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In R's survival::coxph function, can I mix a covariate representing proportions (in the range 0.0-0.5) with an integer covariate (in the range 1-15), or should I transform the first one also to integers (0-50)?

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2 Answers 2

You can mix them. As in other forms of regression, changing the scale will change the parameter estimates, but only in the same way that changing height from meters to feet would change it.

The meaning of the resulting model will be the same.

But you have to keep track of what you've done to the variables.

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@PeterFlom makes good points: this kind of rescaling will not materially affect the fit of your model, but it will change the interpretation of the coefficients.

If you use the proportions in your model (stored as 0 to 0.5) then the hazard ratio (HR) will refer to the relative hazard difference for each one unit increase in that proportion (i.e. as though a difference of 100%!) .

So this variable might be a good candidate for rescaling (so that you can talk about a hazard ratio for each one percentage point difference, for instance, or a ten percentage point difference.) Same model: one is often easier to explain than another because the units are more interpretable.

Example: modelling risk of dying from myocardial infarction based on someone's weight (and let's assume that there is a relationship).

You could use weight in grams or weight in kilograms as the scaling for the predictor: both provide the same "information" in the model, but the HR when using grams will look barely different from one (HR for each one gram increase in weight -- most software probably couldn't print enough digits to make sense of such an HR,) while the HR when using kilograms will be more easily interpretable (one might even rescale weight into five or ten-kilo units in this scenario.)

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