- Email: [email protected]
14 Clinical equivalence test and confidence interval for the difference in proportions for the paired-sample design
49s
Abstracts 13 A UNIFIED FAMILY OF GROUP SEQUENTIAL DESIGNS Scott S. Emerson and John M. Kittelson University of Washington Seattle, Washington
It is increasingly standard practice to incorporate a formal stopping rule in the design of a clinical trial. Failure to consider the sequential nature of such hypothesis testing can inflate the type I statistical error above the nominal level. A number of group sequential designs which control the type I error have been proposed in the statistical literature. Most of these designs extend fixed sample (nonsequential) hypothesis tests by generalizing a single characteristic of a fixed sample test. The end result has been the proliferation of families of group sequential tests having only limited flexibility within a family to address the many issues which need to be considered when choosing a stopping rule. In this talk, we present a large family of group sequential test designs that includes many of the previously proposed families. Because this family is parameterized such that a user may move continuously among those designs, we believe that the use of this family in software packages will greatly facilitate the process of designing a clinical trial. We use as an example the history of the design of a large multicenter clinical trial of a new treatment for gram negative sepsis, and we illustrate the various steps of selecting a design using S-Plus. 14 CLINICAL EQUIVALENCE TEST AND CONFIDENCE INTERVAL FOR THE DIFFERENCE IN PROPORTIONS FOR THE PAIRED-SAMPLE DESIGN Toshiro Tango The Institute of Public Health Tokyo, Japan
This paper considers the model for the difference between two proportions in a paired or matched design of cliical trials. This model includes a parameter indicating both inter-patients variability of response probabilities and their correlation. Under the proposed model, we derive a one-sided test for clinical equivalence based upon the efficient score: H~:~N=zs-A,H~:xN>~S-A Further, a score-based confidence interval for the difference of two proportions, IFN - xs is derived. Especially, one of the merits of these methods is the applicability to 2x2 table data with off-diagonal zero cells. Monte Carlo simulation study shows that the proposed test is shown to have empirical significance levels closer to nominal a-level than the other tests recently proposed and further that the proposed confidence interval is shown to have better empirical coverage probability compared with those of the published methods. To illustrate our proposed methods, let us consider the following 2x2 data tables having zero off-diagonal cells:
50s
Abstracts While we cannot make any inference for this data based on established methods so far, based on the proposed procedures, we have that the test statistic (HO vs. Hl with A = 0.1) is Z = 2.37 (one tailed p = 0.009) and 90 per cent Confidence Interval is + 0.054. 15 OPTIMIZATION OF TESTING TIMES AND CRITICAL VALUES IN SEQUENTIAL EQUIVALENCE TESTING Hans-Helge Miiller and Helmut Scbfer Universityof Marburg Marburg, Germany In long-term clinical trials interim analyses are planned to reduce the number of patients needed. Testing the difference of two treatments, Brittain and Bailey developed two- and threestage designs nearly minimizing the average sample size for the proposed difference in efficacy[l]. Generally, controlled clinical trials to demonstrate bioequivalence of two drugs or therapeutic equivalence of two treatments require more patients than trials on difference in efficacy. Consequently, minimizing the average number of patients is at least as relevant to equivalence trials as to superiority trials. Group sequential equivalence test procedures published in literature are based on the approach of Jennison and Turnbull of repeated confidence intervals [2, 31. They do not exhaust the type I - error level. Furthermore, they do not optimize sample size behavior. In this contribution, optimized group sequential designs testing equivalence in the case of normal response data are presented. Their characteristics in sample size behavior will be discussed. Up to five stages, testing times and critical values are determined to minimize the expected sample size, for example with expectation under the assumption of equal efficacy of the two treatments. As another example, the criterion “sum of maximal and expected sample size” for minimization leads to nearly optimal designs over the whole range of possible differences in efficacy. References: [l] Brittain,, E. H. and Bailey, K. R. (1993): Optimization of Multistage Testing times and Critical Values in Clinical Trials. Biometrics49, 763-772. [2] Durrleman, S. and Simon, R. (1990): Planning and Monitoring of Equivalence Studies. Biometrics46, 329-336. [3] Jennison, C. and Turnbull, B. W. (1993): Sequential Equivalence Testing and Repeated Confidence Intervals, with Applications to Normal and Binary Responses. Biometrics49, 3 I-43.
Abstracts 13 A UNIFIED FAMILY OF GROUP SEQUENTIAL DESIGNS Scott S. Emerson and John M. Kittelson University of Washington Seattle, Washington
It is increasingly standard practice to incorporate a formal stopping rule in the design of a clinical trial. Failure to consider the sequential nature of such hypothesis testing can inflate the type I statistical error above the nominal level. A number of group sequential designs which control the type I error have been proposed in the statistical literature. Most of these designs extend fixed sample (nonsequential) hypothesis tests by generalizing a single characteristic of a fixed sample test. The end result has been the proliferation of families of group sequential tests having only limited flexibility within a family to address the many issues which need to be considered when choosing a stopping rule. In this talk, we present a large family of group sequential test designs that includes many of the previously proposed families. Because this family is parameterized such that a user may move continuously among those designs, we believe that the use of this family in software packages will greatly facilitate the process of designing a clinical trial. We use as an example the history of the design of a large multicenter clinical trial of a new treatment for gram negative sepsis, and we illustrate the various steps of selecting a design using S-Plus. 14 CLINICAL EQUIVALENCE TEST AND CONFIDENCE INTERVAL FOR THE DIFFERENCE IN PROPORTIONS FOR THE PAIRED-SAMPLE DESIGN Toshiro Tango The Institute of Public Health Tokyo, Japan
This paper considers the model for the difference between two proportions in a paired or matched design of cliical trials. This model includes a parameter indicating both inter-patients variability of response probabilities and their correlation. Under the proposed model, we derive a one-sided test for clinical equivalence based upon the efficient score: H~:~N=zs-A,H~:xN>~S-A Further, a score-based confidence interval for the difference of two proportions, IFN - xs is derived. Especially, one of the merits of these methods is the applicability to 2x2 table data with off-diagonal zero cells. Monte Carlo simulation study shows that the proposed test is shown to have empirical significance levels closer to nominal a-level than the other tests recently proposed and further that the proposed confidence interval is shown to have better empirical coverage probability compared with those of the published methods. To illustrate our proposed methods, let us consider the following 2x2 data tables having zero off-diagonal cells:
50s
Abstracts While we cannot make any inference for this data based on established methods so far, based on the proposed procedures, we have that the test statistic (HO vs. Hl with A = 0.1) is Z = 2.37 (one tailed p = 0.009) and 90 per cent Confidence Interval is + 0.054. 15 OPTIMIZATION OF TESTING TIMES AND CRITICAL VALUES IN SEQUENTIAL EQUIVALENCE TESTING Hans-Helge Miiller and Helmut Scbfer Universityof Marburg Marburg, Germany In long-term clinical trials interim analyses are planned to reduce the number of patients needed. Testing the difference of two treatments, Brittain and Bailey developed two- and threestage designs nearly minimizing the average sample size for the proposed difference in efficacy[l]. Generally, controlled clinical trials to demonstrate bioequivalence of two drugs or therapeutic equivalence of two treatments require more patients than trials on difference in efficacy. Consequently, minimizing the average number of patients is at least as relevant to equivalence trials as to superiority trials. Group sequential equivalence test procedures published in literature are based on the approach of Jennison and Turnbull of repeated confidence intervals [2, 31. They do not exhaust the type I - error level. Furthermore, they do not optimize sample size behavior. In this contribution, optimized group sequential designs testing equivalence in the case of normal response data are presented. Their characteristics in sample size behavior will be discussed. Up to five stages, testing times and critical values are determined to minimize the expected sample size, for example with expectation under the assumption of equal efficacy of the two treatments. As another example, the criterion “sum of maximal and expected sample size” for minimization leads to nearly optimal designs over the whole range of possible differences in efficacy. References: [l] Brittain,, E. H. and Bailey, K. R. (1993): Optimization of Multistage Testing times and Critical Values in Clinical Trials. Biometrics49, 763-772. [2] Durrleman, S. and Simon, R. (1990): Planning and Monitoring of Equivalence Studies. Biometrics46, 329-336. [3] Jennison, C. and Turnbull, B. W. (1993): Sequential Equivalence Testing and Repeated Confidence Intervals, with Applications to Normal and Binary Responses. Biometrics49, 3 I-43.