Uncertainty and models
Cumulative hazard plot
Shows accumulated hazard over follow-up, using a stated estimator or model.
- Plot
- Time to event
- Risk accumulation
What it answers
How does accumulated hazard change over follow-up?
- Shape
- Non-decreasing hazard curve
- What it shows
- Accumulated event intensity.
Example
The question
Is the risk of machine breakdown rising as machines age?
Cumulative hazard of breakdown by machine age (Nelson-Aalen estimate)
Illustrative data. It belongs to no company.
When to use it
Use it when
Survival analysis focused on accumulated hazard.
Avoid it when
Reading hazard as a probability or ignoring censoring.
How to read it
Read cumulative hazard and its estimator; compare slopes or jumps.
Note
Cumulative hazard is not cumulative event probability.
The data you need
- Layout
- Long table
- Fields
- SubjectID: text; Duration: nonnegative number; Event: 0/1
- One row is
- One subject follow-up, ending in an event or censoring. What is the grain?
- Rules
- Define Event=1 and censoring=0, a common time origin and time units. Use appropriate methods for truncation or competing risks.
- Optional
- Group,EntryTime. A precomputed curve needs Time,Survival or CumulativeHazard and optional bounds.
- Preparation
- Use valid event/censor follow-up to estimate cumulative hazard with a stated estimator such as Nelson-Aalen.
- Units
- Cumulative hazard is unitless accumulated hazard and can exceed 1; it is not a probability.
Worked example
For the same three subjects, Nelson-Aalen increments are 1/3 at 12 and 1 at 25, total 4/3. The total can exceed 1 because it is not a probability.
| SubjectID | Duration | Event |
|---|---|---|
| S1 | 12 | 1 |
| S2 | 18 | 0 |
| S3 | 25 | 1 |