I am trying to calculate relative risks of an adverse outcome (cardiovascular event over 5 years) according to a physiological measurement (arterial stiffness) which I have taken on a group of patients.

It has been established that the relative risk of the outcome increases by 1.45 for every standard deviation increase of the measurement above the population mean.

I am struggling to find the equation to use to find the relative risk of outcome vs the measured value, mean and standard deviation (particularly as some patients have a measurement below the mean and need to have their risk downgraded). The correct equation would show that patients with a measurement on the mean would have a relative risk of 1, patients with a measurement of 1sd above the mean would have a RR of 1.45, patients with measurements below the mean would have relative risk somewhere between 0 and 1.

I think that the equation for patients above the mean is:

**RR = ((observed-mean)/sd) x 0.45) +1**, but this doesn't work for negative values as it continues to progress towards 0 in a linear fashion and at a few standard deviations below the mean patients will end up with a negative value for RR which can't be right.

Many thanks