Survival Analysis

In medicine, we often ask: "How long until X happens?"

• How long until the patient dies?
• How long until the cancer returns?
• How long until the machine breaks?

This is Survival Analysis.

The Problem with Averages

You cannot just calculate the average time to death.

Why? Because at the end of the study, some people are still alive.

If you ignore them, you bias the results towards the people who died early. If you wait for everyone to die, the study will take 80 years.

Censoring

We call the people who are still alive (or who dropped out) censored data.

We know they survived at least until the study ended. But we don't know how much longer.

Survival analysis uses special math (like the Kaplan-Meier curve) to include these people. It uses their data for as long as we have it, then "censors" them.

The Hazard Ratio

This leads to the Hazard Ratio. It compares the speed of dying in two groups.

• HR = 1: No difference.
• HR = 0.5: The treatment group dies at half the speed of the control group.
• HR = 2: The treatment group dies twice as fast.

The Diagnosis

When you see a "survival curve," look at the tail.

If the curve drops steeply at the start, the risk is immediate. If it drops slowly, the risk is constant.

And remember: "Survival" can mean anything. Survival from death. Survival from a headache. Survival from a relapse. Check the definition.