Unblinded Sample Size Re-estimation (SSR)

While blinded SSR re-estimates nuisance parameters (variance, pooled rate), unblinded SSR goes further: it uses the observed treatment effect from unblinded interim data to decide whether to increase the sample size.

This is particularly valuable when the treatment effect was overestimated at planning. A trial designed with 90% power under an optimistic effect may have much lower conditional power at interim if the observed effect is smaller. Unblinded SSR can rescue such trials by increasing the sample size in the “promising zone”—where conditional power is too low to succeed at the current N but the effect is real enough to justify continued enrollment.

Mehta & Pocock (2011) proposed a four-zone decision framework based on the conditional power (CP) at interim, computed under the current sample size plan:

When the sample size is adjusted based on unblinded interim data, the standard z-test at the final analysis may inflate the Type I error. The inverse-normal combination test (Lehmacher & Wassmer 1999; Müller & Schäfer 2001) provides rigorous Type I error control regardless of the re-estimation rule.

The Method

The trial is divided into two stages at the interim. Independent z-statistics $Z_1$ (stage 1) and $Z_2$ (stage 2) are computed from the data in each stage. The combined test statistic is:

where the weights are determined by the information fraction at interim:

Under $H_0$, $Z_1 \sim N(0,1)$ and $Z_2 \sim N(0,1)$ independently, so $Z_{\text{comb}} \sim N(0,1)$ because $w_1^2 + w_2^2 = 1$. The critical value is simply $z_\alpha$:

Example Weights

The unblinded SSR procedure follows these steps:

Conditional power is computed under two scenarios: the observed effect (used for zone classification) and the planned effect (for comparison). The formula is the same as for blinded SSR:

The stage 1 z-statistic differs from the blinded case because it uses unblinded per-arm estimates:

Zone Decision Table

Continuous & Binary Endpoints

Unlike blinded SSR which varies the nuisance parameter, unblinded SSR sensitivity analysis varies the observed treatment effect as multiples of the planned effect: 25%, 50%, 75%, 100% (planned), 125%, and 150%.

For each hypothetical effect size, the table reports:

• The resulting zone classification
• Conditional power at the current N
• Recalculated N (increased only in the promising zone)
• Inflation factor relative to the initial design

Survival Endpoints

For survival endpoints, the sensitivity analysis varies the observed hazard ratio on the log scale using multipliers 0.50, 0.65, 0.75, 0.85, 1.0 (planned), and 1.15. The scenario HR is computed as $\text{HR}_{\text{scenario}} = \text{HR}^{m}$, so multiplier $m$ scales $\log(\text{HR})$. For example, with a planned HR = 0.70, $m = 0.5$ yields $0.70^{0.5} \approx 0.84$ (weaker effect) and $m = 1.15$ yields $0.70^{1.15} \approx 0.66$ (stronger effect).

In the promising zone, the required events $d$ are recomputed from the scenario HR via the Schoenfeld formula, and $N = \lceil d_{\text{new}} / \bar{P}(\text{event}) \rceil$ is derived using the planned event probability. The sensitivity table shows how the zone classification, required events, and recalculated $N$ shift as the true HR departs from the planned value.

Unblinded SSR requires more regulatory documentation than blinded SSR. The FDA Guidance (2019, Section IV.B) specifies that the re-estimation rule must be pre-specified and Type I error control demonstrated through simulation.

Documentation Checklist

Automated Warnings

Simulation validation is particularly important for unblinded SSR because the FDA requires simulation evidence of Type I error control. The Tier 2 Monte Carlo engine simulates:

1. Generate stage 1 data under true parameters (unblinded per arm)
2. Compute $Z_1$, conditional power, and zone
3. If promising: recalculate N using the observed effect
4. Generate stage 2 data to the adjusted target
5. Compute $Z_2$ from stage 2 data only
6. Evaluate $Z_{\text{comb}} = w_1 Z_1 + w_2 Z_2 > z_\alpha$
7. Repeat 1,000–100,000 times

Reported Metrics

Request Parameters

Example Request (Continuous Endpoint)

{
  "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,
  "cp_futility": 0.1,
  "cp_promising_lower": 0.3,
  "cp_promising_upper": 0.8,
  "observed_effect": 0.2,
  "observed_variance": 1.1,
  "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_hazard_ratio": 0.75,
  "simulate": true,
  "n_simulations": 10000
}

Response Fields

1. Mehta CR, Pocock SJ. Adaptive increase in sample size when interim results are promising: a practical guide with examples. Statistics in Medicine. 2011;30(28):3267–3284.
2. Chen YHJ, DeMets DL, Lan KKG. Increasing the sample size when the unblinded interim result is promising. Statistics in Medicine. 2004;23(7):1023–1038.
3. Lehmacher W, Wassmer G. Adaptive sample size calculations in group sequential trials. Biometrics. 1999;55(4):1286–1290.
4. Müller HH, Schäfer H. Adaptive group sequential designs for clinical trials: combining the advantages of adaptive and of classical group sequential approaches. Biometrics. 2001;57(3):886–891.
5. FDA. Adaptive Designs for Clinical Trials of Drugs and Biologics: Guidance for Industry. 2019. Section IV.B.
6. EMA. Reflection Paper on Methodological Issues in Confirmatory Clinical Trials Planned with an Adaptive Design. CHMP/EWP/2459/02. 2007.
7. Cui L, Hung HMJ, Wang SJ. Modification of sample size in group sequential clinical trials. Biometrics. 1999;55(3):853–857.
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.