Understanding Log-Rank Test Sample Size Planning
Planning clinical trials and longitudinal survival studies requires robust statistical methodologies to guarantee that experiments detect genuine clinical differences. The log-rank test remains the definitive standard for comparing survival distributions between two independent cohorts. Determining appropriate participant numbers prevents underpowered trials while optimizing resource allocation across medical research.
Formula Used
Calculations rely primarily on Schoenfeld's derivation for proportional hazards models. The total number of required events $D$ is computed through the standard formula:
$$D = \frac{(Z_{1 - \alpha/2} + Z_{1 - \beta})^2}{(1 - p) \cdot (\ln(HR))^2 \cdot \frac{r}{(1+r)^2}}$$
Where $Z$ represents critical standard normal distribution values, $HR$ denotes the target hazard ratio, $r$ represents the patient allocation ratio between treatment groups, and $p$ accounts for average event censoring adjustments.
How to Use This Calculator
Input your desired significance threshold into the alpha field, followed by statistical power parameters. Provide anticipated survival rates for both control and experimental cohorts, configure accrual and follow-up durations, specify potential drop-out expectations, and click submit to evaluate exact totals.
Frequently Asked Questions
Why is the log-rank test preferred for survival data?
It accounts for censored observations where patient outcomes remain unknown by trial conclusion.
How does the allocation ratio impact total sample size?
Balanced equal allocations optimize efficiency, whereas unequal ratios increase overall requirements.
Can dropout rates alter final subject counts?
Anticipated loss to follow-up inflates baseline requirements to preserve statistical integrity.
What constitutes a valid hazard ratio assumption?
Historical clinical literature or pilot data informs realistic proportional hazard expectations safely.