Power Analysis for Survival Studies
Sample Size and Power Analysis for Survival Analysis (Log-rank and Cox Regression) · Also known as: log-rank power analysis, cox regression power analysis, survival power analysis, Sağkalım Analizi Güç Analizi
Power analysis for survival studies determines how many participants — and how many observed events — are required so that a log-rank test or Cox regression has a sufficient probability of detecting a clinically meaningful difference in survival between groups. The foundational formulas were derived by Schoenfeld (1981) and Lachin (1981) and remain the standard approach in clinical trial planning.
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When to use it
Apply this method when planning a study with a time-to-event outcome — clinical trials for mortality or disease progression, longitudinal cohort studies, reliability engineering tests, or any design where participants may be censored before the event occurs. Key inputs that must be specified in advance are the expected hazard ratio (or the difference in median survival times), the anticipated event rate, the planned follow-up duration, and whether the survival distributions are reasonably approximated by exponential or Weibull curves. The proportional hazards assumption should hold; if it does not, simulation-based power analysis is the recommended fallback. A minimum total sample of 30 is required for analytical formulas to be reliable.
Strengths & limitations
- Accounts for censoring explicitly: patients who do not experience the event within the study window contribute partial information rather than being discarded.
- Provides a principled way to translate a clinically meaningful hazard ratio into a concrete recruitment target.
- Widely accepted in trial registries and ethics applications; backed by seminal 1981 derivations that have been validated across decades of clinical research.
- Assumes proportional hazards throughout follow-up; crossing survival curves or time-varying effects invalidate the formula.
- Requires reliable prior estimates of the event rate and follow-up duration, which may be unavailable for novel interventions.
- The exponential or Weibull distribution assumption about baseline survival may not hold in complex populations.
Frequently asked
Why is the number of events more important than the total sample size?
The log-rank test gains information from each observed event. Participants who are censored (lost to follow-up or event-free at study end) contribute less statistical information. Schoenfeld's formula shows that power depends on the event count d, not on N directly. A trial with 200 participants but only 20 events is far less informative than one with 200 participants and 120 events.
What hazard ratio should I use in planning?
Use the minimum clinically meaningful hazard ratio — the smallest difference between groups that would change clinical practice. This is ideally drawn from a pilot study, published meta-analyses, or clinical expert consensus. Using an overly optimistic HR produces an underpowered study; using an overly conservative one produces an unnecessarily large sample.
What if I cannot assume proportional hazards?
The Schoenfeld formula is derived under the proportional hazards assumption. If survival curves are expected to cross or if the treatment effect changes over time, simulation-based power analysis is a more appropriate approach, as it does not require a closed-form hazard model.
How do dropout and censoring affect the required sample size?
Administrative censoring (participants event-free at study end) is already accounted for through the event probability. Additional dropout due to withdrawal or loss to follow-up reduces the effective event count, so the total recruited sample must be inflated accordingly. If you expect 15 % dropout, divide the analytically required N by 0.85 to ensure the target event count is still met.
Sources
- Schoenfeld, D. A. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316–319. DOI: 10.1093/biomet/68.1.316 ↗
- Lachin, J. M. (1981). Introduction to sample size determination and power analysis for clinical trials. Controlled Clinical Trials, 2(2), 93–113. DOI: 10.1016/0197-2456(81)90001-5 ↗
How to cite this page
ScholarGate. (2026, June 1). Sample Size and Power Analysis for Survival Analysis (Log-rank and Cox Regression). ScholarGate. https://scholargate.app/en/statistics/power-analysis-survival
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Cox proportional hazardsEpidemiology↔ compare
- Kaplan-MeierSurvival↔ compare
- Log-Rank TestSurvival↔ compare
- Power Analysis for ProportionsStatistics↔ compare
- Power Analysis for t-testStatistics↔ compare
- Simulation-Based Power AnalysisStatistics↔ compare