Why Is the Median Preferred over the Average in Cancer Research?

Why Use the Median? Why Can the Average Be Misleading?

In clinical trials, survival data are generally reported using the mean less often than the median . This is more than a statistical preference; it is an approach that balances heterogeneous patient distributions and the influence of outliers , reflecting clinical reality more accurately.

Particularly when Kaplan–Meier curves are used to analyze OS (overall survival) and PFS (progression-free survival) and other time-to-event endpoints, a few patients living for a very long time can pull the mean upward. Median , by contrast, is a fair, highly representative summary saying ‘half the patients lived longer than this’.

Why can the mean be misleading?

The meanis calculated by adding all values and dividing by their number, and is strongly affected by extreme values. Responses in oncology are heterogeneous: some patients die early, while others may benefit from treatment for a very long time. Those few ‘long survivors’ make the average look better than it really is.

• The actual clinical distribution is often asymmetric (right-skewed).
• A small number of ‘very long survivors’ do not reflect the typical experience of the population.
• In physician–patient communication, the mean may create false-positive hope.

What Is the Median, and What Does It Mean Clinically?

Medianis, when values are ordered from smallest to largest, the value in the exact middle ; half the patients lived longer than this and half for less time. Its clinical interpretation is therefore clear:

‘With this treatment, half the patients live for at least X months .’

The median is unaffected by outliers and fairly summarizes the population’s overall tendency. For OS, PFS, TTP and other time-to-event endpoints, it is therefore considered the gold-standard summary measure .

How Do We Read the Median and ‘Not Reached (NR)’ on Kaplan–Meier Curves?

On a Kaplan–Meier curve, the median is the time when the graph crosses the 50% survival line . If the curve remains above this level at the end of follow-up, it is reported as median not yet reached (NR) . This may signal, particularly in immunotherapy trials, long-term benefit .

• Early separation: Rapid separation of the curves early on indicates strong efficacy.
• Plateau effect: A late plateau may indicate the presence of a ‘long-surviving subgroup’.
• HR and p-value: The median should be interpreted not alone, but together with the hazard ratio and p value.

Example: The Same Data, Two Different Summaries

In the hypothetical example below, one patient’s very long survival artificially raises the mean, while the median preserves the population’s typical experience.

When Is the Average More Meaningful?

Not every measure serves the same purpose. HRQoL scores (quality of life), adverse-event counts and other more balanced distributions can benefit from the mean. However, for OS/PFS and other right-skewed distributions, the median better informs clinical decisions.

• Quality of life: Mean/standard deviation can summarize change.
• Toxicity burden: The mean number of adverse events can be compared.
• Time-to-event endpoints: The median is preferred.

4 Frequently Asked Questions (with Short Answers)

1) If median OS increases, do patients necessarily live longer?
Generally yes, but subgroup differences and follow-up duration matter. It is interpreted alongside the HR and p-value.

2) What does median NR mean?
By the end of follow-up, more than half the population has not experienced the event (progression/death). It signals long-term benefit.

3) Why not prefer the mean when it is ‘easier to understand’?
With heterogeneous survival, a few outliers can distort the whole picture and be misleading.

4) How should it be explained clinically?
‘With this treatment, half the patients live for at least X months.’ — A patient-friendly, honest framework.

Why does it matter?

The median provides physicians with decision support, patients with an understandable anchorand researchers with a fair comparison . In oncology, when interpreting time-to-event endpoints, placing the medianat the center represents reality in the field more accurately .

For further reading: response-based clinical endpoints are discussed in our article.