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Flexible Sample Size Re-estimation Design

Flexible Sample Size Re-estimation Design

Flexible Sample Size Re-estimation DesignIn the development process of drug products, biologic products and devices, there are a lot of uncertain key factors that make sample size estimation essential for confirmatory clinical trials. These uncertainties may be from the quantitative information used to calculate sample size such as effect size and any other nuisance parameters including the variability associated with primary outcome and the control group event rate. Indeed, the accuracy of the estimated sample size contributes to the success of a study and the accuracy of assumptions made for the parameters contributes to the accuracy of the estimated sample size. A reliable estimation of parameters related to the sample size calculation is influenced by many practical reasons. As for the confirmatory clinical trials in which the endpoint is systematically studied for the first time, reducing uncertainty is more important. For this primary purpose, a flexible adaptive design, namely, sample size re-estimation (SSR) design has emerged. This design allows the reassessment of sample size in the mid-course of the study to ensure adequate power (Figure 1). Generally, researchers may acquire encouraging results at the early phase of the study, however, the duration may be shorter and the endpoint may be different from that required in the confirmatory phase clinical trial. SSR design can mitigate the negative impact caused by those uncertain key factors. Since the FDA released the draft guidance for adaptive design clinical trials for drugs and biologics in 2010, many surveys have shown an upward trend in the application of SSR designs in clinical trials. To better understand and accept SSR designs, we introduce you the statistical methods applied in SSR designs, and the points to consider when choosing a design option.

Flexible Sample Size Re-estimation Design
Figure 1. Sample size re-estimation (SSR): if interim analysis shows worse results than expected, the sample size can be re-estimated and increased to ensure that the trial is adequately powered.

Unblinded Sample Size Re-estimation (ubSSR)

The ubSSR is a type of adaptive design using unblinded data based on prespecified criterion to re-estimate the sample size during interim analysis. UbSSR is somehow similar to GSDs (group sequential designs) because both designs prespecify the number and spacing of interim looks, evaluate the interim accumulating data and estimate the treatment effect at each interim look. When the prespecified criteria are successful or futile, the study can be stopped. Generally, there could be an increase in sample size in the mid-course of the ubSSR study, which is an important modification of study design. Many approaches are based on the invariance principle, calculating separate standardized test statistics from different stages and combining them in a predefined manner for statistical inferences while ensuring control of the Type I error rate. Some common adaptive group sequential methods can be categorized into methods for the product of p-values, methods for inverse normal combination of p-values, and methods using conditional error functions. No matter which method you use, the interim treatment effect represented by the current trend of the data or the assumed parameters could determine if there is an increase in the sample size. What needs to be emphasized is that researchers should carefully consider the maximum sample size because its power is inefficient in SSRs when you increase the sample size significantly.

Blinded Sample Size Re-estimation (bSSR)

The bSSR is another type of adaptive design. It uses aggregated data in the mid-course of the trial and re-estimates nuisance parameters involved in the power calculation of the trial. The nuisance parameters could be the variance of a continuous variable, the control group event rate or the subject discontinuation rate. When applying bSSR to re-estimate the sample size, researchers would not estimate and use the treatment effect of an ongoing study in the algorithm of SSR. This method can be dated to 1945 according to Friede and Kieser. Through analysis and simulation, the Type I error rate has been proven to be unaffected by the bSSR procedure. Thus, we can use the data as a whole without adjustment and use the nominal level for final data analysis if the sample size re-estimation of clinical trials is designed as bSSRs. That's why FDA encourages the application of bSSRs and says it well understand in its adaptive designs draft guidance. In practical applications of bSSR, researchers can use either the completely pooled data (purely blinded) or unblinded treatment group information (partially blinded) to re-estimate the nuisance parameters.

Blinded SSR vs unblinded SSR

As mentioned above, bSSR has a different statistical procedure and greater regulatory acceptance than ubSSR. If researchers try to design a clinical trial with good potential treatment effects or known minimum clinical effects, they can apply bSSR to mitigate the uncertainty of the nuisance parameters involved in the estimation of sample size. Because they can estimate the nuisance parameters from the aggregated data with an assumed treatment effect, which makes bSSR statistically and operationally simpler than ubSSR. In fact, even in a more complicated bSSR, as long as no interim treatment effect is used in the SSR algorithm, the use of treatment information to adjust the sample size in the mid-course of the study will have no impact on the final analysis statistics. Actually, the key advantage of using bSSR instead of ubSSR is the reduced impact on the final analysis.

However, under the circumstance that the primary efficacy endpoint of the test drug's effect is uncertain at the design stage, it is better for researchers to choose unblinded interim data to estimate treatment effect and evaluate the adequacy of the originally planned sample size. The ubSSR design provides us a chance to detect viable treatment effects with adequate power.

In summary, if the assumptions made at the design stage are found to be unreliable, the SSR designs can offer an opportunity to improve study efficiency by allowing mid-course sample size re-estimation, so that the sample size can be adjusted while maintaining the scientificity and preciseness of trial results.

At CD BioSciences, we can not only help you with the SSR design but also help you make an appropriate choice of statistical strategy. If you have any questions, please feel free to contact us.

1. Pritchett, Y. L., Menon, S., Marchenko, O., Antonijevic, Z., Miller, E., & Sanchez-Kam, M., et al. (2015) ‘Sample size re-estimation designs in confirmatory clinical trials - current state, statistical considerations, and practical guidance’, Statistics in Biopharmaceutical Research, 7(4), 309-321.
2. Friede, T. and Kieser, M. (2006) ‘Sample Size Recalculation in Internal Pilot Study Designs: A Review’, Biometrical Journal, 48, 537–555.
3. Chuang-Stein, C., Anderson, K., Gallo, P., and Collins, S. (2006) ‘Sample Size Re-estimation: A Review and Recommendations’, Drug Information Journal, 40, 475–484.

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