Article
Analysis and sample size calculation within the Response Specific Exponential Survival (RSES) model
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Authors
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Samuel Kilian
- Institute of Medical Biometry and Informatics, University of Heidelberg, Heidelberg, Germany
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Johannes Krisam
- Institute of Medical Biometry and Informatics, University of Heidelberg, Heidelberg, Germany
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Meinhard Kieser
- Institute of Medical Biometry and Informatics, University of Heidelberg, Heidelberg, Germany
| Published: | February 26, 2021 |
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Outline
Text
Background: Endpoints of clinical trials should be appropriate for the medical question, objectively measurable, and relevant for patients. Therefore, overall survival is usually the primary endpoint in oncology. However, when comparing a new therapy with the present gold standard, differences in overall survival may only be observable after many years. To avoid withholding of a promising therapy, accelerated and preliminary approval based on a surrogate endpoint associated with overall survival is possible in certain situations [1]. The preliminary approval has to be confirmed later when overall survival can be assessed. As an example, the FDA published a guidance for using pathological Complete Response (pCR) as surrogate endpoint for accelerated approval of therapies against breast cancer [2]. Preliminary and final approval can both be obtained with the same study. In this case, the correlation between surrogate endpoint and overall survival has to be taken into account for sample size calculation and analysis. This relation can be modeled by means of the Response Specific Exponential Survival (RSES) model which was proposed by Xia et al. [3]. They investigated the correlation and assessed power of the logrank test for different scenarios but did not develop methods for statistical testing, parameter estimation, and sample size calculation for their model.
Methods: In this talk, a new statistical testing procedure based on the RSES model and Maximum Likelihood (ML) estimators for its parameters will be presented. An asymptotic test for survival difference based on ML estimators will be given and an approximate sample size formula will be derived. Furthermore, an exact test for survival difference and an algorithm for exact sample size determination will be provided. Type I error rate, power, and required sample size for both newly developed tests will be determined exactly. Sample sizes will be compared to those required for the logrank test and to an already existing sample size calculation method allowing non-proportional hazards [4].
Results: It will be shown that for small sample sizes the asymptotic parametric test and the logrank test exceed the nominal significance level under the RSES model. For a given sample size, the power of the asymptotic and the exact parametric test is similar, whereas the power of the logrank test is considerably lower in many situations. The other way round, the sample size needed to attain a prespecified power is comparable for the asymptotic and the exact parametric test, but considerably higher for the logrank test in many situations.
Conclusion: We conclude that the presented exact test performs very well under the assumptions of the RSES model and is a better choice than the asymptotic parametric test or the logrank test, respectively. Furthermore, the talk will give some insights in performing exact calculations for parametric survival time models. This provides a fast and powerful method to evaluate parametric tests for survival difference, thus facilitating the planning, conduct, and analysis of oncology trials with the option of accelerated approval.
The authors declare that they have no competing interests.
The authors declare that an ethics committee vote is not required.
References
- 1.
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- Center for Drug Evaluation and Research (FDA). Guidance for Industry: Pathological Complete Response in Neoadjuvant Treatment of High-Risk Early-Stage Breast Cancer: Use as an Endpoint to Support Accelerated Approval. 2014.
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- Xia Y, Cui L, Yang B. A note on breast cancer trials with pCR-based accelerated approval. J Biopharm Stat. 2014;24(5):1102-1114. DOI: 10.1080/10543406.2014.931410
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- Lakatos E. Sample sizes based on the log-rank statistic in complex clinical trials. Biometrics. 1988;44(1):229-241.
