Relative Risk calculation

Hi bit of help would be much appreciated for what is probably a bit of a silly question.

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


Omega Contributor
Can you post a reference for the approach you are trying to use or a publication that just presented their data in this way.

How are you defining population mean?

How big is your sample?

Not completely following what you are trying to do. Apply an existing cut-off or determine your own risk. Applying their numbers to your sample can be iffy, since your sample may have different characteristics than those of the source you are trying to replicate. And are you exclusively focusing on their mean and SD?

If you are just looking for the RR for your sample, you just need to trichotomize the sample to those > 1 SD above mean, those < 1 SD below mean, and those >/= 1 SD to those </= 1 SD. Then conduct the RR for the low group and then high group both time treating the middle group as the reference category. This will obviously give you three categorical groups (e.g., low 15.9%, middle 68.2, and high 15.9%).
Thanks hlsmith.

This is the paper that I've used to reference the relative risk increase: (I can email you the pdf if you like). It's a meta-analysis of population studies on arterial stiffness (what I am measuring) looking at cardiovascular end points. Arterial stiffness is known to be a reliable predictor of cardiovascular morbidity/mortality (eg. heart attacks and strokes). I have measured arterial stiffness in 101 patients with a respiratory condition with the hypothesis that they have elevated arterial stiffness and, thus, increased cardiovascular risk.

I would like to quantify the elevated risk by, for instance, quoting the average increase in RR of cardiovascular events across my sample. The Ben-Shlomo paper I have linked gives RRs for the "change in risk of an outcome for a 1-SD increase in loge aPWV from the average in that population". PWV is pulsewave velocity which is how we measure arterial stiffness. They used a log transformation because it tends to be right-skewed. I have calculated standard deviations for my own data (which I had to categorise in age deciles because arterial stiffness varies according to age) and the log medians I am comparing to come from large studies of 'normal values' per age decile. So for instance, my group of patients aged 40-50 has a sd in log(PWV) of 0.23 and the log median PWV in this group according to normal data is 1.93. I have a patient aged 45 whose log PWV is 2.17. It is just over 1sd from the normal median so her RR should be just over 1.45 compared with someone with a normal PWV.

Is that clear?


Omega Contributor
Hmmm. I skim the article and I guess we need to start with the basics. There is a meta-analysis that was conducted using proportional hazards regression controlling for age and sex that found for ever standard deviation of stiffness (defined as z-score of logetransformed aPWV) above the population mean, risk for cvd went up 45%. OK that is straightforward.

Now the confusion, what are you trying to do? Replicate their study just using your own data, just calculate RR given your data, or are you trying to merge your data with their results. If so, why. I can quite follow your actions.​
Now the confusion, what are you trying to do? Replicate their study just using your own data, just calculate RR given your data, or are you trying to merge your data with their results. If so, why. I can quite follow your actions.​
Thanks again. I am trying to do the second one - apply their relative risk calculation to my data. I want to try to quantify the elevated cardiovascular risk in my population using the known relative risk increase caused by increased arterial stiffness and known normative values for arterial stiffness.


Omega Contributor
Well, I think we are very limited here. Ideally the most feasible approach would be to use their mean and standard deviation level. Then you could see if your 101 patients had a value above the 1 standard deviation marker. However the authors only seem to provide the hazard ratio, no beta coefficients from the model, mean, or standard deviation. Not sure how much confidence you can have trying to replicate this using 101 patients, when their population mean was based on a substantially higher n-value (especially not knowing the mean or standard deviation they used, so you would have no idea how different your sample may be).
Thanks - I'm not sure you have understood what I'm trying to do. I am comparing my means to normal age-related values from another paper (Reference Values for Arterial Stiffness, C., Determinants of pulse wave velocity in healthy people and in the presence of cardiovascular risk factors: 'establishing normal and reference values'. Eur Heart J, 2010. 31(19): p. 2338-50.).

I can compare my values to the 'normal' and see how many standard deviations above or below the expected each patient lies.

The area I need help with is knowing how to apply the relevant 1.45 relative risk that the ben-shlomo paper quotes. For instance, I know that patient X has a PWV 0.5sd above expected. Does this mean their risk is 1 + (0.45 x 0.5)? Likewise, if i have a patient whose value is 2sd below the expected then do I have to do 1/(1.45 x 2) to find their resultant relative risk reduction??