101
|
Bauer P. Adaptive designs: looking for a needle in the haystack-a new challenge in medical research. Stat Med 2008; 27:1565-80. [PMID: 17935261 DOI: 10.1002/sim.3090] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
The statistical principles of fully adaptive designs are outlined. The options of flexibility and the price to be paid in terms of statistical properties of the test procedures are discussed. It is stressed that controlled inference after major design modifications (changing hypotheses) will include a penalty: Intersections among all the hypotheses considered throughout the trial have to be rejected before testing individual hypotheses. Moreover, feasibility in terms of integrity and persuasiveness of the results achieved after adaptations based on unblinded data is considered as the crucial issue in practice. In the second part, sample size adaptive procedures are considered testing a large number of hypotheses under constraints on total sample size as in genetic studies. The advantage of sequential procedures is sketched for the example of two-stage designs with a pilot phase for screening promising hypotheses (markers) and controlling the false discovery rate. Finally, we turn to the clinical problem how to select markers and estimate a score from limited samples, e.g. for predicting the response to therapy of a future patient. The predictive ability of such scores will be rather poor when investigating a large number of hypotheses and truly large marker effects are lacking. An obvious dilemma will show up: More optimistic selection rules may be superior if in fact effective markers exist, but will produce more nuisance prediction if no effective markers exist compared with more cautious strategies, e.g. aiming at some control of type I error probabilities.
Collapse
Affiliation(s)
- Peter Bauer
- Section of Medical Statistics, Medical University of Vienna, Vienna, Austria.
| |
Collapse
|
102
|
Brannath W, Mehta CR, Posch M. Exact Confidence Bounds Following Adaptive Group Sequential Tests. Biometrics 2008; 65:539-46. [DOI: 10.1111/j.1541-0420.2008.01101.x] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
|
103
|
Sagkriotis A, Scholpp J. Combining proof-of-concept with dose-finding: utilization of adaptive designs in migraine clinical trials. Cephalalgia 2008; 28:805-12. [PMID: 18513264 DOI: 10.1111/j.1468-2982.2008.01595.x] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
There is an obvious need to improve clinical trial designs with respect to efficiency, duration and the number of patients recruited. Adaptive (flexible) designs may be valuable in this respect. We simulated the properties of a two-stage adaptive proof-of-concept and dose-finding trial design in adult migraine patients with moderate to severe headache, with or without aura. We also assessed the usefulness of a combined Bayesian and frequentist approach in the estimation of the probability of success of subsequent Phase III studies. Applying such an innovative approach would result in a reduction of the required sample size by 30 patients and no prolongation of the trial duration. The probability of success in Phase III is > 81%. An innovative adaptive design can facilitate testing of investigational migraine medications by reducing patient numbers and improving predictivity of success in Phase III.
Collapse
Affiliation(s)
- A Sagkriotis
- Boehringer Ingelheim Pharma GmbH & Co. KG, Ingelheim, Germany
| | | |
Collapse
|
104
|
Desseaux K, Porcher R. Flexible two-stage design with sample size reassessment for survival trials. Stat Med 2008; 26:5002-13. [PMID: 17577242 DOI: 10.1002/sim.2966] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Flexible trials with adaptive design modification at interim analyses have been recently proposed as an answer to cope with some limitations of traditional designs for phase III trials. Actually, the sample size and duration of fixed design trials strongly depend on the determination, prior to the study, of key parameters such as the expected treatment effect and the event rates. A misspecification of these parameters may result in an underpowered or overpowered trial. In the flexible framework, the remainder of a design can be modified at an interim analysis, while preserving the initially specified global error rates. In this work, we present a flexible design with sample size re-evaluation for survival trials and study its properties in practical settings. The results show that, if parameters are initially misspecified, the proposed method allows an improved power control with a reasonable increase in sample size, if any. Practical guidelines concerning the choice of the trial parameters are also given.
Collapse
Affiliation(s)
- K Desseaux
- Inserm U717, Département de Biostatistique et Informatique Médicale, Hôpital Saint-Louis, AP-HP, Université Paris 7, Paris, France.
| | | |
Collapse
|
105
|
Abstract
Clinical trials incorporating treatment selection at pre-specified interim analyses allow to integrate two clinical studies into a single, confirmatory study. In an adaptive interim analysis, treatment arms are selected based on interim data as well as external information. The specific selection rule does not need to be pre-specified in advance in order to control the multiple type I error rate. We propose an adaptive Dunnett test procedure based on the conditional error rate of the single-stage Dunnett test. The adaptive procedure uniformly improves the classical Dunnett test, which is shown to be strictly conservative if treatments are dropped at interim. The adaptive Dunnett test is compared in a simulation with the classical Dunnett test as well as with adaptive combination tests based on the closure principle. The method is illustrated with a real-data example.
Collapse
Affiliation(s)
- Franz Koenig
- Medical University of Vienna, Spitalgasse 23, A-1090 Wien, Austria
| | | | | | | |
Collapse
|
106
|
|
107
|
Jennison C, Turnbull BW. Adaptive Seamless Designs: Selection and Prospective Testing of Hypotheses. J Biopharm Stat 2007; 17:1135-61. [DOI: 10.1080/10543400701645215] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
| | - Bruce W. Turnbull
- b Department of Statistical Science , Cornell University , Ithaca, New York, USA
| |
Collapse
|
108
|
Faldum A, Hommel G. Strategies for Including Patients Recruited During Interim Analysis of Clinical Trials. J Biopharm Stat 2007; 17:1211-25. [DOI: 10.1080/10543400701645439] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Andreas Faldum
- a Institute of Medical Biostatistics, Epidemiology and Informatics, University of Mainz , Germany
| | - Gerhard Hommel
- a Institute of Medical Biostatistics, Epidemiology and Informatics, University of Mainz , Germany
| |
Collapse
|
109
|
|
110
|
Gallo P, Chuang-Stein C, Dragalin V, Gaydos B, Krams M, Pinheiro J. Adaptive designs in clinical drug development--an Executive Summary of the PhRMA Working Group. J Biopharm Stat 2007; 16:275-83; discussion 285-91, 293-8, 311-2. [PMID: 16724485 DOI: 10.1080/10543400600614742] [Citation(s) in RCA: 187] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
A PhRMA Working Group on adaptive clinical trial designs has been formed to investigate and facilitate opportunities for wider acceptance and usage of adaptive designs and related methodologies. A White Paper summarizing the findings of the group is in preparation; this article is an Executive Summary for that full White Paper, and summarizes the findings and recommendations of the group. Logistic, operational, procedural, and statistical challenges associated with adaptive designs are addressed. Three particular areas where it is felt that adaptive designs can be utilized beneficially are discussed: dose finding, seamless Phase II/III trials designs, and sample size reestimation.
Collapse
Affiliation(s)
- Paul Gallo
- Novartis Pharmaceuticals, East Hanover, NJ 07936, USA.
| | | | | | | | | | | |
Collapse
|
111
|
|
112
|
Victor A, Hommel G. Combining adaptive designs with control of the false discovery rate--a generalized definition for a global p-value. Biom J 2007; 49:94-106. [PMID: 17342952 DOI: 10.1002/bimj.200510311] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
When combining adaptive designs with control of the False Discovery Rate one has to keep in mind that the most frequently used procedure for controlling the False Discovery Rate--the explorative Simes procedure--is a stepwise multiple testing procedure. At the interim analysis of an adaptive design it is however not yet known what the boundaries for rejection of hypotheses in the final analysis will be as these boundaries depend on the size of the final p-values. Therefore classical adaptive designs with a predefined stopping criterion for early rejection of hypotheses are not well suited. We propose a generalized definition of a global p-value for a two-stage adaptive design permitting a flexible decision for stopping at the interim analysis. By means of a simulation study in the field of genetic epidemiology we illustrate how applying such a two-stage design can reduce costs.
Collapse
Affiliation(s)
- Anja Victor
- Institut für Medizinische Biometrie, Epidemiologie und Informatik, Obere Zahlbacher Strasse 69, 55101 Mainz, Germany.
| | | |
Collapse
|
113
|
Abstract
When performing a trial using an adaptive sequential design, it is usually assumed that the data for each stage come from different units; for example, patients. However, sometimes it is not possible to satisfy this condition or to check whether it is satisfied. In these cases, the test statistics and p-values of each stage may be dependent. In this paper we investigate the type I error of two-stage adaptive designs when the test statistics from the stages are assumed to be bivariate normal. Analytical considerations are performed under the restriction that the conditional error function is constant in the continuation region. We show that the decisions can become conservative as well as anticonservative, depending on the design parameters and on the sign of the correlation coefficient. Further, we discuss properties and advantages of this design and compare it with the Bauer-Köhne method.
Collapse
Affiliation(s)
- Gerhard Hommel
- Institute for Medical Biometry, Epidemiology and Informatics, University of Mainz, Mainz, Germany.
| | | | | |
Collapse
|
114
|
Hung HMJ, Cui L, Wang SJ, Lawrence J. Adaptive Statistical Analysis Following Sample Size Modification Based on Interim Review of Effect Size. J Biopharm Stat 2007; 15:693-706. [PMID: 16022173 DOI: 10.1081/bip-200062855] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
In designing a comparative clinical trial, the required sample size is a function of the effect size, the value of which is unknown and at best may be estimated from historical data. Insufficiency in sample size as a result of overestimating the effect size can be destructive to the success of the clinical trial. Sample size re-estimation may need to be properly considered as a part of clinical trial planning. This paper is intended to give the motivations for the sample size re-estimation based partly on the effect size observed at an interim analysis and for a resulting simple adaptive test strategy. The performance of this adaptive design strategy is assessed by comparing it with a fixed maximum sample size design that is properly adjusted in anticipation of the possible sample size adjustment.
Collapse
Affiliation(s)
- H M James Hung
- Division of Biometrics I, OB/OPaSS/CDER, FDA, Rockville, Maryland, USA.
| | | | | | | |
Collapse
|
115
|
Wassmer G. Data-Driven Analysis Strategies for Proportion Studies in Adaptive Group Sequential Test Designs. J Biopharm Stat 2007; 13:585-603. [PMID: 14584710 DOI: 10.1081/bip-120024196] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
Using multistage adaptive group sequential test designs, the investigator may perform data-driven changes in the design during the course of the trial without inflation of the Type I error rate. This is possible, for example, through the use of the inverse normal method of combining the p-values from the separate stages of the trial. Generally, conditional error functions are useful instruments for midtrial design modifications of clinical trials. Particularly, it is worthwhile to consider sample size reassessment strategies based on conditional power arguments. In this paper, approximate techniques will be proposed for the application of the inverse normal combination testing principle in superiority and noninferiority proportion studies. Planning facilities and the adaptive analysis strategies will be discussed in terms of the Type I error rate, the necessary sample size, and the power within the adaptive design. Furthermore, how to calculate confidence intervals and overall p-values will be shown.
Collapse
Affiliation(s)
- Gernot Wassmer
- Institute for Medical Statistics, Informatics, and Epidemiology, University of Cologne, Cologne, Germany.
| |
Collapse
|
116
|
Timmesfeld N, Schäfer H, Müller HH. Increasing the sample size during clinical trials witht-distributed test statistics without inflating the type I error rate. Stat Med 2007; 26:2449-64. [PMID: 17080491 DOI: 10.1002/sim.2725] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
In clinical trials with t-distributed test statistics the required sample size depends on the unknown variance. Taking estimates from previous studies often leads to a misspecification of the true value of the variance. Hence, re-estimation of the variance based on the collected data and re-calculation of the required sample size is attractive. We present a flexible method for extensions of fixed sample or group-sequential trials with t-distributed test statistics. The method can be applied at any time during the course of the trial and does not require the necessity to pre-specify a sample size re-calculation rule. All available information can be used to determine the new sample size. The advantage of our method when compared with other adaptive methods is maintenance of the efficient t-test design when no extensions are actually made. We show that the type I error rate is preserved.
Collapse
Affiliation(s)
- Nina Timmesfeld
- Institute of Medical Biometry and Epidemiology, Philipps University of Marburg, Bunsenstr. 3, Marburg D-35037, Germany.
| | | | | |
Collapse
|
117
|
Jahn-Eimermacher A, Hommel G. Performance of adaptive sample size adjustment with respect to stopping criteria and time of interim analysis. Stat Med 2007; 26:1450-61. [PMID: 16900553 DOI: 10.1002/sim.2652] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The benefit of adjusting the sample size in clinical trials on the basis of treatment effects observed in interim analysis has been the subject of several recent papers. Different conclusions were drawn about the usefulness of this approach for gaining power or saving sample size, because of differences in trial design and setting. We examined the benefit of sample size adjustment in relation to trial design parameters such as 'time of interim analysis' and 'choice of stopping criteria'. We compared the adaptive weighted inverse normal method with classical group sequential methods for the most common and for optimal stopping criteria in early, half-time and late interim analyses. We found that reacting to interim data might significantly reduce average sample size in some situations, while classical approaches can out-perform the adaptive designs under other circumstances. We characterized these situations with respect to time of interim analysis and choice of stopping criteria.
Collapse
Affiliation(s)
- Antje Jahn-Eimermacher
- Institute of Medical Biostatistics, Epidemiology and Informatics (IMBEI), University of Mainz, 55101 Mainz, Germany.
| | | |
Collapse
|
118
|
|
119
|
Maca J, Bhattacharya S, Dragalin V, Gallo P, Krams M. Adaptive Seamless Phase II/III Designs—Background, Operational Aspects, and Examples. ACTA ACUST UNITED AC 2006. [DOI: 10.1177/216847900604000412] [Citation(s) in RCA: 100] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
120
|
Schäfer H, Timmesfeld N, Müller HH. An overview of statistical approaches for adaptive designs and design modifications. Biom J 2006; 48:507-20. [PMID: 16972702 DOI: 10.1002/bimj.200510234] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
With adaptive design methods for clinical trials, design elements such as sample size or further interim sample sizes may be changed during the course of the trial depending on all previously collected data. The focus of the overview is on group sequential approaches where the types of adaptations need not be specified in advance. An overview of the different statistical approaches for adaptive design methods proposed in the literature is given, relations between these methods are described and some perspectives of application and for future research are discussed.
Collapse
Affiliation(s)
- Helmut Schäfer
- Institute of Medical Biometry and Epidemiology, Philipps-University of Marburg, Bunsenstrasse 3, D-35037 Marburg, Germany.
| | | | | |
Collapse
|
121
|
Bretz F, Schmidli H, König F, Racine A, Maurer W. Confirmatory seamless phase II/III clinical trials with hypotheses selection at interim: general concepts. Biom J 2006; 48:623-34. [PMID: 16972714 DOI: 10.1002/bimj.200510232] [Citation(s) in RCA: 275] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Traditional drug development consists of a sequence of independent trials organized in different phases. Full development typically involves (i) a learning phase II trial and (ii) one or two confirmatory phase III trial(s). For example, in the phase II trials several doses of the new compound might be compared to a control and/or placebo with the goal of deciding whether to stop or continue development and, in the latter case, selecting one or two "best" doses to carry forward into the confirmatory phase. The phase III trials are then conducted as stand-alone confirmatory studies, not incorporating in their statistical analyses data collected in the previous phases. Seamless phase II/III designs are aimed at interweaving the two phases of full development by combining them into one single, uninterrupted study conducted in two stages. In the dose-finding example above, one (or more) dose(s) are selected after the first stage based on the available data at interim, and are then observed further in the second stage. The final analysis of the selected dose(s) includes patients from both stages and is performed such that the overall type I error rate is controlled at a prespecified level regardless of the dose selection rule used at interim. The adequacy of the dose selection at interim is obviously a critical step for the success of a seamless phase II/III trial. In this paper we focus on the description of flexible test procedures allowing for adaptively selecting hypotheses at interim and thus allowing the combination of learning and confirming in a single seamless trial. We review the statistical background, introduce different test procedures and compare them in a power study. In a subsequent paper (Schmidli et al., 2006) we give several applications from our daily practice and discuss related implementation issues in conducting adaptive seamless designs.
Collapse
Affiliation(s)
- Frank Bretz
- Novartis Pharma AG, Lichtstrasse 35, 4002 Basel, Switzerland.
| | | | | | | | | |
Collapse
|
122
|
Mehta CR, Jemiai Y. A consultant's perspective on the regulatory hurdles to adaptive trials. Biom J 2006; 48:604-8; discussion 613-22. [PMID: 16972712 DOI: 10.1002/bimj.200610249] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
This is a discussion of the following two papers appearing in this special issue on adaptive designs: 'A regulatory view on adaptive/flexible clinical trial design' by H. M. James Hung, Robert T. O'Neill, Sue-Jane Wang and John Lawrence and 'Confirmatory clinical trials with an adaptive design' by Armin Koch.
Collapse
Affiliation(s)
- Cyrus R Mehta
- Cytel Inc., 675 Massachusetts Ave., Cambridge, MA 02139-3309, USA.
| | | |
Collapse
|
123
|
Abstract
The use of adaptive methods has experienced increasing interest in the current literature on group sequential designs. Group sequential analysis in survival trials usually apply the error spending function approach due to the unpredictable amount of information available in an interim analysis. An alternative way is to apply adaptive methods where additionally the maximum amount of information and other designing parameters can be changed based on the information available at the interim stage. In this paper, it is shown how the inverse normal method can be used within a survival design using the log-rank test for comparing two survival functions. This method allows for many kinds of design modifications. In case of no modifications, the inverse normal method coincides with the commonly used analysis strategy. It is straightforward to specify effect estimates. Confidence intervals for the hazard ratio that can be calculated at each stage of the trial and intervals that can only be computed by the end of the trial are proposed. The latter also enables the calculation of median unbiased estimates. Overall p-values can be defined analogously. Properties of the analyses techniques are investigated and compared with alternative approaches. It is shown that the proposed analysis technique might help to rescue an underpowered study and opens the way to other types of changes in design. The proposed technique is implemented in the software ADDPLAN Adaptive Design, Plans and Analyses (http://www.addplan.com).
Collapse
Affiliation(s)
- Gernot Wassmer
- Institute for Medical Statistics, Informatics, and Epidemiology, University of Cologne, Cologne, Germany.
| |
Collapse
|
124
|
Hung HMJ, O'Neill RT, Wang SJ, Lawrence J. A regulatory view on adaptive/flexible clinical trial design. Biom J 2006; 48:565-73. [PMID: 16972707 DOI: 10.1002/bimj.200610229] [Citation(s) in RCA: 62] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Recently there is growing interest in use of adaptive or flexible designs for development of pharmaceutical products. Statistical methodology has been greatly advanced in the literature. However, there are still some important issues with the methodology and application. In addition, there are many other challenges with these designs, including efficiency of these designs in the entire development program, trial conduct and logistics, the infrastructure of an adaptive trial, the regulatory evaluation of trial results and trial conduct, etc. Up till now, regulatory experience in these designs is very limited. We share some of the challenges.
Collapse
Affiliation(s)
- H M James Hung
- Division of Biometrics I, OB/OTS/CDER/FDA, Rockville, MD, USA.
| | | | | | | |
Collapse
|
125
|
|
126
|
Abstract
Flexible designs allow large modifications of a design during an experiment. In particular, the sample size can be modified in response to interim data or external information. A standard flexible methodology combines such design modifications with a weighted test, which guarantees the type I error level. However, this inference violates basic inference principles. In an example with independent N(mu, 1) observations, the test rejects the null hypothesis of mu < or = 0 while the average of the observations is negative. We conclude that flexible design in its most general form with the corresponding weighted test is not valid. Several possible modifications of the flexible design methodology are discussed with a focus on alternative hypothesis tests.
Collapse
|
127
|
Abstract
Adaptive designs are one of the most promising developments in statistics with applications to clinical trials. Obviously, knowledge at the beginning of a clinical trial will always be limited. Thus it may seem logical that the knowledge from accumulating information should be used to optimize the design of the trial. This paper discusses conditions under which this may be possible in phase III clinical trials where the principal aim is confirmation of hypotheses that have been developed in earlier stages of drug development.
Collapse
Affiliation(s)
- Armin Koch
- Bundesinstitut für Arzneimittel und Medizinprodukte, Kurt-Georg-Kiesinger Allee 3, 53175 Bonn, Germany.
| |
Collapse
|
128
|
Wang J. An Adaptive Two-stage Design with Treatment Selection Using the Conditional Error Function Approach. Biom J 2006; 48:679-89. [PMID: 16972720 DOI: 10.1002/bimj.200510236] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
As an approach to combining the phase II dose finding trial and phase III pivotal trials, we propose a two-stage adaptive design that selects the best among several treatments in the first stage and tests significance of the selected treatment in the second stage. The approach controls the type I error defined as the probability of selecting a treatment and claiming its significance when the selected treatment is indifferent from placebo, as considered in Bischoff and Miller (2005). Our approach uses the conditional error function and allows determining the conditional type I error function for the second stage based on information observed at the first stage in a similar way to that for an ordinary adaptive design without treatment selection. We examine properties such as expected sample size and stage-2 power of this design with a given type I error and a maximum stage-2 sample size under different hypothesis configurations. We also propose a method to find the optimal conditional error function of a simple parametric form to improve the performance of the design and have derived optimal designs under some hypothesis configurations. Application of this approach is illustrated by a hypothetical example.
Collapse
Affiliation(s)
- Jixian Wang
- Novartis Pharma AG, Lichtstrasse 35, 4002 Basel, Switzerland.
| |
Collapse
|
129
|
Abstract
A literature search has been performed to review applications of the adaptive design methodology based on the combination test or conditional error function approach. Some features of the 60 papers identified are summarized, e.g., the specific methodology used, calendar year, country, impact factor of the journal, number of planned and performed stages respectively, stopping for futility boundaries, type of adaptations and others. A selection of the ten recent publications in journals with the highest impact factors is discussed in more detail. Most applications up to now aim at sample size reassessment, the majority of papers is coming from Germany. Although we found that renowned journals allow for sufficient space to present the new statistical methodology in all its necessary details, the general impression is that the presentation of the adaptive designs methodology in applied papers has to be improved. Education and development of standards could help to achieve this.
Collapse
Affiliation(s)
- P Bauer
- Section of Medical Statistics, Medical University of Vienna, Spitalgasse 23, A-1090 Vienna, Austria.
| | | |
Collapse
|
130
|
Bretz F, Schmidli H, König F, Racine A, Maurer W. Rejoinder. Biom J 2006. [DOI: 10.1002/bimj.200610255] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
|
131
|
Wassmer G, Vandemeulebroecke M. A Brief Review on Software Developments for Group Sequential and Adaptive Designs. Biom J 2006; 48:732-7. [PMID: 16972726 DOI: 10.1002/bimj.200510233] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
In this paper the currently available software we know for group sequential and adaptive designs is briefly reviewed. Stand-alone packages as well as modules within software packages or programming languages exist. New software developments for adaptive designs enable the user to perform data dependent design adaptations while controlling the Type I error rate.
Collapse
Affiliation(s)
- Gernot Wassmer
- Institute for Medical Statistics, Informatics, and Epidemiology, University of Cologne, Joseph-Stelzmann-Str. 9, 50931 Cologne, Germany.
| | | |
Collapse
|
132
|
Hartung J, Knapp G. Repeated Confidence Intervals in Self-Designing Clinical Trials and Switching between Noninferiority and Superiority. Biom J 2006; 48:697-709. [PMID: 16972722 DOI: 10.1002/bimj.200510213] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
In self-designing clinical trials, repeated confidence intervals are derived for the parameter of interest where the results of the independent study stages are combined using the generalized inverse chi-square-method. The confidence intervals can be calculated at each interim analysis and always hold the predefined overall nominal confidence level. Moreover, the confidence intervals calculated during the course of the trial are nested in the sense that a calculated interval is completely contained in all the previously calculated intervals. During the course of the self-designing trial the sample sizes as well as the number of study stages can be determined simultaneously in a completely adaptive way. The adaptive procedure allows an early stop for significance. The clinical trial may be originally designed either to show noninferiority or superiority. However, in each interim analysis, it is possible to change the planning from showing superiority to showing noninferiority or vice versa. Since the repeated confidence intervals are nested, there is no risk to loose the noninferiority once showed when, after an interim analysis, the trial is continued in an attempt to reach superiority. A simulation study investigates the behavior of the considered confidence intervals. The performance of the derived nested repeated confidence intervals is also demonstrated in examples showing both kinds of switching during an ongoing trial.
Collapse
Affiliation(s)
- Joachim Hartung
- Department of Statistics, University of Dortmund, 44221 Dortmund, Germany.
| | | |
Collapse
|
133
|
Liu Q, Pledger G. On design and inference for two-stage adaptive clinical trials with dependent data. J Stat Plan Inference 2006. [DOI: 10.1016/j.jspi.2005.08.015] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
134
|
Abstract
Adaptive test designs for clinical trials allow for a wide range of data driven design adaptations using all information gathered until an interim analysis. The basic principle is to use a test statistics which is invariant with respect to the design adaptations under the null hypothesis. This allows for a control of the type I error rate for the primary hypothesis even for adaptations not specified a priori in the study protocol. Estimation is usually another important part of a clinical trial, however, is more difficult in adaptive designs. In this research paper we give an overview of point and interval estimates for flexible designs and compare methods for typical sample size rules. We also make some proposals for confidence intervals which have nominal coverage probability also after an unforeseen design adaptation and which contain the maximum likelihood estimate and the usual unadjusted confidence interval.
Collapse
Affiliation(s)
- Werner Brannath
- Section of Medical Statistics, Core Unit for Medical Statistics and Informatics, Medical University of Vienna, Spitalgasse 23, A-1090 Wien, Austria.
| | | | | |
Collapse
|
135
|
Lachin JM. Operating characteristics of sample size re-estimation with futility stopping based on conditional power. Stat Med 2006; 25:3348-65. [PMID: 16345019 DOI: 10.1002/sim.2455] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Various methods have been described for re-estimating the final sample size in a clinical trial based on an interim assessment of the treatment effect. Many re-weight the observations after re-sizing so as to control the pursuant inflation in the type I error probability alpha. Lan and Trost (Estimation of parameters and sample size re-estimation. Proceedings of the American Statistical Association Biopharmaceutical Section 1997; 48-51) proposed a simple procedure based on conditional power calculated under the current trend in the data (CPT). The study is terminated for futility if CPT < or = CL, continued unchanged if CPT > or = CU, or re-sized by a factor m to yield CPT = CU if CL < CPT < CU, where CL and CU are pre-specified probability levels. The overall level alpha can be preserved since the reduction due to stopping for futility can balance the inflation due to sample size re-estimation, thus permitting any form of final analysis with no re-weighting. Herein the statistical properties of this approach are described including an evaluation of the probabilities of stopping for futility or re-sizing, the distribution of the re-sizing factor m, and the unconditional type I and II error probabilities alpha and beta. Since futility stopping does not allow a type I error but commits a type II error, then as the probability of stopping for futility increases, alpha decreases and beta increases. An iterative procedure is described for choice of the critical test value and the futility stopping boundary so as to ensure that specified alpha and beta are obtained. However, inflation in beta is controlled by reducing the probability of futility stopping, that in turn dramatically increases the possible re-sizing factor m. The procedure is also generalized to limit the maximum sample size inflation factor, such as at m max = 4. However, doing so then allows for a non-trivial fraction of studies to be re-sized at this level that still have low conditional power. These properties also apply to other methods for sample size re-estimation with a provision for stopping for futility. Sample size re-estimation procedures should be used with caution and the impact on the overall type II error probability should be assessed.
Collapse
Affiliation(s)
- John M Lachin
- The Biostatistics Center, Department of Epidemiology and Biostatistics and Statistics, The George Washington University, Rockville, MD 20852, USA.
| |
Collapse
|
136
|
Hung HMJ, Wang SJ, O'Neill RT. Methodological issues with adaptation of clinical trial design. Pharm Stat 2006; 5:99-107. [PMID: 17080766 DOI: 10.1002/pst.219] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Adaptation of clinical trial design generates many issues that have not been resolved for practical applications, though statistical methodology has advanced greatly. This paper focuses on some methodological issues. In one type of adaptation such as sample size re-estimation, only the postulated value of a parameter for planning the trial size may be altered. In another type, the originally intended hypothesis for testing may be modified using the internal data accumulated at an interim time of the trial, such as changing the primary endpoint and dropping a treatment arm. For sample size re-estimation, we make a contrast between an adaptive test weighting the two-stage test statistics with the statistical information given by the original design and the original sample mean test with a properly corrected critical value. We point out the difficulty in planning a confirmatory trial based on the crude information generated by exploratory trials. In regards to selecting a primary endpoint, we argue that the selection process that allows switching from one endpoint to the other with the internal data of the trial is not very likely to gain a power advantage over the simple process of selecting one from the two endpoints by testing them with an equal split of alpha (Bonferroni adjustment). For dropping a treatment arm, distributing the remaining sample size of the discontinued arm to other treatment arms can substantially improve the statistical power of identifying a superior treatment arm in the design. A common difficult methodological issue is that of how to select an adaptation rule in the trial planning stage. Pre-specification of the adaptation rule is important for the practicality consideration. Changing the originally intended hypothesis for testing with the internal data generates great concerns to clinical trial researchers.
Collapse
Affiliation(s)
- H M James Hung
- Division of Biometrics I, OB/CDER/FDA, 10903 New Hampshire Avenue, BLDG 22 Rm 4238, HFD-710, Mail Stop 4105, Silver Spring, MD 20993-0002, USA.
| | | | | |
Collapse
|
137
|
Neuhäuser M, Bretz F. Adaptive designs based on the truncated product method. BMC Med Res Methodol 2005; 5:30. [PMID: 16171518 PMCID: PMC1242234 DOI: 10.1186/1471-2288-5-30] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2004] [Accepted: 09/19/2005] [Indexed: 11/10/2022] Open
Abstract
Background Adaptive designs are becoming increasingly important in clinical research. One approach subdivides the study into several (two or more) stages and combines the p-values of the different stages using Fisher's combination test. Methods Alternatively to Fisher's test, the recently proposed truncated product method (TPM) can be applied to combine the p-values. The TPM uses the product of only those p-values that do not exceed some fixed cut-off value. Here, these two competing analyses are compared. Results When an early termination due to insufficient effects is not appropriate, such as in dose-response analyses, the probability to stop the trial early with the rejection of the null hypothesis is increased when the TPM is applied. Therefore, the expected total sample size is decreased. This decrease in the sample size is not connected with a loss in power. The TPM turns out to be less advantageous, when an early termination of the study due to insufficient effects is possible. This is due to a decrease of the probability to stop the trial early. Conclusion It is recommended to apply the TPM rather than Fisher's combination test whenever an early termination due to insufficient effects is not suitable within the adaptive design.
Collapse
Affiliation(s)
- Markus Neuhäuser
- Institute for Medical Informatics, Biometry and Epidemiology, University of Duisburg-Essen, Hufelandstr. 55, D-45122 Essen, Germany
| | - Frank Bretz
- Novartis Pharma AG, WSJ-27.1.005, 4002 Basel, Switzerland
| |
Collapse
|
138
|
|
139
|
Posch M, Koenig F, Branson M, Brannath W, Dunger-Baldauf C, Bauer P. Testing and estimation in flexible group sequential designs with adaptive treatment selection. Stat Med 2005; 24:3697-714. [PMID: 16320264 DOI: 10.1002/sim.2389] [Citation(s) in RCA: 172] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Integrating selection and confirmation phases into a single trial can expedite the development of new treatments and allows to use all accumulated data in the decision process. In this paper we review adaptive treatment selection based on combination tests and propose overall adjusted p-values and simultaneous confidence intervals. Also point estimation in adaptive trials is considered. The methodology is illustrated in a detailed example based on an actual planned study.
Collapse
Affiliation(s)
- Martin Posch
- Section of Medical Statistics, Core Unit for Medical Statistics and Informatics, Medical University of Vienna, Spitalgasse 23, A-1090 Wien, Austria.
| | | | | | | | | | | |
Collapse
|
140
|
Schaefer H, Engert A, Grass G, Mansmann G, Wassmer G, Hubel K, Loehlein D, Ulrich BC, Lippert H, Knoefel WT, Hoelscher AH. Perioperative granulocyte colony-stimulating factor does not prevent severe infections in patients undergoing esophagectomy for esophageal cancer: a randomized placebo-controlled clinical trial. Ann Surg 2004; 240:68-75. [PMID: 15213620 PMCID: PMC1356376 DOI: 10.1097/01.sla.0000129705.00210.24] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
OBJECTIVE Esophagectomy for esophageal cancer is associated with substantial postoperative morbidity as a result of infectious complications. In a prior phase II study, granulocyte colony-stimulating factor (G-CSF) was shown to improve leukocyte function and to reduce infection rates after esophagectomy. The aim of the current randomized, placebo-controlled, multicenter phase III trial was to investigate the clinical efficacy of perioperative G-CSF administration in reducing infection and mortality after esophagectomy for esophageal cancer. PATIENTS AND METHODS One hundred fifty five patients with resectable esophageal cancer were randomly assigned to perioperative G-CSF at standard doses (77 patients) or placebo (76 patients), administered from 2 days before until day 7 after esophagectomy. The G-CSF and placebo groups were comparable as regards age, gender, risk, cancer stage, frequency of neoadjuvant radiochemotherapy, and type of esophagectomy (transthoracic or transhiatal esophageal resection). RESULTS Of 155 randomized patients, 153 were eligible for the intention-to-treat analysis. The rate of infection occurring within the first 10 days after esophagectomy was 43.4% (confidence interval 32.8-55.9%) in the placebo and 44.2% (confidence interval 32.1-55.3%) in the G-CSF group (P = 0.927). 30-day mortality amounted to 5.2% in the G-CSF group versus 5.3% in the placebo group (P = 0.985). Similar results were found in the per-protocol analysis. CONCLUSION Perioperative administration of G-CSF failed to reduce postoperative morbidity, infection rate, or mortality in patients with esophageal cancer who underwent esophagectomy.
Collapse
Affiliation(s)
- Hartmut Schaefer
- Department of Visceral and Vascular Surgery, University of Cologne, Germany
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
141
|
Abstract
Flexible designs for clinical trials permit mid-trial design modifications, which are based on interim information from inside or outside the trial while meeting (regulatory) requirements for the control of the type I error rate. The basic principle is to combine stage standardized test statistics such as p-values or z-scores in a pre-specified way. The flexibility covers changes of sample sizes, treatment allocation ratios and the number of interim analyses, as well as the selection of treatments, doses and end points. The price to be paid is that non-standard test statistics must be used after an adaptation.
Collapse
Affiliation(s)
- Peter Bauer
- Department of Medical Statistics University of Vienna, Schwarzspanierstr 17, A-1090 Vienna, Austria.
| | | |
Collapse
|
142
|
|
143
|
Schwartz TA, Denne JS. Common threads between sample size recalculation and group sequential procedures. Pharm Stat 2003. [DOI: 10.1002/pst.68] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
|
144
|
Abstract
We outline the general framework of adaptive combination tests and discuss their relationship to flexible group sequential designs. An important field of applications is sample size reassessment. We discuss reassessment rules based on conditional power arguments using either the observed or the prefixed effect size. These rules tend to lead to large expected sample sizes for small actual effects. However, the application of a maximal bound for the second stage sample size leads to more favourable properties. Additionally, we consider an optimized reassessment rule in terms of expected sample sizes. Since the adaptive design does not use the classical test statistics for some types of sample size reassessments, the adaptive test may reject the null hypothesis while the classical one-sample test does not. We characterize sample size reassessment rules, where such inconsistencies are avoided. Finally, the extension of flexibility to the number of stages is explored. In the first interim analysis a second interim analysis is only planned if the chance to achieve a decision there is high. This leads to savings in the average number of interim analysis performed, without paying a noticeable price in terms of expected sample size.
Collapse
Affiliation(s)
- Martin Posch
- Department of Medical Statistics, University of Vienna, Schwarzspanierstrasse 17, A-1090 Wien, Austria
| | | | | |
Collapse
|
145
|
Jennison C, Turnbull BW. Mid-course sample size modification in clinical trials based on the observed treatment effect. Stat Med 2003; 22:971-93. [PMID: 12627413 DOI: 10.1002/sim.1457] [Citation(s) in RCA: 146] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
It is not uncommon to set the sample size in a clinical trial to attain specified power at a value for the treatment effect deemed likely by the experimenters, even though a smaller treatment effect would still be clinically important. Recent papers have addressed the situation where such a study produces only weak evidence of a positive treatment effect at an interim stage and the organizers wish to modify the design in order to increase the power to detect a smaller treatment effect than originally expected. Raising the power at a small treatment effect usually leads to considerably higher power than was first specified at the original alternative. Several authors have proposed methods which are not based on sufficient statistics of the data after the adaptive redesign of the trial. We discuss these proposals and show in an example how the same objectives can be met while maintaining the sufficiency principle, as long as the eventuality that the treatment effect may be small is considered at the design stage. The group sequential designs we suggest are quite standard in many ways but unusual in that they place emphasis on reducing the expected sample size at a parameter value under which extremely high power is to be achieved. Comparisons of power and expected sample size show that our proposed methods can out-perform L. Fisher's 'variance spending' procedure. Although the flexibility to redesign an experiment in mid-course may be appealing, the cost in terms of the number of observations needed to correct an initial design may be substantial.
Collapse
|
146
|
Abstract
The problem of simultaneous sequential tests for noninferiority and superiority of a treatment, as compared to an active control, is considered in terms of continuous hierarchical families of one-sided null hypotheses, in the framework of group sequential and adaptive two-stage designs. The crucial point is that the decision boundaries for the individual null hypotheses may vary over the parameter space. This allows one to construct designs where, e.g., a rigid stopping criterion is chosen, rejecting or accepting all individual null hypotheses simultaneously. Another possibility is to use monitoring type stopping boundaries, which leave some flexibility to the experimenter: he can decide, at the interim analysis, whether he is satisfied with the noninferiority margin achieved at this stage, or wants to go for more at the second stage. In the case where he proceeds to the second stage, he may perform midtrial design modifications (e.g., reassess the sample size). The proposed approach allows one to "spend," e.g., less of alpha for an early proof of noninferiority than for an early proof of superiority, and is illustrated by typical examples.
Collapse
Affiliation(s)
- W Brannath
- Department of Medical Statistics, University of Vienna, Schwarzspanierstr. 17, A-1090 Vienna, Austria.
| | | | | | | |
Collapse
|