I am reading an article which shows Hazard Ratios for continuous variables, but I'm not sure how to interpret the given values.
My current understanding of hazard ratios is that the number represents the relative likelihood of [event] given some condition. E.g: if the hazard ratio for death from lung cancer given smoking (a binary event) is 2, then smokers were twice as likely to die in the monitored time period than non-smokers.
Looking on wikipedia, the interpretation for continuous variables is that the hazard ratio applies to a unit of difference. This makes sense to me for ordinal variables (e.g number of cigarettes smoked a day), but I don't know how to apply this concept to continuous variables (e.g. grams of nicotine smoked a day?)
Best Answer
Assuming proportional hazards (as in a Cox model) and the hazard ratio for a 1 mg increase in nicotine smoked a day is 1.02, then this tells you that persons smoking 11 mgs were 1.02 as likely to die in the monitored time period than persons smoking 10 mgs. The same applies to 12 vs 11 mgs etc. If the units of your continuous covariable are too small for interpretation, then simply exponentiate the hazard ratio correspondingly: Persons smoking 20 mgs where (1.02)^10 = 1.22 as likely to die than persons smoking 10 mgs etc. (This is caused by the multiplicative model structure of Cox regression.)