Blinded Sample Size Re-estimation (SSR)

A clinical trial's initial sample size depends on assumptions about nuisance parameters—the variance for continuous endpoints or the pooled event rate for binary endpoints. If these assumptions are wrong, the trial may be underpowered or wastefully overpowered.

Blinded sample size re-estimation (SSR) addresses this by re-estimating nuisance parameters from pooled (blinded) interim data and adjusting the target sample size accordingly. Because treatment assignments are never revealed, blinding is preserved and Type I error is controlled under mild regularity conditions.

Continuous Endpoints

For a two-arm trial comparing means with common variance $\sigma^2$ and treatment effect $\delta$, the required sample size per arm is:

where $z_\alpha = \Phi^{-1}(1-\alpha)$ and $z_\beta = \Phi^{-1}(\text{power})$. The treatment effect $\delta$ is assumed known (the minimally clinically important difference), while $\sigma^2$ is the nuisance parameter to be re-estimated.

At the interim analysis with information fraction $t$, the pooled sample variance is computed from all $n_{\text{interim}} = \lceil t \cdot 2n \rceil$ patients without unblinding:

This estimate is positively biased by $\delta^2/4$ (Kieser & Friede 2003), but the bias is conservative—it leads to slight overestimation of the required sample size, which protects power.

Binary Endpoints

For binary endpoints with control rate $p_C$ and treatment rate $p_T$, the sample size per arm uses the pooled-variance normal approximation (Fleiss, Levin & Paik):

where $\bar{p} = (p_C + p_T)/2$ is the pooled rate. At interim, the observed blinded pooled rate $\hat{\bar{p}}$ replaces the planned $\bar{p}$ while the planned effect size $|p_T - p_C|$ is maintained (Friede & Kieser 2004).

Survival (Time-to-Event) Endpoints

For event-driven trials comparing survival curves with hazard ratio $\text{HR}$ and allocation ratio $r$ (treatment:control), the required number of events is given by the Schoenfeld (1981) formula:

The number of events $d$ is the primary quantity. To convert to a sample size $N$, compute the expected event probability under an exponential model with uniform accrual over $T_a$ months and total study duration $T$:

where $m_C$ is the median survival in the control arm. At interim, the blinded pooled event rate $\hat{P}$ is re-estimated from observed events across both arms. Because events $d$ are fixed, only $N$ changes.

The blinded SSR procedure follows these steps:

After re-estimation, the conditional power quantifies the probability of rejecting $H_0$ at the final analysis, given the interim data and the adjusted sample size:

where $R = N_{\text{final}} / n_{\text{interim}}$ is the ratio of final to interim sample size and $z_1$ is the expected interim z-statistic under the assumed treatment effect:

The calculator generates a sensitivity table showing how the recalculated sample size responds to different nuisance parameter values. This supports protocol planning and DMC communication.

Continuous Endpoints

The observed variance is varied as multiples of the planned variance: 50%, 75%, 100% (planned), 125%, 150%, and 200%. For each scenario, the recalculated N, inflation factor, and conditional power are reported.

Binary Endpoints

The pooled event rate is varied in offsets of −0.10, −0.05, 0.00 (planned), +0.05, and +0.10, clamped to [0.01, 0.99]. Each scenario reports the resulting sample size under the updated nuisance parameter.

Survival Endpoints

The observed event rate is varied as multiples of the planned event probability: 0.5×, 0.75×, 1.0× (planned), 1.25×, 1.5×, and 2.0×. Lower event rates require more patients to achieve the same number of events, so N increases.

Blinded SSR is one of the most regulatory-friendly adaptive designs. The FDA Guidance on Adaptive Designs (2019) explicitly acknowledges that blinded re-estimation preserves Type I error under standard conditions.

Documentation Checklist

Automated Warnings

The calculator generates context-specific regulatory notes:

The calculator supports Tier 2 simulation validation through the Adaptive Core engine. Monte Carlo simulations independently verify the analytical results by:

1. Generating interim data under the true parameters
2. Computing the blinded variance (or pooled rate) estimate
3. Recalculating the sample size with the same algorithm
4. Generating remaining data to the adjusted target
5. Performing the final z-test
6. Repeating 1,000–100,000 times

Reported Metrics

Request Parameters

Example Request

{
  "endpoint_type": "continuous",
  "alpha": 0.025,
  "power": 0.90,
  "mean_difference": 0.3,
  "initial_variance": 1.0,
  "interim_fraction": 0.5,
  "n_max_factor": 2.0,
  "observed_variance": 1.4,
  "simulate": true,
  "n_simulations": 10000
}

Example Request (Survival Endpoint)

{
  "endpoint_type": "survival",
  "alpha": 0.025,
  "power": 0.90,
  "hazard_ratio": 0.7,
  "median_control": 12,
  "accrual_time": 24,
  "follow_up_time": 12,
  "allocation_ratio": 1.0,
  "interim_fraction": 0.5,
  "n_max_factor": 2.0,
  "observed_event_rate": 0.55,
  "simulate": true,
  "n_simulations": 10000
}

Response Fields

1. Kieser M, Friede T. Simple procedures for blinded sample size adjustment that do not affect the type I error rate. Statistics in Medicine. 2003;22(23):3571–3581.
2. Friede T, Kieser M. Sample size recalculation for binary data in internal pilot study designs. Pharmaceutical Statistics. 2004;3(4):269–279.
3. Zucker DM, Wittes JT. The bias and efficiency of blinded variance estimates in clinical trials. Statistics in Medicine. 2004;23(4):565–574.
4. FDA. Adaptive Designs for Clinical Trials of Drugs and Biologics: Guidance for Industry. 2019. Section IV.B.2.
5. EMA. Reflection Paper on Methodological Issues in Confirmatory Clinical Trials Planned with an Adaptive Design. CHMP/EWP/2459/02. 2007.
6. Cui L, Hung HMJ, Wang SJ. Modification of sample size in group sequential clinical trials. Biometrics. 1999;55(3):853–857.
7. Fleiss JL, Levin B, Paik MC. Statistical Methods for Rates and Proportions. 3rd ed. Wiley; 2003.
8. Schoenfeld D. The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika. 1981;68(1):316–319.
9. Gould AL. Interim analyses for monitoring clinical trials that do not materially affect the type I error rate. Statistics in Medicine. 1992;11(1):55–66.
10. Friede T, et al. Blinded sample size re-estimation in event-driven clinical trials. Pharmaceutical Statistics. 2019;18(5):578–588.