Hazard ratios
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An overview for nonstatisticians of what hazard ratios are
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Hazard ratios
- 1. Interpreting Hazard Ratios Terry Shaneyfelt, MD, MPH Associate Professor of Medicine UAB Department of Medicine ebmteacher.com
- 2. • Time-to-event analysis • Ratio of hazards • Hazard – Instantaneous event rate • Probability that an individual at time t has an event at that time (assuming event-free survival to time t) Hazard Ratio Hazard in treatment arm Hazard in control arm HR=
- 3. • HR = 1 (event rates are the same in both arms) • HR = 2 (at any time twice as many patients in the treatment group are having an event proportionally to the comparator group) • HR = 0.5 (at an time half as many patients in the treatment group are having an event proportionally to the comparator group) Interpreting Hazard Ratios
- 4. • Often interpreted as a relative risk – Not technically the same Interpreting Hazard Ratios http://cancerguide.org/scurve_basic.html Lancet 2003;361:1149
Notas del editor
- Disclaimer- this is intended for nonstatisticians. If you are looking for fancy formulas depicting hazards you have come to the wrong place.
- Hazard ratios are used when studies measure time to events- from enrollment in the study to some outcome. For example, disease free survival, time to relapse, etc. This is called survival analysis. Hazard ratios are just a ratio of hazards with the hazard in the treatment arm divided by the hazard in the control arm. A hazard is an instantaneous event rate. It’s the risk of an event happening at a particular time (assuming the patient hasn’t experienced the event up to that time).
- This is a graph of the primary outcome (nonfatal MI and fatal CHD) in the ASCOT-LLA trial. The reference at the bottom of the slide is a website describing how to interpret survival curves (which is depicted here). Outcomes are measured over time from enrollment in the study (year 0 at the bottom) to development of the outcome or ending of the study (year 3.5). The solid black line represents outcomes accruing over time in the atorvastatin patients and the dotted line that in the placebo assigned patients. The hazard ratio (HR) derived from a cox proportional hazards model is 0.64. What does this mean? It means at any given time patients assigned to atorvastatin are 36% less likely to experience the primary outcome than those assigned to placebo (assuming they haven't experienced the outcome already). This is in contrast to a relative risk which is usually measured at the end of a trial and would be interpreted as those assigned to atorvastin experienced 36% less outcomes relative to placebo. A subtle difference but an important one.