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Blinded sample size re-estimation accounting for uncertainty in mid-trial estimation

Hirotada Maeda, Satoshi Hattori, Tim Friede

TL;DR

The paper tackles variance misspecification as a driver of underpowered trials by proposing a blinded mid-trial sample size re-estimation that uses a conservative $100\cdot(1-\gamma)\%$ upper confidence limit for the nuisance variance $\sigma^2$ estimated from blinded data. It derives a power-likelihood bound that is independent of the unknown effect size $\Delta/\sigma$ and prescribes selecting $1-\gamma$ to meet the target power, yielding a practical procedure for design, internal pilot, and final analysis that is robust to small internal pilot sizes. Numerical studies show the method improves power control without inflating Type I error and illustrate the distributional behavior of the re-estimated final sample size under various pilot sizes. Real-drug trial examples on postpancreatectomy pancreatitis and Parkinson's disease demonstrate the method's practical value and highlight trade-offs between pilot size, power, and final sample size, with particular relevance to rare-disease settings where recruitment is challenging.

Abstract

For randomized controlled trials to be conclusive, it is important to set the target sample size accurately at the design stage. Comparing two normal populations, the sample size calculation requires specification of the variance other than the treatment effect and misspecification can lead to underpowered studies. Blinded sample size re-estimation is an approach to minimize the risk of inconclusive studies. Existing methods proposed to use the total (one-sample) variance that is estimable from blinded data without knowledge of the treatment allocation. We demonstrate that, since the expectation of this estimator is greater than or equal to the true variance, the one-sample variance approach can be regarded as providing an upper bound of the variance in blind reviews. This worst-case evaluation can likely reduce a risk of underpowered studies. However, blinded reviews of small sample size may still lead to underpowered studies. We propose a refined method accounting for estimation error in blind reviews using an upper confidence limit of the variance. A similar idea had been proposed in the setting of external pilot studies. Furthermore, we developed a method to select an appropriate confidence level so that the re-estimated sample size attains the target power. Numerical studies showed that our method works well and outperforms existing methods. The proposed procedure is motivated and illustrated by recent randomized clinical trials.

Blinded sample size re-estimation accounting for uncertainty in mid-trial estimation

TL;DR

The paper tackles variance misspecification as a driver of underpowered trials by proposing a blinded mid-trial sample size re-estimation that uses a conservative upper confidence limit for the nuisance variance estimated from blinded data. It derives a power-likelihood bound that is independent of the unknown effect size and prescribes selecting to meet the target power, yielding a practical procedure for design, internal pilot, and final analysis that is robust to small internal pilot sizes. Numerical studies show the method improves power control without inflating Type I error and illustrate the distributional behavior of the re-estimated final sample size under various pilot sizes. Real-drug trial examples on postpancreatectomy pancreatitis and Parkinson's disease demonstrate the method's practical value and highlight trade-offs between pilot size, power, and final sample size, with particular relevance to rare-disease settings where recruitment is challenging.

Abstract

For randomized controlled trials to be conclusive, it is important to set the target sample size accurately at the design stage. Comparing two normal populations, the sample size calculation requires specification of the variance other than the treatment effect and misspecification can lead to underpowered studies. Blinded sample size re-estimation is an approach to minimize the risk of inconclusive studies. Existing methods proposed to use the total (one-sample) variance that is estimable from blinded data without knowledge of the treatment allocation. We demonstrate that, since the expectation of this estimator is greater than or equal to the true variance, the one-sample variance approach can be regarded as providing an upper bound of the variance in blind reviews. This worst-case evaluation can likely reduce a risk of underpowered studies. However, blinded reviews of small sample size may still lead to underpowered studies. We propose a refined method accounting for estimation error in blind reviews using an upper confidence limit of the variance. A similar idea had been proposed in the setting of external pilot studies. Furthermore, we developed a method to select an appropriate confidence level so that the re-estimated sample size attains the target power. Numerical studies showed that our method works well and outperforms existing methods. The proposed procedure is motivated and illustrated by recent randomized clinical trials.
Paper Structure (13 sections, 2 theorems, 25 equations, 1 figure, 2 tables)

This paper contains 13 sections, 2 theorems, 25 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Existing sample size re-estimation methods
  3. Settings
  4. A brief review of blinded sample size re-estimation methods for a normal outcome with an internal pilot study
  5. Blinded sample size re-estimation with upper confidence limit accounting for uncertainty in mid-trial estimation
  6. The motivation and idea of the proposed method
  7. Asymptotically valid but infeasible upper confidence limit approach
  8. Proposed method: Use of a conservative upper confidence limit of $\sigma^2$ estimable in a blind review
  9. Numerical studies
  10. Clinical trial examples
  11. A randomized clinical trial for postpancreatectomy acute pancreatitis
  12. A randomized clinical trial for Parkinson's disease
  13. Discussion

Key Result

Lemma 1

For the central and non-central chi-squared distributions with common degree of freedom, the following inequality holds: Hence, the following inequality also holds:

Figures (1)

  • Figure 1: Distribution (median with the $1^{st}$ and $3^{rd}$ quartiles) of the re-calculated $\hat{n}_{z,fin}$ with the Proposed and the One-sample methods under balanced allocation ($n_{1,int}=n_{0,int},\pi=0.5$) for the cases of (a) $N=32$, (b) $N=63$, and (c) $N=174$.

Theorems & Definitions (2)

  • Lemma 1
  • Lemma 2