1
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Lyu T, Bornkamp B, Mueller-Velten G, Schmidli H. Bayesian inference for a principal stratum estimand on recurrent events truncated by death. Biometrics 2023; 79:3792-3802. [PMID: 36647690 DOI: 10.1111/biom.13831] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 01/05/2023] [Indexed: 01/18/2023]
Abstract
Recurrent events are often important endpoints in randomized clinical trials. For example, the number of recurrent disease-related hospitalizations may be considered as a clinically meaningful endpoint in cardiovascular studies. In some settings, the recurrent event process may be terminated by an event such as death, which makes it more challenging to define and estimate a causal treatment effect on recurrent event endpoints. In this paper, we focus on the principal stratum estimand, where the treatment effect of interest on recurrent events is defined among subjects who would be alive regardless of the assigned treatment. For the estimation of the principal stratum effect in randomized clinical trials, we propose a Bayesian approach based on a joint model of the recurrent event and death processes with a frailty term accounting for within-subject correlation. We also present Bayesian posterior predictive check procedures for assessing the model fit. The proposed approaches are demonstrated in the randomized Phase III chronic heart failure trial PARAGON-HF (NCT01920711).
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Affiliation(s)
- Tianmeng Lyu
- Novartis Pharmaceuticals Corporation, East Hanover, New Jersey, USA
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2
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Graves JS, Thomas M, Li J, Shah AR, Goodyear A, Lange MR, Schmidli H, Häring DA, Friede T, Gärtner J. Improving pediatric multiple sclerosis interventional phase III study design: a meta-analysis. Ther Adv Neurol Disord 2022; 15:17562864211070449. [PMID: 35514529 PMCID: PMC9066624 DOI: 10.1177/17562864211070449] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2021] [Accepted: 12/13/2021] [Indexed: 11/16/2022] Open
Abstract
Background: To support innovative trial designs in a regulatory setting for pediatric-onset multiple sclerosis (MS), the study aimed to perform a systematic literature review and meta-analysis of relapse rates with interferon β (IFN β), fingolimod, and natalizumab and thereby demonstrate potential benefits of Bayesian and non-inferiority designs in this population. Methods: We conducted a literature search in MEDLINE and EMBASE from inception until 17 June 2020 of all studies reporting annualized relapse rates (ARR) in IFN β-, fingolimod-, or natalizumab-treated patients with pediatric-onset relapsing–remitting MS. These interventions were chosen because the literature was mainly available for these treatments, and they are currently used for the treatment of pediatric MS. Two researchers independently extracted data and assessed study quality using the Cochrane Effective Practice and Organization of Care – Quality Assessment Tool. The meta-analysis estimates were obtained by Bayesian random effects model. Data were summarized as ARR point estimates and 95% credible intervals. Results: We found 19 articles, including 2 randomized controlled trials. The baseline ARR reported was between 1.4 and 3.7. The meta-analysis-based ARR was significantly higher in IFN β-treated patients (0.69, 95% credible interval: 0.51–0.91) versus fingolimod (0.11, 0.04–0.27) and natalizumab (0.17, 0.09–0.31). Based on the meta-analysis results, an appropriate non-inferiority margin versus fingolimod could be in the range of 2.29–2.67 and for natalizumab 1.72–2.29 on the ARR ratio scale. A Bayesian design, which uses historical information for a fingolimod or natalizumab control arm, could reduce the sample size of a new trial by 18 or 14 patients, respectively. Conclusion: This meta-analysis provides evidence that relapse rates are considerably higher with IFNs versus fingolimod or natalizumab. The results support the use of innovative Bayesian or non-inferiority designs to avoid exposing patients to less effective comparators in trials and bringing new medications to patients more efficiently.
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Affiliation(s)
- Jennifer S. Graves
- Department of Neurosciences, University of California, San Diego, Box 0662 ACTRI, 9452 Medical Center Drive, Suite 4W-222, San Diego, CA 92037, USA
| | | | - Jun Li
- Novartis Pharma AG, Basel, Switzerland
| | | | - Alexandra Goodyear
- Novartis Pharmaceuticals Corporation, East Hanover, NJ, USA at the time of article development
| | | | | | | | - Tim Friede
- Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany
| | - Jutta Gärtner
- Department of Pediatrics and Adolescent Medicine, German Center for Multiple Sclerosis in Childhood and Adolescence, University Medical Center Göttingen, Göttingen, Germany
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3
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Ocampo A, Schmidli H, Quarg P, Callegari F, Pagano M. Identifying treatment effects using trimmed means when data are missing not at random. Pharm Stat 2021; 20:1265-1277. [PMID: 34169641 DOI: 10.1002/pst.2147] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Revised: 05/28/2021] [Accepted: 06/01/2021] [Indexed: 11/06/2022]
Abstract
Patients often discontinue from a clinical trial because their health condition is not improving or they cannot tolerate the assigned treatment. Consequently, the observed clinical outcomes in the trial are likely better on average than if every patient had completed the trial. If these differences between trial completers and non-completers cannot be explained by the observed data, then the study outcomes are missing not at random (MNAR). One way to overcome this problem-the trimmed means approach for missing data due to study discontinuation-sets missing values as the worst observed outcome and then trims away a fraction of the distribution from each treatment arm before calculating differences in treatment efficacy (Permutt T, Li F. Trimmed means for symptom trials with dropouts. Pharm Stat. 2017;16(1):20-28). In this paper, we derive sufficient and necessary conditions for when this approach can identify the average population treatment effect. Simulation studies show the trimmed means approach's ability to effectively estimate treatment efficacy when data are MNAR and missingness due to study discontinuation is strongly associated with an unfavorable outcome, but trimmed means fail when data are missing at random. If the reasons for study discontinuation in a clinical trial are known, analysts can improve estimates with a combination of multiple imputation and the trimmed means approach when the assumptions of each hold. We compare the methodology to existing approaches using data from a clinical trial for chronic pain. An R package trim implements the method. When the assumptions are justifiable, using trimmed means can help identify treatment effects notwithstanding MNAR data.
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Affiliation(s)
- Alex Ocampo
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts, USA
| | | | | | | | - Marcello Pagano
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts, USA
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4
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Akacha M, Bartels C, Bornkamp B, Bretz F, Coello N, Dumortier T, Looby M, Sander O, Schmidli H, Steimer JL, Vong C. Estimands-What they are and why they are important for pharmacometricians. CPT Pharmacometrics Syst Pharmacol 2021; 10:279-282. [PMID: 33951755 PMCID: PMC8090974 DOI: 10.1002/psp4.12617] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Revised: 02/02/2021] [Accepted: 02/09/2021] [Indexed: 11/08/2022]
Affiliation(s)
- Mouna Akacha
- Clinical Development and Analytics, Novartis Pharma AG, Basel, Switzerland
| | - Christian Bartels
- Clinical Development and Analytics, Novartis Pharma AG, Basel, Switzerland
| | - Björn Bornkamp
- Clinical Development and Analytics, Novartis Pharma AG, Basel, Switzerland
| | - Frank Bretz
- Clinical Development and Analytics, Novartis Pharma AG, Basel, Switzerland
| | - Neva Coello
- Clinical Development and Analytics, Novartis Pharma AG, Basel, Switzerland
| | - Thomas Dumortier
- Clinical Development and Analytics, Novartis Pharma AG, Basel, Switzerland
| | - Michael Looby
- Clinical Development and Analytics, Novartis Pharma AG, Basel, Switzerland
| | - Oliver Sander
- Clinical Development and Analytics, Novartis Pharma AG, Basel, Switzerland
| | - Heinz Schmidli
- Clinical Development and Analytics, Novartis Pharma AG, Basel, Switzerland
| | - Jean-Louis Steimer
- Clinical Development and Analytics, Novartis Pharma AG, Basel, Switzerland
| | - Camille Vong
- Clinical Development and Analytics, Novartis Pharma AG, Basel, Switzerland
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5
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Affiliation(s)
| | - James H. Roger
- Medical Statistics Department, London School of Hygiene & Tropical Medicine, London, UK
| | - Mouna Akacha
- Statistical Methodology, Novartis, Basel, Switzerland, on behalf of the Recurrent Event Qualification Opinion Consortium
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6
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Bornkamp B, Rufibach K, Lin J, Liu Y, Mehrotra DV, Roychoudhury S, Schmidli H, Shentu Y, Wolbers M. Principal stratum strategy: Potential role in drug development. Pharm Stat 2021; 20:737-751. [PMID: 33624407 DOI: 10.1002/pst.2104] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 12/01/2020] [Accepted: 02/05/2021] [Indexed: 12/12/2022]
Abstract
A randomized trial allows estimation of the causal effect of an intervention compared to a control in the overall population and in subpopulations defined by baseline characteristics. Often, however, clinical questions also arise regarding the treatment effect in subpopulations of patients, which would experience clinical or disease related events post-randomization. Events that occur after treatment initiation and potentially affect the interpretation or the existence of the measurements are called intercurrent events in the ICH E9(R1) guideline. If the intercurrent event is a consequence of treatment, randomization alone is no longer sufficient to meaningfully estimate the treatment effect. Analyses comparing the subgroups of patients without the intercurrent events for intervention and control will not estimate a causal effect. This is well known, but post-hoc analyses of this kind are commonly performed in drug development. An alternative approach is the principal stratum strategy, which classifies subjects according to their potential occurrence of an intercurrent event on both study arms. We illustrate with examples that questions formulated through principal strata occur naturally in drug development and argue that approaching these questions with the ICH E9(R1) estimand framework has the potential to lead to more transparent assumptions as well as more adequate analyses and conclusions. In addition, we provide an overview of assumptions required for estimation of effects in principal strata. Most of these assumptions are unverifiable and should hence be based on solid scientific understanding. Sensitivity analyses are needed to assess robustness of conclusions.
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Affiliation(s)
- Björn Bornkamp
- Clinical Development and Analytics, Novartis, Basel, Switzerland
| | - Kaspar Rufibach
- Methods, Collaboration, and Outreach Group (MCO), Department of Biostatistics, Hoffmann-La Roche Ltd, Basel, Switzerland
| | - Jianchang Lin
- Statistical & Quantitative Sciences (SQS), Takeda Pharmaceuticals, Cambridge, Massachusetts, USA
| | - Yi Liu
- Nektar Therapeutics, San Francisco, California, USA
| | - Devan V Mehrotra
- Clinical Biostatistics, Merck & Co., Inc., North Wales, Pennsylvania, USA
| | | | - Heinz Schmidli
- Clinical Development and Analytics, Novartis, Basel, Switzerland
| | - Yue Shentu
- Merck & Co., Inc., Rahway, New Jersey, USA
| | - Marcel Wolbers
- Methods, Collaboration, and Outreach Group (MCO), Department of Biostatistics, Hoffmann-La Roche Ltd, Basel, Switzerland
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7
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Röver C, Bender R, Dias S, Schmid CH, Schmidli H, Sturtz S, Weber S, Friede T. On weakly informative prior distributions for the heterogeneity parameter in Bayesian random-effects meta-analysis. Res Synth Methods 2021; 12:448-474. [PMID: 33486828 DOI: 10.1002/jrsm.1475] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Revised: 01/13/2021] [Accepted: 01/16/2021] [Indexed: 12/13/2022]
Abstract
The normal-normal hierarchical model (NNHM) constitutes a simple and widely used framework for meta-analysis. In the common case of only few studies contributing to the meta-analysis, standard approaches to inference tend to perform poorly, and Bayesian meta-analysis has been suggested as a potential solution. The Bayesian approach, however, requires the sensible specification of prior distributions. While noninformative priors are commonly used for the overall mean effect, the use of weakly informative priors has been suggested for the heterogeneity parameter, in particular in the setting of (very) few studies. To date, however, a consensus on how to generally specify a weakly informative heterogeneity prior is lacking. Here we investigate the problem more closely and provide some guidance on prior specification.
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Affiliation(s)
- Christian Röver
- Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany
| | - Ralf Bender
- Department of Medical Biometry, Institute for Quality and Efficiency in Health Care (IQWiG), Köln, Germany
| | - Sofia Dias
- Centre for Reviews and Dissemination, University of York, York, UK
| | - Christopher H Schmid
- Department of Biostatistics and Center for Evidence Synthesis in Health, Brown University School of Public Health, Providence, Rhode Island, USA
| | - Heinz Schmidli
- Statistical Methodology, Development, Novartis Pharma AG, Basel, Switzerland
| | - Sibylle Sturtz
- Department of Medical Biometry, Institute for Quality and Efficiency in Health Care (IQWiG), Köln, Germany
| | - Sebastian Weber
- Advanced Exploratory Analytics, Novartis Pharma AG, Basel, Switzerland
| | - Tim Friede
- Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany
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8
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Weber S, Li Y, III JWS, Kakizume T, Schmidli H. Applying Meta-Analytic-Predictive Priors with the R Bayesian Evidence Synthesis Tools. J Stat Softw 2021. [DOI: 10.18637/jss.v100.i19] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022] Open
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9
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Mütze T, Salem S, Benda N, Schmidli H, Friede T. Blinded continuous information monitoring of recurrent event endpoints with time trends in clinical trials. Stat Med 2020; 39:3968-3985. [DOI: 10.1002/sim.8702] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2019] [Revised: 05/07/2020] [Accepted: 07/01/2020] [Indexed: 11/12/2022]
Affiliation(s)
- Tobias Mütze
- Statistical Methodology Novartis Pharma AG Basel Switzerland
| | - Susanna Salem
- Department of Medical Statistics University Medical Center Göttingen Göttingen Germany
| | - Norbert Benda
- Department of Medical Statistics University Medical Center Göttingen Göttingen Germany
- Biostatistics and Special Pharmacokinetics Unit Federal Institute for Drugs and Medical Devices Bonn Germany
| | - Heinz Schmidli
- Statistical Methodology Novartis Pharma AG Basel Switzerland
| | - Tim Friede
- Department of Medical Statistics University Medical Center Göttingen Göttingen Germany
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10
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Neuenschwander B, Weber S, Schmidli H, O'Hagan A. Rejoinder to "Predictively consistent prior effective sample sizes," by Beat Neuenschwander, Sebastian Weber, Heinz Schmidli, and Anthony O'Hagan. Biometrics 2020; 76:602-605. [PMID: 32251524 DOI: 10.1111/biom.13245] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2020] [Accepted: 02/25/2020] [Indexed: 12/01/2022]
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11
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Neuenschwander B, Weber S, Schmidli H, O'Hagan A. Predictively consistent prior effective sample sizes. Biometrics 2020; 76:578-587. [DOI: 10.1111/biom.13252] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2019] [Accepted: 09/09/2019] [Indexed: 11/28/2022]
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12
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Schmidli H, Häring DA, Thomas M, Cassidy A, Weber S, Bretz F. Beyond Randomized Clinical Trials: Use of External Controls. Clin Pharmacol Ther 2019; 107:806-816. [DOI: 10.1002/cpt.1723] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2019] [Accepted: 11/07/2019] [Indexed: 12/30/2022]
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13
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Magnusson BP, Schmidli H, Rouyrre N, Scharfstein DO. Bayesian inference for a principal stratum estimand to assess the treatment effect in a subgroup characterized by postrandomization event occurrence. Stat Med 2019; 38:4761-4771. [DOI: 10.1002/sim.8333] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2018] [Revised: 06/14/2019] [Accepted: 07/02/2019] [Indexed: 01/08/2023]
Affiliation(s)
| | - Heinz Schmidli
- Biostatistics and PharmacometricsNovartis Pharma AG Basel Switzerland
| | - Nicolas Rouyrre
- Biostatistics and PharmacometricsNovartis Pharma AG Basel Switzerland
| | - Daniel O. Scharfstein
- Department of BiostatisticsJohns Hopkins Bloomberg School of Public Health Baltimore Maryland
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14
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Friede T, Pohlmann H, Schmidli H. Blinded sample size reestimation in event‐driven clinical trials: Methods and an application in multiple sclerosis. Pharm Stat 2019; 18:351-365. [DOI: 10.1002/pst.1927] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2018] [Revised: 10/28/2018] [Accepted: 12/14/2018] [Indexed: 11/10/2022]
Affiliation(s)
- Tim Friede
- Department of Medical StatisticsUniversity Medical Center Göttingen Göttingen Germany
| | - Harald Pohlmann
- Biostatistics NSO FranchiseNovartis Pharma AG Basel Switzerland
| | - Heinz Schmidli
- Statistical MethodologyNovartis Pharma AG Basel Switzerland
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15
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Asendorf T, Henderson R, Schmidli H, Friede T. Sample size re‐estimation for clinical trials with longitudinal negative binomial counts including time trends. Stat Med 2018; 38:1503-1528. [DOI: 10.1002/sim.8061] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Revised: 11/16/2018] [Accepted: 11/19/2018] [Indexed: 11/11/2022]
Affiliation(s)
- Thomas Asendorf
- Department of Medical StatisticsUniversity Medical Center Göttingen Göttingen Germany
| | - Robin Henderson
- School of Mathematics, Statistics and PhysicsNewcastle University Newcastle upon Tyne UK
| | - Heinz Schmidli
- Statistical Methodology GroupNovartis Pharma AG Basel Switzerland
| | - Tim Friede
- Department of Medical StatisticsUniversity Medical Center Göttingen Göttingen Germany
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16
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Friede T, Häring DA, Schmidli H. Blinded continuous monitoring in clinical trials with recurrent event endpoints. Pharm Stat 2018; 18:54-64. [PMID: 30345693 PMCID: PMC6587844 DOI: 10.1002/pst.1907] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Revised: 07/21/2018] [Accepted: 09/18/2018] [Indexed: 11/12/2022]
Abstract
In studies with recurrent event endpoints, misspecified assumptions of event rates or dispersion can lead to underpowered trials or overexposure of patients. Specification of overdispersion is often a particular problem as it is usually not reported in clinical trial publications. Changing event rates over the years have been described for some diseases, adding to the uncertainty in planning. To mitigate the risks of inadequate sample sizes, internal pilot study designs have been proposed with a preference for blinded sample size reestimation procedures, as they generally do not affect the type I error rate and maintain trial integrity. Blinded sample size reestimation procedures are available for trials with recurrent events as endpoints. However, the variance in the reestimated sample size can be considerable in particular with early sample size reviews. Motivated by a randomized controlled trial in paediatric multiple sclerosis, a rare neurological condition in children, we apply the concept of blinded continuous monitoring of information, which is known to reduce the variance in the resulting sample size. Assuming negative binomial distributions for the counts of recurrent relapses, we derive information criteria and propose blinded continuous monitoring procedures. The operating characteristics of these are assessed in Monte Carlo trial simulations demonstrating favourable properties with regard to type I error rate, power, and stopping time, ie, sample size.
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Affiliation(s)
- Tim Friede
- Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany
| | - Dieter A Häring
- Biostatistics Neuroscience Development Unit, Novartis Pharma AG, Basel, Switzerland
| | - Heinz Schmidli
- Statistical Methodology, Novartis Pharma AG, Basel, Switzerland
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17
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Schmidli H. Dividends with tax and capital injection in a spectrally negative Lévy risk model. Theor Probability and Math Statist 2018. [DOI: 10.1090/tpms/1043] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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18
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Abstract
Robust semiparametric models for recurrent events have received increasing attention in the analysis of clinical trials in a variety of diseases including chronic heart failure. In comparison to parametric recurrent event models, robust semiparametric models are more flexible in that neither the baseline event rate nor the process inducing between-patient heterogeneity needs to be specified in terms of a specific parametric statistical model. However, implementing group sequential designs in the robust semiparametric model is complicated by the fact that the sequence of Wald statistics does not follow asymptotically the canonical joint distribution. In this manuscript, we propose two types of group sequential procedures for a robust semiparametric analysis of recurrent events. The first group sequential procedure is based on the asymptotic covariance of the sequence of Wald statistics and it guarantees asymptotic control of the type I error rate. The second procedure is based on the canonical joint distribution and does not guarantee asymptotic type I error rate control but is easy to implement and corresponds to the well-known standard approach for group sequential designs. Moreover, we describe how to determine the maximum information when planning a clinical trial with a group sequential design and a robust semiparametric analysis of recurrent events. We contrast the operating characteristics of the proposed group sequential procedures in a simulation study motivated by the ongoing phase 3 PARAGON-HF trial (ClinicalTrials.gov identifier: NCT01920711) in more than 4600 patients with chronic heart failure and a preserved ejection fraction. We found that both group sequential procedures have similar operating characteristics and that for some practically relevant scenarios, the group sequential procedure based on the canonical joint distribution has advantages with respect to the control of the type I error rate. The proposed method for calculating the maximum information results in appropriately powered trials for both procedures.
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Affiliation(s)
- Tobias Mütze
- Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany
| | - Ekkehard Glimm
- Statistical Methodology, Novartis Pharma AG, Basel, Switzerland
- Institute for Biometrics and Medical Informatics, Medical Faculty, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany
| | - Heinz Schmidli
- Statistical Methodology, Novartis Pharma AG, Basel, Switzerland
| | - Tim Friede
- Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany
- DZHK (German Centre for Cardiovascular Research), partner site Göttingen, Göttingen, Germany
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19
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Abstract
Count data and recurrent events in clinical trials, such as the number of lesions in magnetic resonance imaging in multiple sclerosis, the number of relapses in multiple sclerosis, the number of hospitalizations in heart failure, and the number of exacerbations in asthma or in chronic obstructive pulmonary disease (COPD) are often modeled by negative binomial distributions. In this manuscript, we study planning and analyzing clinical trials with group sequential designs for negative binomial outcomes. We propose a group sequential testing procedure for negative binomial outcomes based on Wald statistics using maximum likelihood estimators. The asymptotic distribution of the proposed group sequential test statistics is derived. The finite sample size properties of the proposed group sequential test for negative binomial outcomes and the methods for planning the respective clinical trials are assessed in a simulation study. The simulation scenarios are motivated by clinical trials in chronic heart failure and relapsing multiple sclerosis, which cover a wide range of practically relevant settings. Our research assures that the asymptotic normal theory of group sequential designs can be applied to negative binomial outcomes when the hypotheses are tested using Wald statistics and maximum likelihood estimators. We also propose two methods, one based on Student's t-distribution and one based on resampling, to improve type I error rate control in small samples. The statistical methods studied in this manuscript are implemented in the R package gscounts, which is available for download on the Comprehensive R Archive Network (CRAN).
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Affiliation(s)
- Tobias Mütze
- 1 Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany
| | - Ekkehard Glimm
- 2 Statistical Methodology, Novartis Pharma AG, Basel, Switzerland.,3 Medical Faculty, Institute for Biometrics and Medical Informatics, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany
| | - Heinz Schmidli
- 2 Statistical Methodology, Novartis Pharma AG, Basel, Switzerland
| | - Tim Friede
- 1 Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany.,4 DZHK (German Centre for Cardiovascular Research), partner site Göttingen, Göttingen, Germany
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Abstract
For the approval of biosimilars, it is, in most cases, necessary to conduct large Phase III clinical trials in patients to convince the regulatory authorities that the product is comparable in terms of efficacy and safety to the originator product. As the originator product has already been studied in several trials beforehand, it seems natural to include this historical information into the showing of equivalent efficacy. Since all studies for the regulatory approval of biosimilars are confirmatory studies, it is required that the statistical approach has reasonable frequentist properties, most importantly, that the Type I error rate is controlled-at least in all scenarios that are realistic in practice. However, it is well known that the incorporation of historical information can lead to an inflation of the Type I error rate in the case of a conflict between the distribution of the historical data and the distribution of the trial data. We illustrate this issue and confirm, using the Bayesian robustified meta-analytic-predictive (MAP) approach as an example, that simultaneously controlling the Type I error rate over the complete parameter space and gaining power in comparison to a standard frequentist approach that only considers the data in the new study, is not possible. We propose a hybrid Bayesian-frequentist approach for binary endpoints that controls the Type I error rate in the neighborhood of the center of the prior distribution, while improving the power. We study the properties of this approach in an extensive simulation study and provide a real-world example.
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Affiliation(s)
- Johanna Mielke
- Statistical Methodology, Novartis Pharma AG, 4002, Basel, Switzerland
| | - Heinz Schmidli
- Statistical Methodology, Novartis Pharma AG, 4002, Basel, Switzerland
| | - Byron Jones
- Statistical Methodology, Novartis Pharma AG, 4002, Basel, Switzerland
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21
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Schmidli H, Friede T. Blinded Sample Size Reestimation with Negative Binomial Counts in Superiority and Non-inferiority Trials. Methods Inf Med 2018; 49:618-24. [DOI: 10.3414/me09-02-0060] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2009] [Accepted: 05/11/2010] [Indexed: 11/09/2022]
Abstract
Summary
Background: In the planning of clinical trials with count outcomes such as the number of exacerbations in chronic obstructive pulmonary disease (COPD) often considerable uncertainty exists with regard to the overall event rate and the level of overdispersion which are both crucial for sample size calculations.
Objectives: To develop a sample size reestimation strategy that maintains the blinding of the trial, controls the type I error rate and is robust against misspecification of the nuisance parameters in the planning phase in that the actual power is close to the target.
Methods: The operation characteristics of the developed sample size reestimation procedure are investigated in a Monte Carlo simulation study.
Results: Estimators of the overall event rate and the overdispersion parameter that do not require unblinding can be used to effectively adjust the sample size without inflating the type I error rate while providing power values close to the target.
Conclusions: If only little information is available regarding the size of the overall event rate and the overdispersion parameter in the design phase of a trial, we recommend the use of a design with sample size reestimation as the one suggested here. Trials in COPD are expected to benefit from the proposed sample size reestimation strategy.
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Mütze T, Schmidli H, Friede T. Sample size re-estimation incorporating prior information on a nuisance parameter. Pharm Stat 2017; 17:126-143. [PMID: 29181869 DOI: 10.1002/pst.1837] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2017] [Revised: 07/05/2017] [Accepted: 10/10/2017] [Indexed: 11/05/2022]
Abstract
Prior information is often incorporated informally when planning a clinical trial. Here, we present an approach on how to incorporate prior information, such as data from historical clinical trials, into the nuisance parameter-based sample size re-estimation in a design with an internal pilot study. We focus on trials with continuous endpoints in which the outcome variance is the nuisance parameter. For planning and analyzing the trial, frequentist methods are considered. Moreover, the external information on the variance is summarized by the Bayesian meta-analytic-predictive approach. To incorporate external information into the sample size re-estimation, we propose to update the meta-analytic-predictive prior based on the results of the internal pilot study and to re-estimate the sample size using an estimator from the posterior. By means of a simulation study, we compare the operating characteristics such as power and sample size distribution of the proposed procedure with the traditional sample size re-estimation approach that uses the pooled variance estimator. The simulation study shows that, if no prior-data conflict is present, incorporating external information into the sample size re-estimation improves the operating characteristics compared to the traditional approach. In the case of a prior-data conflict, that is, when the variance of the ongoing clinical trial is unequal to the prior location, the performance of the traditional sample size re-estimation procedure is in general superior, even when the prior information is robustified. When considering to include prior information in sample size re-estimation, the potential gains should be balanced against the risks.
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Affiliation(s)
- Tobias Mütze
- Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany
| | - Heinz Schmidli
- Statistical Methodology, Novartis Pharma AG, Basel, Switzerland
| | - Tim Friede
- Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany.,DZHK (German Centre for Cardiovascular Research), Partner Site Göttingen, Göttingen, Germany
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23
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Holzhauer B, Wang C, Schmidli H. Evidence synthesis from aggregate recurrent event data for clinical trial design and analysis. Stat Med 2017; 37:867-882. [PMID: 29152777 DOI: 10.1002/sim.7549] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2017] [Revised: 08/11/2017] [Accepted: 10/09/2017] [Indexed: 01/19/2023]
Abstract
Information from historical trials is important for the design, interim monitoring, analysis, and interpretation of clinical trials. Meta-analytic models can be used to synthesize the evidence from historical data, which are often only available in aggregate form. We consider evidence synthesis methods for trials with recurrent event endpoints, which are common in many therapeutic areas. Such endpoints are typically analyzed by negative binomial regression. However, the individual patient data necessary to fit such a model are usually unavailable for historical trials reported in the medical literature. We describe approaches for back-calculating model parameter estimates and their standard errors from available summary statistics with various techniques, including approximate Bayesian computation. We propose to use a quadratic approximation to the log-likelihood for each historical trial based on 2 independent terms for the log mean rate and the log of the dispersion parameter. A Bayesian hierarchical meta-analysis model then provides the posterior predictive distribution for these parameters. Simulations show this approach with back-calculated parameter estimates results in very similar inference as using parameter estimates from individual patient data as an input. We illustrate how to design and analyze a new randomized placebo-controlled exacerbation trial in severe eosinophilic asthma using data from 11 historical trials.
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Affiliation(s)
- Mouna Akacha
- Novartis Pharma AG, Statistical Methodology and Consulting, Basel, Switzerland
| | - Frank Bretz
- Novartis Pharma AG, Statistical Methodology and Consulting, Basel, Switzerland
- Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Wien, Austria
| | - David Ohlssen
- Novartis Pharmaceuticals Corporation, Statistical Methodology and Consulting, East Hanover, NJ
| | - Gerd Rosenkranz
- Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Wien, Austria
| | - Heinz Schmidli
- Novartis Pharma AG, Statistical Methodology and Consulting, Basel, Switzerland
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25
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Asendorf T, Henderson R, Schmidli H, Friede T. Modelling and sample size reestimation for longitudinal count data with incomplete follow up. Stat Methods Med Res 2017. [DOI: 10.1177/0962280217715664] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We consider modelling and inference as well as sample size estimation and reestimation for clinical trials with longitudinal count data as outcomes. Our approach is general but is rooted in design and analysis of multiple sclerosis trials where lesion counts obtained by magnetic resonance imaging are important endpoints. We adopt a binomial thinning model that allows for correlated counts with marginal Poisson or negative binomial distributions. Methods for sample size planning and blinded sample size reestimation for randomised controlled clinical trials with such outcomes are developed. The models and approaches are applicable to data with incomplete observations. A simulation study is conducted to assess the effectiveness of sample size estimation and blinded sample size reestimation methods. Sample sizes attained through these procedures are shown to maintain the desired study power without inflating the type I error. Data from a recent trial in patients with secondary progressive multiple sclerosis illustrate the modelling approach.
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Affiliation(s)
- Thomas Asendorf
- Department of Medical Statistics, University Medical Center Göttingen, Germany
| | - Robin Henderson
- School of Mathematics and Statistics, University of Newcastle, UK
| | - Heinz Schmidli
- Statistical Methodology, Novartis Pharma AG, Switzerland
| | - Tim Friede
- Department of Medical Statistics, University Medical Center Göttingen, Germany
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26
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Bornkamp B, Ohlssen D, Magnusson BP, Schmidli H. Model averaging for treatment effect estimation in subgroups. Pharm Stat 2016; 16:133-142. [DOI: 10.1002/pst.1796] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2016] [Revised: 10/18/2016] [Accepted: 10/26/2016] [Indexed: 11/09/2022]
Affiliation(s)
| | - David Ohlssen
- Novartis Pharmaceuticals Corporation East Hanover New Jersey 07936-1080 USA
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27
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28
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Pozzi L, Schmidli H, Ohlssen DI. A Bayesian hierarchical surrogate outcome model for multiple sclerosis. Pharm Stat 2016; 15:341-8. [DOI: 10.1002/pst.1749] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2015] [Revised: 12/14/2015] [Accepted: 02/29/2016] [Indexed: 01/08/2023]
Affiliation(s)
- Luca Pozzi
- Division of Biostatistics; University of California Berkeley; Berkeley 94720-7358 CA USA
| | - Heinz Schmidli
- Statistical Methodology, Development; Novartis Pharma AG; Basel Switzerland
| | - David I. Ohlssen
- Statistical Methodology, Development; Novartis Pharmaceuticals Corporation; East Hanover 07936-1080 NJ USA
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30
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Gamalo-Siebers M, Gao A, Lakshminarayanan M, Liu G, Natanegara F, Railkar R, Schmidli H, Song G. Bayesian methods for the design and analysis of noninferiority trials. J Biopharm Stat 2015; 26:823-41. [PMID: 26247350 DOI: 10.1080/10543406.2015.1074920] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Abstract
The gold standard for evaluating treatment efficacy of a medical product is a placebo-controlled trial. However, when the use of placebo is considered to be unethical or impractical, a viable alternative for evaluating treatment efficacy is through a noninferiority (NI) study where a test treatment is compared to an active control treatment. The minimal objective of such a study is to determine whether the test treatment is superior to placebo. An assumption is made that if the active control treatment remains efficacious, as was observed when it was compared against placebo, then a test treatment that has comparable efficacy with the active control, within a certain range, must also be superior to placebo. Because of this assumption, the design, implementation, and analysis of NI trials present challenges for sponsors and regulators. In designing and analyzing NI trials, substantial historical data are often required on the active control treatment and placebo. Bayesian approaches provide a natural framework for synthesizing the historical data in the form of prior distributions that can effectively be used in design and analysis of a NI clinical trial. Despite a flurry of recent research activities in the area of Bayesian approaches in medical product development, there are still substantial gaps in recognition and acceptance of Bayesian approaches in NI trial design and analysis. The Bayesian Scientific Working Group of the Drug Information Association provides a coordinated effort to target the education and implementation issues on Bayesian approaches for NI trials. In this article, we provide a review of both frequentist and Bayesian approaches in NI trials, and elaborate on the implementation for two common Bayesian methods including hierarchical prior method and meta-analytic-predictive approach. Simulations are conducted to investigate the properties of the Bayesian methods, and some real clinical trial examples are presented for illustration.
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Affiliation(s)
| | - Aijun Gao
- b InVentiv Health Clinical , Princeton , New Jersey , USA
| | - Mani Lakshminarayanan
- c Biotechnology Clinical Development Statistics, Pfizer Inc. , Collegeville , Pennsylvania , USA
| | - Guanghan Liu
- d Merck Sharp & Dohme Corp. , North Wales , Pennsylvania , USA
| | | | - Radha Railkar
- c Biotechnology Clinical Development Statistics, Pfizer Inc. , Collegeville , Pennsylvania , USA
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31
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Lange MR, Schmidli H. Analysis of clinical trials with biologics using dose-time-response models. Stat Med 2015; 34:3017-28. [DOI: 10.1002/sim.6551] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2013] [Revised: 01/09/2015] [Accepted: 05/17/2015] [Indexed: 01/02/2023]
Affiliation(s)
- Markus R. Lange
- Statistical Methodology; Development, Novartis Pharma AG; Basel Switzerland
- Institute for Biometry; Hannover Medical School; Hannover Germany
| | - Heinz Schmidli
- Statistical Methodology; Development, Novartis Pharma AG; Basel Switzerland
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32
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Schmidli H, Gsteiger S, Roychoudhury S, O'Hagan A, Spiegelhalter D, Neuenschwander B. Robust meta-analytic-predictive priors in clinical trials with historical control information. Biometrics 2014; 70:1023-32. [PMID: 25355546 DOI: 10.1111/biom.12242] [Citation(s) in RCA: 238] [Impact Index Per Article: 23.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2013] [Revised: 06/01/2014] [Accepted: 07/01/2014] [Indexed: 11/27/2022]
Abstract
Historical information is always relevant for clinical trial design. Additionally, if incorporated in the analysis of a new trial, historical data allow to reduce the number of subjects. This decreases costs and trial duration, facilitates recruitment, and may be more ethical. Yet, under prior-data conflict, a too optimistic use of historical data may be inappropriate. We address this challenge by deriving a Bayesian meta-analytic-predictive prior from historical data, which is then combined with the new data. This prospective approach is equivalent to a meta-analytic-combined analysis of historical and new data if parameters are exchangeable across trials. The prospective Bayesian version requires a good approximation of the meta-analytic-predictive prior, which is not available analytically. We propose two- or three-component mixtures of standard priors, which allow for good approximations and, for the one-parameter exponential family, straightforward posterior calculations. Moreover, since one of the mixture components is usually vague, mixture priors will often be heavy-tailed and therefore robust. Further robustness and a more rapid reaction to prior-data conflicts can be achieved by adding an extra weakly-informative mixture component. Use of historical prior information is particularly attractive for adaptive trials, as the randomization ratio can then be changed in case of prior-data conflict. Both frequentist operating characteristics and posterior summaries for various data scenarios show that these designs have desirable properties. We illustrate the methodology for a phase II proof-of-concept trial with historical controls from four studies. Robust meta-analytic-predictive priors alleviate prior-data conflicts ' they should encourage better and more frequent use of historical data in clinical trials.
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Affiliation(s)
- Heinz Schmidli
- Statistical Methodology, Development, Novartis Pharma AG, Basel, Switzerland
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33
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Lange MR, Schmidli H. Optimal design of clinical trials with biologics using dose-time-response models. Stat Med 2014; 33:5249-64. [DOI: 10.1002/sim.6299] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2013] [Revised: 07/31/2014] [Accepted: 08/20/2014] [Indexed: 12/23/2022]
Affiliation(s)
- Markus R. Lange
- Statistical Methodology, Development; Novartis Pharma AG; Basel Switzerland
- Hannover Medical School; Institute for Biometry; Hannover Germany
| | - Heinz Schmidli
- Statistical Methodology, Development; Novartis Pharma AG; Basel Switzerland
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34
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Schneider S, Schmidli H, Friede T. Blinded sample size re-estimation for recurrent event data with time trends. Stat Med 2013; 32:5448-57. [DOI: 10.1002/sim.5977] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2012] [Accepted: 08/27/2013] [Indexed: 11/09/2022]
Affiliation(s)
- S. Schneider
- Department of Medical Statistics; University Medical Center Göttingen; Göttingen Germany
| | - H. Schmidli
- Statistical Methodology; Novartis Pharma AG; Basel Switzerland
| | - T. Friede
- Department of Medical Statistics; University Medical Center Göttingen; Göttingen Germany
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35
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Pozzi L, Schmidli H, Gasparini M, Racine-Poon A. A Bayesian adaptive dose selection procedure with an overdispersed count endpoint. Stat Med 2013; 32:5008-27. [DOI: 10.1002/sim.5932] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2012] [Revised: 06/28/2013] [Accepted: 07/08/2013] [Indexed: 11/10/2022]
Affiliation(s)
- L. Pozzi
- Division of Biostatistics; University of California; Berkeley CA U.S.A
| | - H. Schmidli
- Statistical Methodology; Novartis Pharma AG; Basel Switzerland
| | - M. Gasparini
- Department of Mathematical Sciences; Politecnico di Torino; Torino Italy
| | - A. Racine-Poon
- Modeling & Simulation; Novartis Pharma AG; Basel Switzerland
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36
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Gsponer T, Gerber F, Bornkamp B, Ohlssen D, Vandemeulebroecke M, Schmidli H. A practical guide to Bayesian group sequential designs. Pharm Stat 2013; 13:71-80. [DOI: 10.1002/pst.1593] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2012] [Revised: 07/25/2013] [Accepted: 08/01/2013] [Indexed: 11/10/2022]
Affiliation(s)
- Thomas Gsponer
- Institute of Social and Preventive Medicine; University of Bern; Bern Switzerland
| | - Florian Gerber
- Institute of Social and Preventive Medicine; University of Bern; Bern Switzerland
| | - Björn Bornkamp
- Statistical Methodology; Novartis Pharma AG; Basel Switzerland
| | - David Ohlssen
- Statistical Methodology; Novartis Pharmaceuticals Corporation; East Hanover, NJ USA
| | | | - Heinz Schmidli
- Statistical Methodology; Novartis Pharma AG; Basel Switzerland
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37
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Gsteiger S, Neuenschwander B, Mercier F, Schmidli H. Using historical control information for the design and analysis of clinical trials with overdispersed count data. Stat Med 2013; 32:3609-22. [DOI: 10.1002/sim.5851] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2012] [Revised: 04/16/2013] [Accepted: 04/23/2013] [Indexed: 01/17/2023]
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Schneider S, Schmidli H, Friede T. Blinded and unblinded internal pilot study designs for clinical trials with count data. Biom J 2013; 55:617-33. [PMID: 23703749 DOI: 10.1002/bimj.201200189] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2012] [Revised: 01/16/2013] [Accepted: 02/25/2013] [Indexed: 11/11/2022]
Abstract
Internal pilot studies are a popular design feature to address uncertainties in the sample size calculations caused by vague information on nuisance parameters. Despite their popularity, only very recently blinded sample size reestimation procedures for trials with count data were proposed and their properties systematically investigated. Although blinded procedures are favored by regulatory authorities, practical application is somewhat limited by fears that blinded procedures are prone to bias if the treatment effect was misspecified in the planning. Here, we compare unblinded and blinded procedures with respect to bias, error rates, and sample size distribution. We find that both procedures maintain the desired power and that the unblinded procedure is slightly liberal whereas the actual significance level of the blinded procedure is close to the nominal level. Furthermore, we show that in situations where uncertainty about the assumed treatment effect exists, the blinded estimator of the control event rate is biased in contrast to the unblinded estimator, which results in differences in mean sample sizes in favor of the unblinded procedure. However, these differences are rather small compared to the deviations of the mean sample sizes from the sample size required to detect the true, but unknown effect. We demonstrate that the variation of the sample size resulting from the blinded procedure is in many practically relevant situations considerably smaller than the one of the unblinded procedures. The methods are extended to overdispersed counts using a quasi-likelihood approach and are illustrated by trials in relapsing multiple sclerosis.
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Affiliation(s)
- Simon Schneider
- Department of Medical Statistics, University Medical Center Göttingen, Germany.
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Affiliation(s)
- Heinz Schmidli
- a Statistical Methodology , Novartis Pharma AG , Basel , Switzerland
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40
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Schneider S, Schmidli H, Friede T. Robustness of methods for blinded sample size re-estimation with overdispersed count data. Stat Med 2013; 32:3623-35. [DOI: 10.1002/sim.5800] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2012] [Revised: 02/09/2013] [Accepted: 02/26/2013] [Indexed: 11/06/2022]
Affiliation(s)
- Simon Schneider
- Department of Medical Statistics; University Medical Center Göttingen; Göttingen Germany
| | - Heinz Schmidli
- Statistical Methodology; Novartis Pharma AG; Basel Switzerland
| | - Tim Friede
- Department of Medical Statistics; University Medical Center Göttingen; Göttingen Germany
- DZHK (German Centre for Cardiovascular Research), partner site Göttingen; Göttingen Germany
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41
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Chen Q, Zeng D, Ibrahim JG, Akacha M, Schmidli H. Estimating time-varying effects for overdispersed recurrent events data with treatment switching. Biometrika 2013; 100:339-354. [PMID: 24465031 DOI: 10.1093/biomet/ass091] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In the analysis of multivariate event times, frailty models assuming time-independent regression coefficients are often considered, mainly due to their mathematical convenience. In practice, regression coefficients are often time dependent and the temporal effects are of clinical interest. Motivated by a phase III clinical trial in multiple sclerosis, we develop a semiparametric frailty modelling approach to estimate time-varying effects for overdispersed recurrent events data with treatment switching. The proposed model incorporates the treatment switching time in the time-varying coefficients. Theoretical properties of the proposed model are established and an efficient expectation-maximization algorithm is derived to obtain the maximum likelihood estimates. Simulation studies evaluate the numerical performance of the proposed model under various temporal treatment effect curves. The ideas in this paper can also be used for time-varying coefficient frailty models without treatment switching as well as for alternative models when the proportional hazard assumption is violated. A multiple sclerosis dataset is analysed to illustrate our methodology.
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Affiliation(s)
- Qingxia Chen
- Department of Biostatistics, Vanderbilt University, 1161 21st Avenue South, S-2323 Medical Center North, Nashville, Tennessee 37232, U.S.A
| | - Donglin Zeng
- Department of Biostatistics, University of North Carolina, 3105-D McGavran-Greenberg Hall, Campus Box 7420, Chapel Hill, North Carolina 27516, U.S.A
| | - Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina, 3105-D McGavran-Greenberg Hall, Campus Box 7420, Chapel Hill, North Carolina 27516, U.S.A
| | - Mouna Akacha
- Statistical Methodology, Novartis Pharma AG, POB CH-4002, Basel, Switzerland
| | - Heinz Schmidli
- Statistical Methodology, Novartis Pharma AG, POB CH-4002, Basel, Switzerland
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42
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Nicholas R, Straube S, Schmidli H, Pfeiffer S, Friede T. Time-patterns of annualized relapse rates in randomized placebo-controlled clinical trials in relapsing multiple sclerosis: A systematic review and meta-analysis. Mult Scler 2012; 18:1290-6. [DOI: 10.1177/1352458511435715] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Background: Although it is known that the annualized relapse rate (ARR) in patients with multiple sclerosis (MS) changes as disease progresses, in the design and analysis of trials in relapsing multiple sclerosis (RMS) constant ARRs are assumed. Objectives: This paper aims to assess time-patterns of trial ARR by conducting a systematic review of randomized, placebo-controlled trials in RMS. Methods: A systematic literature search was conducted by searching PubMed for randomized, placebo-controlled trials in RMS. In meta-analyses the following comparisons of trial ARR were carried out for the placebo controls and active treatment arms: months 1–6 vs. months 7–12, and months 1–12 vs. months 13–24. Results: A total of 52 trials was identified. Out of these, information on the time-dependence of trial ARR could be extracted from 13 trials. The ARR was by 25% ( p = 0.0005) and 40% ( p < 0.0001) higher in months 1–12 compared with months 13–24 for placebo and active treatments, respectively. Consequently, the treatment effects were by 13% ( p = 0.23) larger in the second year compared with the first year. Within the first year of follow-up the ARR was by 4% ( p = 0.75) and 23% ( p = 0.06) higher in months 1–6 compared with months 7–12 for placebo controls and active arms, respectively. Conclusions: Trial ARR decreases during a trial in RMS, which is in line with epidemiological findings and has implications for design and analysis of future trials. The observed decrease in trial ARR might be at least partially explained by regression to the mean. Individual patient data analyses are warranted.
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Affiliation(s)
| | - Sebastian Straube
- Department of Occupational, Social and Environmental Medicine, University Medical Center Göttingen, Germany
| | - Heinz Schmidli
- Statistical Methodology, Novartis Pharma AG, Basel, Switzerland
| | - Sebastian Pfeiffer
- Department of Medical Statistics, University Medical Center Göttingen, Germany
| | - Tim Friede
- Department of Medical Statistics, University Medical Center Göttingen, Germany
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Schmidli H, Neuenschwander B. Discussions. Biometrics 2012; 68:212-4; discussion 224-5. [DOI: 10.1111/j.1541-0420.2011.01624.x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Abstract
In non-inferiority clinical trials, a test treatment is compared to an active-control rather than to placebo. Such designs are considered when placebo is unethical or not feasible. The critical question is whether the test treatment would have been superior to placebo, had placebo been used in the non-inferiority trial. This question can only be addressed indirectly, based on information from relevant historical trials with data on active-control and placebo. The network meta-analytic-predictive approach to non-inferiority trials is based on a network meta-analysis of the data from the historical trials and the non-inferiority trial, and the prediction of the putative test vs. placebo effect in the non-inferiority trial. The approach extends previous work by incorporating between-trial variability for all relevant parameters and focusing on the parameters in the non-inferiority trial rather than on population means. Two prominent examples with binary outcomes are used to illustrate the approach.
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Affiliation(s)
- Heinz Schmidli
- Statistical Methodology, Development, Novartis Pharma AG, CH-4002 Basel, Switzerland
| | - Simon Wandel
- Biometrics, Oncology, Novartis Pharma AG, CH-4002 Basel, Switzerland
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Witte S, Schmidli H, O'Hagan A, Racine A. Designing a non-inferiority study in kidney transplantation: a case study. Pharm Stat 2011; 10:427-32. [DOI: 10.1002/pst.511] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2011] [Revised: 07/19/2011] [Accepted: 07/19/2011] [Indexed: 01/05/2023]
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46
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Nicholas R, Straube S, Schmidli H, Schneider S, Friede T. Trends in annualized relapse rates in relapsing-remitting multiple sclerosis and consequences for clinical trial design. Mult Scler 2011; 17:1211-7. [PMID: 21586489 DOI: 10.1177/1352458511406309] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Abstract
BACKGROUND Sample size calculation is a key aspect in the planning of any trial. Planning a randomized placebo-controlled trial in relapsing-remitting multiple sclerosis (RRMS) requires knowledge of the annualized relapse rate (ARR) in the placebo group. OBJECTIVES This paper aims (i) to characterize the uncertainty in ARR by conducting a systematic review of placebo-controlled, randomized trials in RRMS and by modelling the ARR over time; and (ii) to assess the feasibility and utility of blinded sample size re-estimation (BSSR) procedures in RRMS. METHODS A systematic literature review was carried out by searching PubMed, Ovid Medline and the Cochrane Register of Controlled Trials. The placebo ARRs were modelled by negative binomial regression. Computer simulations were conducted to assess the utility of BSSR in RRMS. RESULTS Data from 26 placebo-controlled randomized trials were included in this analysis. The placebo ARR decreased by 6.2% per year (p < 0.0001; 95% CI (4.2%; 8.1%)) resulting in substantial uncertainty in the planning of future trials. BSSR was shown to be feasible and to maintain power at a prespecified level also if the ARR was misspecified in the planning phase. CONCLUSIONS Our investigations confirmed previously reported trends in ARR. In this context adaptive strategies such as BSSR designs are recommended for consideration in the planning of future trials in RRMS.
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Koehne-Voss S, Schmidli H, Smith DM, Pigeot I. The impact of period effects on dose level contrasts in alternating cross-over designs for first-time-in-human studies. Pharm Stat 2011; 10:45-9. [DOI: 10.1002/pst.409] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Friede T, Schmidli H. Blinded sample size reestimation with count data: Methods and applications in multiple sclerosis. Stat Med 2010; 29:1145-56. [DOI: 10.1002/sim.3861] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
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Holz FG, Korobelnik JF, Lanzetta P, Mitchell P, Schmidt-Erfurth U, Wolf S, Markabi S, Schmidli H, Weichselberger A. The Effects of a Flexible Visual Acuity–Driven Ranibizumab Treatment Regimen in Age-Related Macular Degeneration: Outcomes of a Drug and Disease Model. ACTA ACUST UNITED AC 2010; 51:405-12. [DOI: 10.1167/iovs.09-3813] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Affiliation(s)
- Frank G. Holz
- From the Department of Ophthalmology, University of Bonn, Bonn, Germany
| | - Jean-François Korobelnik
- the Department of Ophthalmology, CHU (Centre Hospitalier Universitaire) de Bordeaux, Université Bordeaux, Bordeaux, France
| | - Paolo Lanzetta
- the Department of Ophthalmology, University of Udine, Udine, Italy
| | - Paul Mitchell
- the Department of Ophthalmology, University of Sydney, Sydney, Australia
| | - Ursula Schmidt-Erfurth
- the Department of Ophthalmology and Optometry, Medical University of Vienna, Vienna, Austria
| | - Sebastian Wolf
- the Department of Ophthalmology, Inselspital, University of Bern, Bern, Switzerland; and
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Abstract
OBJECTIVES The rivastigmine transdermal patch is the first transdermal treatment for Alzheimer's disease (AD) and dementia associated with Parkinson's disease. The objective of this study was to evaluate the pharmacokinetics of rivastigmine following transdermal delivery by a patch versus oral delivery with conventional capsules in a population of AD patients. METHODS Both non-compartmental and compartmental analyses were performed on the same database showing relatively large inter-patient variations in pharmacokinetic parameters (up to 73% for the capsule group). The compartmental analysis provided model-based predictions of pharmacokinetic parameters, with the aim of comparing the two modes of administration when adjusting for confounding factors such as patient body weight and gender. RESULTS According to both non-compartmental and compartmental analyses, the patch provided significantly lower peak rivastigmine plasma concentrations (C(max)) and slower times to C(max) (t(max)), compared with capsules. However, drug exposure (area under the curve; AUC) was not significantly different between the 4.6 mg/24 hour (5 cm(2)) patch and 3 mg BID (6 mg/day) capsule doses, or between the 9.5 mg/24 hour (10 cm(2)) patch and 6 mg BID (12 mg/day) capsule doses, according to both analyses. This suggests comparable exposure from these two rivastigmine delivery systems. CONCLUSION The analyses were consistent with previous reports of a markedly less fluctuating, more continuous drug delivery with the rivastigmine patch. This characteristic delivery profile is associated with similar efficacy yet improved tolerability, compared with capsules.
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