I am new to survival analysis and I was wondering whether you could, similar to the logistic regression, calculate the intercept and the risk probability with the coefficients you acquire from the cox regression? And how you could do so within R.
There is no single "intercept" in a Cox regression model. After the model is fit, you can infer a baseline hazard, which can be transformed to a baseline survival curve as a function of time. The covariates then alter that entire baseline hazard or survival function according to their regression coefficients. You can choose whether to display entire survival curves for different covariate values, or estimate median survival (or some other quantile) as a function of covariate values if you want a point estimate of some type.
predict.coxph function in the R
survival package provides basic tools for this. The
rms package can be more useful. If you are going to be doing a lot of regression modeling of any type, it's well worth learning how to use that package despite its initially steep learning curve.