Advanced Planning for Cox Model Studies
A Cox proportional hazards model is used when the outcome is time until an event. The event may be failure, recovery, relapse, death, or another endpoint. The model compares hazards between groups while allowing adjustment for covariates. Sample size planning must focus on the number of observed events, not only the number of enrolled subjects.
Why Events Matter
The Schoenfeld approach links power to the required event count. A rare endpoint needs many participants because fewer enrolled subjects reach the endpoint during follow up. A common endpoint needs fewer subjects for the same hazard ratio. This calculator first estimates the number of events needed. It then converts that target into an enrollment size using the expected event probability.
Advanced Inputs
The tool supports direct event probabilities and a time based exponential option. Direct mode is useful when a prior trial reports event rates for each group. Time based mode is useful during early design. It uses control median survival, hazard ratio, accrual duration, and extra follow up to estimate average event probability under uniform recruitment.
Interpreting Results
The total sample size is divided by the allocation ratio. A one to one design gives the highest efficiency for many comparisons. Unequal allocation can still be useful when treatment cost, ethics, or recruitment limits differ. The dropout adjustment inflates enrollment so the final analyzable sample remains closer to the target.
Practical Notes
Use realistic assumptions. Small changes in hazard ratio, event probability, or dropout can strongly change the answer. Review feasibility with clinical, engineering, physics, or reliability experts before launch. For complex designs, clustered data, non proportional hazards, interim analyses, or many covariates, confirm the plan with simulation or a statistician. Treat this calculator as a planning aid, not as a regulatory decision by itself.
Checking Assumptions
Before using final numbers, check whether the proportional hazards assumption is plausible. The model expects the hazard ratio to stay reasonably stable through time. If curves cross, the design may need another method. Also check that censoring is independent. Informative censoring can reduce validity. Keep a record of every input, source, and design reason. That record helps reviewers understand why the final enrollment target was selected with more confidence.