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Fougeray R, Vidot L, Ratta M, Teng Z, Skanji D, Saint-Hilary G. Futility Interim Analysis Based on Probability of Success Using a Surrogate Endpoint. Pharm Stat 2024. [PMID: 38956450 DOI: 10.1002/pst.2410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2024] [Revised: 05/06/2024] [Accepted: 05/29/2024] [Indexed: 07/04/2024]
Abstract
In clinical trials with time-to-event data, the evaluation of treatment efficacy can be a long and complex process, especially when considering long-term primary endpoints. Using surrogate endpoints to correlate the primary endpoint has become a common practice to accelerate decision-making. Moreover, the ethical need to minimize sample size and the practical need to optimize available resources have encouraged the scientific community to develop methodologies that leverage historical data. Relying on the general theory of group sequential design and using a Bayesian framework, the methodology described in this paper exploits a documented historical relationship between a clinical "final" endpoint and a surrogate endpoint to build an informative prior for the primary endpoint, using surrogate data from an early interim analysis of the clinical trial. The predictive probability of success of the trial is then used to define a futility-stopping rule. The methodology demonstrates substantial enhancements in trial operating characteristics when there is a good agreement between current and historical data. Furthermore, incorporating a robust approach that combines the surrogate prior with a vague component mitigates the impact of the minor prior-data conflicts while maintaining acceptable performance even in the presence of significant prior-data conflicts. The proposed methodology was applied to design a Phase III clinical trial in metastatic colorectal cancer, with overall survival as the primary endpoint and progression-free survival as the surrogate endpoint.
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Affiliation(s)
- Ronan Fougeray
- Institut de Recherches Internationales Servier (IRIS), Gif-sur-Yvette, France
| | - Loïck Vidot
- Institut de Recherches Internationales Servier (IRIS), Gif-sur-Yvette, France
| | | | | | - Donia Skanji
- Institut de Recherches Internationales Servier (IRIS), Gif-sur-Yvette, France
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2
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Di Stefano F, Rodrigues C, Galtier S, Guilleminot S, Robert V, Gasparini M, Saint-Hilary G. Incorporation of healthy volunteers data on receptor occupancy into a phase II proof-of-concept trial using a Bayesian dynamic borrowing design. Biom J 2023; 65:e2200305. [PMID: 37888795 DOI: 10.1002/bimj.202200305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 07/09/2023] [Accepted: 07/23/2023] [Indexed: 10/28/2023]
Abstract
Receptor occupancy in targeted tissues measures the proportion of receptors occupied by a drug at equilibrium and is sometimes used as a surrogate of drug efficacy to inform dose selection in clinical trials. We propose to incorporate data on receptor occupancy from a phase I study in healthy volunteers into a phase II proof-of-concept study in patients, with the objective of using all the available evidence to make informed decisions. A minimal physiologically based pharmacokinetic modeling is used to model receptor occupancy in healthy volunteers and to predict it in the patients of a phase II proof-of-concept study, taking into account the variability of the population parameters and the specific differences arising from the pathological condition compared to healthy volunteers. Then, given an estimated relationship between receptor occupancy and the clinical endpoint, an informative prior distribution is derived for the clinical endpoint in both the treatment and control arms of the phase II study. These distributions are incorporated into a Bayesian dynamic borrowing design to supplement concurrent phase II trial data. A simulation study in immuno-inflammation demonstrates that the proposed design increases the power of the study while maintaining a type I error at acceptable levels for realistic values of the clinical endpoint.
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Affiliation(s)
- Fulvio Di Stefano
- Dipartimento di Scienze Matematiche (DISMA) "Giuseppe Luigi Lagrange,", Politecnico di Torino, Torino, Italy
| | - Christelle Rodrigues
- Department of Quantitative Pharmacology, Institut de Recherches Internationales Servier, Suresnes, France
| | - Stephanie Galtier
- Department of Clinical Statistics, Institut de Recherches Internationales Servier, Suresnes, France
| | - Sandrine Guilleminot
- Department of Quantitative Pharmacology, Institut de Recherches Internationales Servier, Suresnes, France
| | - Veronique Robert
- Department of Clinical Statistics, Institut de Recherches Internationales Servier, Suresnes, France
| | - Mauro Gasparini
- Dipartimento di Scienze Matematiche (DISMA) "Giuseppe Luigi Lagrange,", Politecnico di Torino, Torino, Italy
| | - Gaelle Saint-Hilary
- Dipartimento di Scienze Matematiche (DISMA) "Giuseppe Luigi Lagrange,", Politecnico di Torino, Torino, Italy
- Department of Statistical Methodology, Saryga, Tournus, France
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3
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Quan H, Xu Z, Luo J, Paux G, Cho M, Chen X. Utilization of treatment effect on a surrogate endpoint for planning a study to evaluate treatment effect on a final endpoint. Pharm Stat 2023. [PMID: 36866697 DOI: 10.1002/pst.2298] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/04/2023]
Abstract
To design a phase III study with a final endpoint and calculate the required sample size for the desired probability of success, we need a good estimate of the treatment effect on the endpoint. It is prudent to fully utilize all available information including the historical and phase II information of the treatment as well as external data of the other treatments. It is not uncommon that a phase II study may use a surrogate endpoint as the primary endpoint and has no or limited data for the final endpoint. On the other hand, external information from the other studies for the other treatments on the surrogate and final endpoints may be available to establish a relationship between the treatment effects on the two endpoints. Through this relationship, making full use of the surrogate information may enhance the estimate of the treatment effect on the final endpoint. In this research, we propose a bivariate Bayesian analysis approach to comprehensively deal with the problem. A dynamic borrowing approach is considered to regulate the amount of historical data and surrogate information borrowing based on the level of consistency. A much simpler frequentist method is also discussed. Simulations are conducted to compare the performances of different approaches. An example is used to illustrate the applications of the methods.
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Affiliation(s)
- Hui Quan
- Biostatistics and Programming, Sanofi, Bridgewater, New Jersey, USA
| | - Zhixing Xu
- Biostatistics and Programming, Sanofi, Bridgewater, New Jersey, USA
| | - Junxiang Luo
- Biostatistics and Programming, Moderna, Cambridge, Massachusetts, USA
| | - Gautier Paux
- Biostatistics and Programming, Sanofi, Bridgewater, New Jersey, USA
| | - Meehyung Cho
- Biostatistics and Programming, Sanofi, Bridgewater, New Jersey, USA
| | - Xun Chen
- Biostatistics and Programming, Sanofi, Bridgewater, New Jersey, USA
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4
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Zhang Z, Lin Y, Liu J. Probability of Study Success (PrSS) Evaluation Based on Multiple Endpoints in Late Phase Oncology Drug Development. Stat Biopharm Res 2022. [DOI: 10.1080/19466315.2022.2120532] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/31/2022]
Affiliation(s)
- Zhen Zhang
- Otsuka Pharmaceutical Development and Commercialization Inc.
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5
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Alt EM, Psioda MA, Ibrahim JG. Bayesian multivariate probability of success using historical data with type I error rate control. Biostatistics 2022; 24:17-31. [PMID: 34981114 PMCID: PMC9748585 DOI: 10.1093/biostatistics/kxab050] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2020] [Revised: 12/09/2021] [Accepted: 12/14/2021] [Indexed: 01/05/2023] Open
Abstract
In clinical trials, it is common to have multiple clinical outcomes (e.g., coprimary endpoints or a primary and multiple secondary endpoints). It is often desirable to establish efficacy in at least one of multiple clinical outcomes, which leads to a multiplicity problem. In the frequentist paradigm, the most popular methods to correct for multiplicity are typically conservative. Moreover, despite guidance from regulators, it is difficult to determine the sample size of a future study with multiple clinical outcomes. In this article, we introduce a Bayesian methodology for multiple testing that asymptotically guarantees type I error control. Using a seemingly unrelated regression model, correlations between outcomes are specifically modeled, which enables inference on the joint posterior distribution of the treatment effects. Simulation results suggest that the proposed Bayesian approach is more powerful than the method of Holm (1979), which is commonly utilized in practice as a more powerful alternative to the ubiquitous Bonferroni correction. We further develop multivariate probability of success, a Bayesian method to robustly determine sample size in the presence of multiple outcomes.
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Affiliation(s)
- Ethan M Alt
- Division of Pharmacoepidemiology and Pharmacoeconomics, Brigham and Women’s Hospital and Harvard Medical School, 75 Francis Street, Boston, MA, 02115, USA,To whom correspondence should be addressed.
| | - Matthew A Psioda
- Department of Biostatistics, University of North Carolina at Chapel Hill, 135 Dauer Drive, Chapel Hill, NC, 27599, USA
| | - Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina at Chapel Hill, 135 Dauer Drive, Chapel Hill, NC, 27599, USA
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Hampson LV, Bornkamp B, Holzhauer B, Kahn J, Lange MR, Luo WL, Cioppa GD, Stott K, Ballerstedt S. Improving the assessment of the probability of success in late stage drug development. Pharm Stat 2021; 21:439-459. [PMID: 34907654 DOI: 10.1002/pst.2179] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Revised: 08/30/2021] [Accepted: 10/31/2021] [Indexed: 11/07/2022]
Abstract
There are several steps to confirming the safety and efficacy of a new medicine. A sequence of trials, each with its own objectives, is usually required. Quantitative risk metrics can be useful for informing decisions about whether a medicine should transition from one stage of development to the next. To obtain an estimate of the probability of regulatory approval, pharmaceutical companies may start with industry-wide success rates and then apply to these subjective adjustments to reflect program-specific information. However, this approach lacks transparency and fails to make full use of data from previous clinical trials. We describe a quantitative Bayesian approach for calculating the probability of success (PoS) at the end of phase II which incorporates internal clinical data from one or more phase IIb studies, industry-wide success rates, and expert opinion or external data if needed. Using an example, we illustrate how PoS can be calculated accounting for differences between the phase II data and future phase III trials, and discuss how the methods can be extended to accommodate accelerated drug development pathways.
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Affiliation(s)
| | | | | | - Joseph Kahn
- Analytics, Novartis Pharmaceuticals Corporation, East Hanover, New Jersey, USA
| | | | - Wen-Lin Luo
- Analytics, Novartis Pharmaceuticals Corporation, East Hanover, New Jersey, USA
| | | | - Kelvin Stott
- Portfolio Analytics, Novartis Pharma AG, Basel, Switzerland
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Callegaro A, Zahaf T, Tibaldi F. Assurance in vaccine efficacy clinical trial design based on immunological responses. Biom J 2021; 63:1434-1443. [PMID: 34254347 PMCID: PMC9292007 DOI: 10.1002/bimj.202100015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Revised: 05/05/2021] [Accepted: 06/05/2021] [Indexed: 11/06/2022]
Abstract
The assurance of a future clinical trial is a key quantitative tool for decision-making in drug development. It is derived from prior knowledge (Bayesian approach) about the clinical endpoint of interest, typically from previous clinical trials. In this paper, we examine assurance in the specific context of vaccine development, where early development (Phase 2) is often based on immunological endpoints (e.g., antibody levels), while the confirmatory trial (Phase 3) is based on the clinical endpoint (very large sample sizes and long follow-up). Our proposal is to use the Phase 2 vaccine efficacy predicted by the immunological endpoint (using a model estimated from epidemiological studies) as prior information for the calculation of the assurance.
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Kunzmann K, Grayling MJ, Lee KM, Robertson DS, Rufibach K, Wason JMS. A Review of Bayesian Perspectives on Sample Size Derivation for Confirmatory Trials. AM STAT 2021; 75:424-432. [PMID: 34992303 PMCID: PMC7612172 DOI: 10.1080/00031305.2021.1901782] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2020] [Revised: 02/28/2021] [Accepted: 03/01/2021] [Indexed: 11/28/2022]
Abstract
Sample size derivation is a crucial element of planning any confirmatory trial. The required sample size is typically derived based on constraints on the maximal acceptable Type I error rate and minimal desired power. Power depends on the unknown true effect and tends to be calculated either for the smallest relevant effect or a likely point alternative. The former might be problematic if the minimal relevant effect is close to the null, thus requiring an excessively large sample size, while the latter is dubious since it does not account for the a priori uncertainty about the likely alternative effect. A Bayesian perspective on sample size derivation for a frequentist trial can reconcile arguments about the relative a priori plausibility of alternative effects with ideas based on the relevance of effect sizes. Many suggestions as to how such "hybrid" approaches could be implemented in practice have been put forward. However, key quantities are often defined in subtly different ways in the literature. Starting from the traditional entirely frequentist approach to sample size derivation, we derive consistent definitions for the most commonly used hybrid quantities and highlight connections, before discussing and demonstrating their use in sample size derivation for clinical trials.
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Affiliation(s)
- Kevin Kunzmann
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
| | - Michael J. Grayling
- Population Health Sciences Institute, Newcastle University, Newcastle upon Tyne, UK
| | - Kim May Lee
- Pragmatic Clinical Trials Unit, Queen Mary University of London, London, UK
| | | | - Kaspar Rufibach
- Methods, Collaboration, and Outreach Group (MCO), Department of Biostatistics, F. Hoffmann-La Roche, Basel
| | - James M. S. Wason
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
- Population Health Sciences Institute, Newcastle University, Newcastle upon Tyne, UK
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Götte H, Xiong J, Kirchner M, Demirtas H, Kieser M. Optimal decision‐making in oncology development programs based on probability of success for phase
III
utilizing phase
II
/
III
data on response and overall survival. Pharm Stat 2020; 19:861-881. [DOI: 10.1002/pst.2042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2019] [Revised: 05/18/2020] [Accepted: 05/27/2020] [Indexed: 11/10/2022]
Affiliation(s)
| | | | - Marietta Kirchner
- Institute of Medical Biometry and Informatics University of Heidelberg Heidelberg Germany
| | - Hakan Demirtas
- Division of Epidemiology and Biostatistics University of Illinois Chicago Illinois USA
| | - Meinhard Kieser
- Institute of Medical Biometry and Informatics University of Heidelberg Heidelberg Germany
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Erdmann S, Kirchner M, Götte H, Kieser M. Optimal designs for phase II/III drug development programs including methods for discounting of phase II results. BMC Med Res Methodol 2020; 20:253. [PMID: 33036572 PMCID: PMC7547445 DOI: 10.1186/s12874-020-01093-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Accepted: 08/03/2020] [Indexed: 11/10/2022] Open
Abstract
Background Go/no-go decisions after phase II and sample size chosen for phase III are usually based on phase II results (e.g., the treatment effect estimate of phase II). Due to the decision rule (only promising phase II results lead to phase III), treatment effect estimates from phase II that initiate a phase III trial commonly overestimate the true treatment effect. Underpowered phase III trials are the consequence. Optimistic findings may then not be reproduced, leading to the failure of potentially expensive drug development programs. For some disease areas these failure rates are described to be quite high: 62.5%. Methods We integrate the ideas of multiplicative and additive adjustment of treatment effect estimates after go decisions in a utility-based framework for optimizing drug development programs. The design of a phase II/III program, i.e., the “right amount of adjustment”, the allocation of the resources to phase II and III in terms of sample size, and the rule applied to decide whether to stop or to proceed with phase III influences its success considerably. Given specific drug development program characteristics (e.g., fixed and variable per patient costs for phase II and III, probable gain in case of market launch), optimal designs with respect to the maximal expected utility can be identified by the proposed Bayesian-frequentist approach. The method will be illustrated by application to practical examples characteristic for oncological studies. Results In general, our results show that the program set-ups with adjusted treatment effect estimate used for phase III planning are superior to the “naïve” program set-ups with respect to the maximal expected utility. Therefore, we recommend considering an adjusted phase II treatment effect estimate for the phase III sample size calculation. However, there is no one-fits-all design. Conclusion Individual drug development planning for a specific program is necessary to find the optimal design. The optimal choice of the design parameters for a specific drug development program at hand can be found by our user friendly R Shiny application and package (both assessable open-source via [1]).
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Affiliation(s)
- Stella Erdmann
- Institute of Medical Biometry and Informatics, University of Heidelberg, Im Neuenheimer Feld 130.3, D-69120, Heidelberg, Germany.
| | - Marietta Kirchner
- Institute of Medical Biometry and Informatics, University of Heidelberg, Im Neuenheimer Feld 130.3, D-69120, Heidelberg, Germany
| | - Heiko Götte
- Merck Healthcare KGaA, Frankfurter Str. 250, D-64293, Darmstadt, Germany
| | - Meinhard Kieser
- Institute of Medical Biometry and Informatics, University of Heidelberg, Im Neuenheimer Feld 130.3, D-69120, Heidelberg, Germany
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