Survival analysis / epidemiology · BEGINNER LESSON
Hazard ratio
A hazard ratio (HR) is a relative measure that compares the instantaneous rate of an event between two groups over time. In survival analysis, it is often estimated with a Cox proportional hazards model, but it does not directly describe absolute risk or cumulative survival.
What it is and what it measures
The hazard ratio compares two groups in a time-to-event study, where the event might be death, relapse, or another outcome that happens over follow-up time. “Hazard” means the instantaneous rate of the event among people who are still event-free at that moment. An HR above 1 means the event rate is higher in the first group named; below 1 means it is lower; 1 means no difference in that relative rate. It is a risk or association measure, not an absolute impact measure.
[3] Interpreting Risk and Impact Measures in Nursing Research [1] The hazards of using hazard ratios from proportional ... - PMC
How it is estimated and interpreted
A common way to estimate an HR is the Cox proportional hazards model. In that model, the baseline hazard is treated as a nuisance parameter and the comparison focuses on the ratio between groups. Under a proportional hazards assumption, the ratio is treated as constant over time. The HR is useful for summarizing relative event rates, but its interpretation should be paired with survival curves or cumulative risks at specific times if the goal is to understand how many people actually experience the event.
[1] The hazards of using hazard ratios from proportional ... - PMC [3] Interpreting Risk and Impact Measures in Nursing Research
Why caution is needed
The sources emphasize several limitations. First, the HR is generally not transitive: if treatment A is compared with C and B is compared with C, the indirect A-versus-B HR may not match a direct A-versus-B HR. That matters in indirect treatment comparisons. Second, the HR is non-collapsible, so its value can change when conditioning on extra variables even without confounding. Third, its causal meaning is limited: one source states that HR(t) can be a causal effect for the full baseline population, but not necessarily for a meaningful group still at risk later in time. Because of these issues, the HR should be used with caution, especially when comparing treatments indirectly.
[1] The hazards of using hazard ratios from proportional ... - PMC [2] Revisiting Hazard Ratios: Can We Define Causal Estimands for Time‐Dependent Treatment Effects?
What it does not tell you
An HR does not directly give the chance that an event has happened by a certain time, and it does not directly measure the size of the absolute benefit or harm. Two groups can have the same HR while their survival curves differ in ways that matter clinically. For that reason, the sources recommend looking at alternative summaries such as restricted mean survival time difference or survival probability at a prespecified time when transitivity or absolute interpretation is important.
[1] The hazards of using hazard ratios from proportional ... - PMC [3] Interpreting Risk and Impact Measures in Nursing Research
SEE THE IDEA
How a hazard ratio is used
Compare group A with group B over follow-up time.
Measure the rate among people still at risk at each moment.
Form the relative comparison of those rates.
Pair with survival curves because it is not absolute risk.
The HR summarizes a relative event rate, but interpretation needs other outcome summaries for absolute meaning.
A hazard ratio compresses time-to-event data into one relative comparison, while survival curves show how outcomes accumulate over time.
TRY IT YOURSELF
Test your understanding
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PUT IT TOGETHER
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.