCE FOR SOME FIXED EFFECTS, RANDOM EFFECTS, AND MIXED EFFECTS MODELS Introduction and Case Study / A One-Factor Experiment with Random Treatment Effects / Extensions of Random-Effects Models / A Mixed Model: Experiments with Both Fixed and Random Treatment Effects / Models with Nested Factors / Rules for Obtaining Expected Mean Squares / Summary / Key Formulas / Supplementary Exercises 20. SPLIT-PLOT DESIGNS AND EXPERIMENTS WITH REPEATED MEASURES Introduction and Case Study / Split-Plot Designs / Single-Factor Experiments with Repeated Measures / Two-Factor Experiments with Repeated Measures on One of the Factors / Crossover Design / Summary / Key Formulas / Supplementary Exercises PART VIII: COMMUNICATING AND DOCUMENTING THE RESULTS OF A STUDY OR EXPERIMENT 21. COMMUNICATING AND DOCUMENTING THE RESULTS OF A STUDY OR EXPERIMENT Introduction / The Difficulty of Good Communication / Communication Hurdles: Graphical Distortions / Communication Hurdles: Biased Samples / Communication Hurdles: Sample Size / The Statistical Report / Documentation and Storage of Results / Summary / Supplementary Exercises
5,674 citations