Model intuition
The hazard ratio (HR) compares instantaneous risk of event between groups. HR=1.5 means 50% higher hazard at any time t (if proportional hazards holds).
Interactive: what does HR do to survival curves?
We draw illustrative survival curves from a simple exponential baseline. This is a teaching visualization, not a Cox fit.
Survival curves (illustration)
If HR>1, survival drops faster for the exposed group.
Real Dental Scenario
Implant Survival: Smokers vs Non-Smokers
A study followed 240 patients with dental implants over 10 years. Researchers found that smoking was a significant predictor of implant failure using Cox regression.
Key Finding: HR = 2.1 for smoking
This means smokers have 2.1 times the hazard of implant failure at any given time compared to non-smokers, after adjusting for age, bone density, and implant type.
Smokers vs Non-Smokers: 10-Year Implant Survival
Explore: How does HR affect 5-year survival?
Adjust the hazard ratio to see how it impacts the 5-year implant survival probability.
Smokers have 2.1x the hazard of implant failure.
5-Year Survival Probability
Dental example
Cox regression can model time-to-implant failure with predictors like smoking, diabetes, bone density, and clinician experience, reporting adjusted hazard ratios.