Kaplan-Meier Survival Curves, Censoring, and Log-Rank Testing
Retaining right-censored follow-up time, estimating median survival, and testing curve separation with the Log-Rank test.
In this lesson you will learn
- 1Define Time-to-Event data as a pair of variables: follow-up duration (T) and binary event status (1 = Event, 0 = Right-Censored).
- 2Explain why right-censored participants must be retained in the Kaplan-Meier risk set up to their last known contact.
- 3Interpret Median Survival Time, the Log-Rank test, and Hazard Ratios (HR) with 95% Confidence Intervals.
On this page▼
Right Censoring & Survival Curve Anatomy
This section defines Right Censoring (+), Median Survival Time, the Log-Rank test, and Hazard Ratios (HR) in longitudinal cohorts.
Analysing survival data with ordinary logistic regression ignores whether a patient relapsed in Week 1 or Year 5 and improperly discards censored follow-up.
In oncology, cardiology, and surgical follow-up studies, participants enter at different calendar dates and are followed until an event (relapse, readmission, or death) or study closure:
| Concept | Clinical Meaning | Reporting Convention |
|---|---|---|
| Right Censoring (+) | Participant remained event-free up to their last documented follow-up (study close or withdrawal). | Marked with tick marks (+) on the Kaplan-Meier curve; survival drops only when events occur. |
| Median Survival | Timepoint at which cumulative survival probability crosses 0.50 (50% of cohort event-free). | If survival stays above 50% at study end, report 'Median survival not reached (NR)'. |
| Log-Rank Test | Non-parametric χ² test comparing observed vs expected events across the entire follow-up curve. | Weights all timepoints equally (Wilcoxon/Breslow weights early events more heavily). |
| Hazard Ratio (HR) | Ratio of instantaneous event rates between arms over time. | HR = 1.0 null; HR < 1.0 protective; 95% CI excluding 1.0 indicates p < .05. |
Kaplan-Meier Survival & Hazard Ratio Lab
Adjust the Hazard Ratio slider to observe survival step-down curves and log-rank significance
Clinical Example
A Phase III oncology trial (N = 240) compares progression-free survival between Novel Immunotherapy and Standard Chemotherapy over 36 months.
Interpretation: An HR of 0.56 indicates a 44% reduction (1 − 0.56) in the instantaneous hazard of progression or death at any follow-up timepoint, prolonging median survival by 11 months.
Common Pitfall
Calculating simple arithmetic mean survival time by averaging time-to-death among only the patients who died, completely ignoring surviving censored patients.
Included with Any Analysez AI Study Package
This deep interactive chapter (Kaplan-Meier Survival Curves, Censoring, and Log-Rank Testing) and its clinical simulation labs are unlocked for everyone who has bought any Analysez AI study package.