The difference between hazard and risk in the relation between bone density and fracture

Abstract

The relation between fracture risk and bone density is frequently defined in terms of a relative hazard derived from the Cox proportional hazards model. The relative hazard is a multiplicative factor representing the rise in hazard for each standard deviation fall in bone mineral density, which has a typical value of about 1.5. It is not generally appreciated that this hazard may only be equated with absolute risk when risk is very low; at higher risk and over long periods, it is inappropriate to apply a multiplicative factor to absolute risk because risk has a range of 0-1 and cannot exceed unity. Here, we show how “hazard” can be converted to risk and how misleading the current practice of equating relative hazards with relative risks can be.