Sample Size Calculator for Cox Proportional Hazards Model

Design Cox survival studies with event based planning. Adjust power, dropout, allocation, and follow-up assumptions. See required subjects before refining advanced trial protocols today.

Calculator Inputs

Formula Used

The calculator uses a Schoenfeld style event target for a Cox proportional hazards comparison.

Events = (Z alpha + Z power)2 / [p control × p treatment × (ln HR)2]

The event target is divided by 1 - covariate R squared. This adjusts for correlation between treatment and covariates.

Analyzable sample = adjusted events / average event probability

Final sample = analyzable sample / (1 - dropout) × design effect

For direct mode, average event probability is the allocation weighted mean of group event probabilities. For time mode, the calculator assumes exponential survival and uniform accrual.

How to Use This Calculator

  1. Enter alpha, power, hazard ratio, and treatment to control allocation.
  2. Add dropout, covariate R squared, and any design effect multiplier.
  3. Choose direct event probabilities or the exponential survival option.
  4. Use direct mode when you know event rates from prior evidence.
  5. Use time mode when planning from median survival and follow up.
  6. Press Calculate Sample Size to show results above the form.
  7. Download the result as CSV or PDF for your study notes.

Example Data Table

Scenario HR Power Control Event Dropout Use Case
Balanced moderate effect 0.70 80% 35% 10% Initial survival design
High power reliability study 0.65 90% 45% 8% Physics failure timing
Unequal allocation 0.75 85% 30% 12% Limited control sampling

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.

FAQs

What does this calculator estimate?

It estimates the event count and total sample size for a Cox proportional hazards comparison. It also splits the final sample by allocation ratio.

Why are events so important?

Cox model power mainly depends on observed events. A large enrolled sample can still be weak if few subjects experience the endpoint.

What hazard ratio should I enter?

Enter the planned treatment hazard divided by control hazard. Values below one suggest lower treatment hazard. Values above one suggest higher treatment hazard.

Can I use unequal allocation?

Yes. Enter treatment to control allocation. For example, enter 2 for a two to one treatment heavy design.

What is direct event mode?

Direct mode uses expected event probabilities for each group. It is best when prior studies or pilot data give credible event rates.

What is time based mode?

Time based mode estimates event probability from median survival, hazard ratio, accrual time, and follow up under an exponential survival assumption.

What does covariate R squared mean?

It represents correlation between treatment and covariates. Higher values increase the required event count in this planning approach.

Is this enough for a final protocol?

No single calculator replaces expert review. Use it for planning, then verify assumptions, censoring, endpoints, and model choice before final approval.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.