In the era of highly effective therapies for may diseases, clinical researchers are increasingly encountering a "good" problem in the time to event analyses: the Kaplan-Meier survival curves are flattening out well above the 50% mark. While this represents a triumph for patient outcomes, it creates a headache for statistical reporting. When the event rate is low (below 50%), the Median Time to Event (e.g., Median Overall Survival) and its 95% Confidence Interval (CI) cannot be estimated (often reported as "NE" (not estimable), "NR" (not reached), or "NC" (not calculable)).
So, how do we robustly describe the efficacy of a treatment when the standard metric fails? This post outlines the best-practice alternatives for summarizing, analyzing, and visualizing survival data in low event settings.
1. The Limitation of the Median
The median survival time is simply the time point at which the survival probability drops to 0.50. If the Kaplan-Meier curve plateaus at 70% or 80% because fewer than half the patients experienced the event, the median is mathematically undefined. Reporting it merely as "Not Reached" (NR) is accurate but clinically uninformative—it tells us what the survival is not, but not what it is.
To provide a complete picture, we must pivot to alternative metrics that describe different parts of the survival distribution.
2. Primary Summary Measures
A. Landmark Survival Probabilities
When we cannot answer "When will half the patients die?", we should ask, "What proportion of patients are event-free at time t ?"
Landmark analysis reports the Kaplan-Meier survival probability (with 95% CIs) at clinically relevant, fixed timepoints (e.g., 24 weeks, 12 months, 24 months, 5 years).
Best Practice: Pre-specify these timepoints in the Statistical Analysis Plan (SAP) to avoid data dredging.
Example Reporting: "Event free rate was 93% at week 24 in the treatment group", "The 3-year recurrence-free survival rate was 88.4% (95% CI: 85.1–91.0) in the treatment arm compared to 82.1% (95% CI: 78.4–85.2) in the placebo arm."
B. Lower-Percentile Survival Times (10th and 25th)
Just because the 50th percentile (median) is missing doesn't mean all percentiles are.
25th Percentile: The time at which 25% of patients have experienced the event (or survival drops to 75%).
10th Percentile: The time at which 10% of patients have experienced the event (or survival drops to 90%).
These metrics characterize the "early failures" or the worst-performing subset of the cohort. They are particularly useful for showing that a treatment delays early progression even if the long-term survival is high.
| Metric | Treatment Group | Control Group |
| Median (50th) | NR (95% CI: NR, NR) | NR (95% CI: 36.7, NR) |
| 25th Percentile | 18.4 months (14.2, 22.1) | 12.1 months (9.8, 14.5) |
| 10th Percentile | 5.4 months (4.1, 6.8) | 3.2 months (2.8, 3.9) |
Note: In the table above, while the median is NR for both, the 25th percentile clearly demonstrates a 6-month delay in progression for the treatment group.
3. Robust Analytical Alternatives
A. The "Reverse Kaplan-Meier" Method for Follow-Up
In low event trials, it is critical to prove that the "NR" result is due to drug efficacy, not just because patients left the study early. The Reverse Kaplan-Meier method is the gold standard for calculating median follow-up.
How it works: You reverse the censoring indicator (Event = Censored; Censored = Event) and run a standard Kaplan-Meier analysis. The resulting median is the median potential follow-up time.
Why use it: Unlike the "median time on study," it is not biased by early deaths or events, providing a true measure of how long the trial centers monitored the patients.
B. Restricted Mean Survival Time (RMST)
RMST is rapidly becoming the preferred alternative to the Hazard Ratio (HR) in low event trials, especially when the Proportional Hazards assumption is violated (e.g., crossing curves).
Definition: RMST is the "area under the survival curve" up to a specific time point ($\tau$). It represents the average survival time a patient lives during that window.
Reporting: You can report the Difference in RMST (Treatment minus Control) or the Ratio.
Interpretation: "Over the 5-year follow-up period, patients on the new therapy lived, on average, 4.2 months longer than those on the control (RMST difference = 4.2 months, p=0.003)."
4. Visualization Best Practices
A. The Kaplan-Meier Plot: Handling the Y-Axis
In trials with very high survival (e.g., >90%), the survival curves may be squeezed into the top 10% of the graph, making it hard to see separation.
Line Break (Axis Break): It is acceptable to "break" the y-axis to focus on the relevant range (e.g., from 80% to 100%), provided this is clearly marked.
Inverted Plot (Failure Plot): Alternatively, plot the Cumulative Incidence of Events (1 - Survival) on a y-axis ranging from 0% to 20%. This often visualizes the difference in event rates more clearly than a survival curve stuck at the top of the chart.
B. The "Number at Risk" Table
Always include a table below the x-axis aligned with the tick marks. In low event trials, this table reveals whether the "flat tail" of the curve is based on hundreds of patients or just a few who haven't been followed long enough.
5. Optional Exploratory Methods
If pre-specified in the protocol, Parametric Modeling can be used to estimate the median survival even if it hasn't been reached observed data.
Weibull Distribution: By fitting a Weibull model to the observed data, you can extrapolate the curve to predict when the median would be reached, assuming the risk profile remains constant.
Caution: This is a prediction, not an observation. It should be labeled clearly as "Estimated Median (Parametric)" and treated as exploratory evidence.
Summary Checklist for Reporting Low Event Data
State clearly that the median is NE/NR.
Report Landmark Rates (e.g., 3-year survival) with CIs.
Report Lower Percentiles (25th, 10th) to show early separation.
Use RMST to quantify the average time gained.
Calculate Follow-up using the Reverse Kaplan-Meier method.
Adjust Plots (zoom/break y-axis) to make differences visible, but keep the full context clear.
Note: AI-assisted writing for this blog article.
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