Group Sequential, Adaptive, and Interim Analysis
Two-look group sequential planning for a two-arm time-to-event endpoint using the log-rank test. Calculates the required number of events, total sample size, interim timing, and efficacy boundaries using a Lan-DeMets O’Brien-Fleming-type alpha-spending design.
This calculator implements a two-sample log-rank group sequential design in the constant-hazard special case of the survival group sequential framework described by for GST3. The design uses two analyses: one interim analysis at a specified information fraction and one final analysis at 100% information. Information is treated as proportional to the number of observed events, which is the standard approximation for the log-rank statistic under proportional hazards.
The efficacy boundary uses the two-sided Lan-DeMets alpha-spending approach with an O’Brien-Fleming-type spending function. At information fraction t, cumulative two-sided alpha spent is
The interim critical value is obtained from the alpha spent at the interim information fraction. The final critical value is then solved from the canonical joint normal distribution of the two correlated log-rank Z statistics, with correlation √t between the interim and final statistics. This preserves the requested overall two-sided type I error.
For equal or unequal randomization, the log-rank information is approximated by D·p(1−p), where D is the total number of events and p is the experimental-arm allocation fraction. Under a proportional-hazards alternative, the stage-k Z statistic has mean
The required maximum number of events is the smallest continuous solution giving the requested power; the displayed event target is rounded up to the next whole event.
For constant event and dropout hazards with uniform accrual, the expected event probability for a subject is calculated using the Kim-Tsiatis survival-design formulation. For an event hazard λ, dropout hazard δ, accrual duration R, and total study duration T = R + follow-up, the average event probability is
The treatment and control event probabilities are weighted by the planned randomization proportions. Required total enrollment is the required event count divided by this weighted event probability. Expected timing of the interim analysis is obtained by solving the same event-accumulation equation for the interim event target.
Zhu, Ni & Yao (2011) describe a two-arm survival group sequential example with median survival 9 months versus 6 months, 1:1 allocation, uniform 18-month accrual, 30 months of maximum follow-up, two-sided α=0.05, 85% power, and one interim analysis at 50% of the events using a Lan-DeMets spending function chosen to approximate O’Brien-Fleming. With the constant-hazard/no-dropout implementation used here, the calculation reproduces approximately 220.81 required events, rounded to 221 events, and approximately 228.44 subjects, rounded to 229 subjects. The expected interim occurs at approximately 17.20 months.
Zhu, L., Ni, L., & Yao, B. (2011). Group Sequential Methods and Software Applications. The American Statistician, 65(2), 127–135. doi:10.1198/tast.2011.10213.
Kim, K., & Tsiatis, A. A. (1990). Study duration for clinical trials with survival response and early stopping rule. Biometrics, 46(1), 81–92. doi:10.2307/2531632.
Lan, K. K. G., & DeMets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika, 70(3), 659–663.
Advanced User Manual, Section 7.2.5.4, Survival (Time-to-Event) Analysis (GST3) — Sample Size Determination, describing the two-sample log-rank survival group sequential framework and Kim-Tsiatis event calculations.