Survival Analysis
Event-driven sample size planning for a two-arm survival trial monitored with one interim analysis and one final analysis. Uses the canonical joint-normal log-rank framework, O'Brien-Fleming-type or Pocock efficacy boundaries, and exponential-survival event-to-enrollment conversion.
This calculator uses the group-sequential log-rank framework described by Lan and DeMets for sequential boundaries and the proportional-hazards/event-count framework associated with Schoenfeld. Under the exponential-survival assumption and equal allocation, the sequential design is first reduced to a required Brownian-motion drift. That drift is then converted to a maximum number of events.
For two equally spaced information looks (50% and 100%), the standardized log-rank statistics have correlation √(0.5) between the interim and final analyses. The calculator determines the efficacy boundaries and then solves for the drift θ that gives the requested power under the alternative.
For the two-look O'Brien-Fleming-type design, the standard 5% two-sided boundaries are approximately 2.963 at the interim look and 1.969 at the final look. These are the same boundaries reported in the documentation example. For other alpha values, the calculator rescales the two-look boundary shape and numerically calibrates the common scale factor so that the overall two-sided type I error equals the requested alpha.
For an exponential proportional-hazards survival model with equal allocation, the maximum event count is obtained from the drift:
The displayed required event count is the ceiling of the continuous event requirement. The calculation is driven by events rather than by the number of randomized patients.
If S1 and S2 are the expected survival probabilities at the specified common time point, the average event probability under equal allocation is (2 − S1 − S2)/2. Thus:
The enrollment total is rounded up. Equal allocation is then reported as the nearest integer split across the two groups.
This implementation is a planning approximation for a two-arm, two-look, efficacy-only design with proportional hazards, exponential survival used for the event-to-enrollment conversion, and equal allocation. It does not model accrual, dropout, non-uniform information times, futility stopping, delayed treatment effects, or non-proportional hazards. Those features require a more detailed survival-design procedure or simulation.
Lan, K. K. Gordon & DeMets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika, 70(3), 659–663. This paper introduced the alpha-spending framework used to construct flexible group-sequential boundaries.
Schoenfeld, D. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316–319; and Schoenfeld, D. A. (1983). Sample-size formula for the proportional-hazards regression model. Biometrics, 39(2), 499–503.
Statistical Solutions / Statsols. Advanced: Group Sequential Test of Two Survivals, software documentation and worked example. The published example reports 462 events and a total sample size of 657 for a two-sided 5% test, 80% power, HR 0.77, survival probabilities 0.344 and 0.25, two total looks, and an O'Brien-Fleming spending function.