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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?)

Manetheran
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3 Answers3

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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.)

Michael M
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If your variable is grams of nicotine (per day?) then the unit is 1 gram of nicotine. If your variable is measured in miligrams then the unit is 1 miligram. The latter sounds like a more reasonable measure to me, as I suspect 1 gram of nicotine to be pretty deadly.

So in this context, the unit does not refer to discrete things (like sigaretes), but to the unit in which the variable is measured (number of sigaretes, grams or miligrams of nicotine, liters or pints of beer, ...)

Maarten Buis
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The R rms package's cph and summary functions compute, by default, the inter-quartile-range hazard ratio. This handles nonlinearities (but not non-monotonicity) and interactions fairly easily, putting almost all variables on an equal basis.

Frank Harrell
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  • Could you elabore a little bit on the comments regarding non-linearity and interaction? – ocram Sep 23 '13 at 12:16
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    If there is more than one coefficient for the predictor in the model, you can't interpret any single coefficient very well. A simple case would be having $x$ and $x^2$ in the model; you need to vary $\beta_{1}x + \beta_{2}x^{2}$ to get a hazard ratio of interest. – Frank Harrell Sep 23 '13 at 15:30