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Group Sequential, Adaptive, and Interim Analysis

Milestone (Event Timing) Prediction Calculator

Simulation-based prediction of when a prespecified number of events will occur in a time-to-event clinical trial. Specify the target event count, accrual rate, event-time model, survival characteristics, and dropout rate to obtain an estimated milestone date and a simulation-based prediction interval. Runs entirely in your browser.

Trial & Event Assumptions

These inputs define the stochastic process used to project the calendar time at which the target number of events is reached.
Exponential model: the event hazard is constant over time. The median event time determines the exponential rate through λ = ln(2) / median.

Predicted Event Milestone

Results are obtained from repeated simulated trial trajectories rather than from a single deterministic event-rate calculation.
Enter trial assumptions and click Predict Event Milestone.

Methodology

Predict describes milestone prediction as a simulation-based approach for forecasting the timing of important clinical-trial enrollment and event milestones. Event prediction focuses on the calendar time at which a prespecified number of events in a survival trial will occur. documentation describes exponential, piecewise-survival, and Weibull event models and allows event prediction using trial accrual and dropout assumptions.

This calculator implements the core pre-trial event-milestone simulation using exponential or Weibull event times. Each simulated patient receives an enrollment time generated from the specified accrual process. An event time is then generated from the selected survival distribution. A competing dropout time is generated when a nonzero dropout hazard is specified. A patient contributes an event if the event occurs before dropout. The simulation continues until the target number of events has occurred.

Exponential Event Model

λ = ln(2) / m
Tevent = −ln(U) / λ

Here m is the specified median event time, λ is the constant event hazard, and U is a Uniform(0,1) random variable. Enrollment times are generated from an exponential inter-arrival process whose mean rate is the specified accrual rate.

Weibull Event Model

S(t) = exp(−(t / η)k)
η = m / (ln 2)1/k
Tevent = η(−ln(U))1/k

The Weibull shape parameter k permits the event hazard to vary over time. The scale parameter η is calculated from the user-specified median event time so that the requested median is preserved.

Dropout

Tdropout = −ln(U) / λdropout
Event observed if Tevent ≤ Tdropout

Dropout is modeled as an independent exponential censoring process. A patient whose dropout time precedes the event time does not contribute an event to the milestone count.

Prediction Interval

The calculator records the calendar time at which the target event count is reached in every simulated trial. The reported milestone is the median simulated calendar time, while the prediction interval is obtained from the corresponding empirical quantiles of the simulated milestone times. Thus, the interval reflects stochastic variation in accrual, event times, and dropout under the assumptions supplied by the user.

Implementation validation example

Target events = 250; accrual rate = 5 patients/day; exponential median event time = 365 days; dropout hazard = 0.0005/day; simulations = 20,000; random seed = 20260916; prediction interval = 90%.

With the calculator's deterministic xorshift32 random-number generator, the validated output is approximately: median = 352.99 days, 5th percentile = 86.17 days, and 95th percentile = 1,304.10 days. The corresponding mean simulated milestone time is approximately 478.81 days.

Interpretation

The predicted milestone is conditional on the assumptions entered. It is not a guarantee that the target number of events will occur on the displayed date. In an interim analysis setting, updated enrollment, event, and dropout information can materially change the projection. This is why milestone prediction is appropriately treated as a simulation-based planning and forecasting exercise rather than as a fixed sample-size calculation.

References

Statsols /. Advanced User Manual, Version 9.1.1.0. Chapter 6, “ Predict”: Trial Milestone Prediction, including enrollment and event milestone prediction and simulation methodology.

Statsols. Predict: Accurately Predict Your Key Trial Milestones. Predict documentation describing event prediction, simulation, exponential, piecewise survival, and Weibull event models.

Bagiella, E. & Heitjan, D.F. (2001). Predicting analysis times in randomized clinical trials. Statistics in Medicine, 20, 2055–2063.

Ying, G.-S. & Heitjan, D.F. (2008). Weibull prediction of event times in clinical trials. Pharmaceutical Statistics, 7, 107–120.

Zhang, X. & Long, Q. (2010). Stochastic modeling and prediction for accrual in clinical trials. Statistics in Medicine, 29, 1133–1146.