# Is it possible to add 2 or more hazard ratios?

I'm trying to establish a connection between interarm systolic blood pressure difference and 10 year cardiovascular disease risk. Since this is a small study, patient-participants will not be followed for 10 years or more to observe the direct outcome. So rather than use logistic regression for the binary outcome, I am conducting a multivariate survival analysis for time-to-event. Various risk factors are being considered. Hazard ratios for each of these are calculated for cardiovascular risk.

The model output I obtain says the following: I have the S0(10)= 0.94833 and the HR of age 15.2, HR of BMI 1.67, HR of smoking 1.86 etc.

How can I interpret these values? Furthermore, I would like to know how to measure and contrast their separate and joint effects on risk. And I would like to know how to predict the absolute risk of the outcome from my model results. For example I want to say that some percentage of my population is found with a high difference of interarm systolic blood pressure and predicted to have a 3-fold cardiovascular risk, how would I report the 10 year absolute risk of CVD?

It is difficult for the Cox model to predict absolute risk. It is impossible for the Cox model to project absolute risk beyond the range of observed failure times. This is because Cox models make use of an arbitrary baseline hazard function. According to the assumptions of the model, it is theoretically possible that immediately after you have observed patients, their hazard for CVD leaps 10,000 fold. We know that's not the case, but there's no way to reflect that in the model's assumptions.

The strength of the Cox model is quantifying the association of a risk factor with disease in terms of a hazard ratio. The hazard is the instantaneous risk of failure and thus is not interpretable on the raw scale, but a hazard ratio approximates a relative risk when the proportional hazards assumption is met.

Interpreting the results is easy: a hazard ratio for age of 15.2 means that participants differing by one unit in age have a 15 fold relative risk for CVD events. I say unit because 15 is a nonsensically large HR. This variable must be scaled by something. Not knowing the software you are using, getting a prediction of surviving proportion S0(10) = 0.95 when you haven't observed participants for 10 years suggests the survival outcome is coded incorrectly. When participants drop out of a study, they are left censored; you do not know if they died or not so you must code an event time for them when they leave and classify that event as a censoring event. This partly explains why the survival proportion is unbelievably high. However another possibility is that the survival prediction doesn't use prediction-at-the-means (predicted survival probability in a participant having all covariates equal to the average covariate value) but prediction-at-the-origin (survival probability in a participant with age 0, bmi 0, interarm systolic BP 0).

I'm afraid there would be very low credibility to a model which predicts 10 year absolute risk of disease that does not actually follow patients for 10 years. This in fact justifies the use of the Cox model for the time being.

The answer to the question in the title is yes. My suggestion would be to fit the adjusted Cox model controlling for as many confounders as possible: age, sex, atrial fibrillation, left ventricular hypertrophy (if available), diagnosed hypertension, treatment for hypertension, diabetes, weight, 1/height^2, BMI, sodium, etc. Then report the adjusted hazard ratio for intraarm SBP and its 95% CI. If this value does not include 1, then you can conclude there is evidence of an effect and that a larger study is warranted to predict risk (as one possibility).