Cox Regression Hazard Ratio in Percentiles

2
votes

I computed a Cox proportional hazards regression in R.

cox.model <- coxph(Surv(time, dead) ~ A + B + C + X, data = df)

Now, I got the hazard ratio (HR, or exp(coef)) for all these covariates, but I'm really only interested in the effects of continuous predictor X. The HR for X is 1.20. X is actually scaled to the sample measurements, such that X has a mean of 0 and SD 1. That is, an individual with a 1 SD increase in X has a 1.23 times higher chance of mortality (the event) than someone with an average value of X (I believe).

I would like to be able to say these results in something that's a bit less awkward, and actually this article does exactly what I would like to. It says:

"In a Cox proportional hazards model adjusting for age, sex and education, a higher level of total daily physical activity was associated with a decreased risk of death (hazard ratio=0.71; 95%CI:0.63, 0.79). Thus, an individual with high total daily physical activity (90th percentile) had about ΒΌ the risk of death as compared to an individual with low total daily physical activity (10th percentile)."

Assuming only the HR (i.e. 1.20) is needed, how does one compute this comparison statement? If you need any other information, please ask me for it.

1
rpercentilecox-regression

1 Answers

1
votes

If you have x1 as your 90th percentile X value and x2 as your 10th percentile X value, and if p,q,r and s (s is1.20 as you have mentioned) and your coefficients of cox regression you need to find exp(p*A + q*B + r*C + s*x1)/exp(p*A + q*B + r*C + s*x2) where A, B, and C can be average values of the variable. This ratio give you the comparison statement.

This question is actually for stats.stackexchange.com though.