# Predicting absolute risk using cox regression

I am trying to use R to predict the absolute risk of developing adverse events in a cohort, and to compare that with the observed outcome. Should I use survreg or coxph to do this? Anyone kind enough to explain how to do this with R code?

The mean follow up period of my cohort is only up to 6 years, so am I able to predict the absolute risk for each individual at the end of the follow up period (including both censored and non censored data)?

• By absolute risk do you mean the probability at some specific point in time? – Michael M Nov 7 '13 at 17:43
• @ Michael Mayer Thanks for your comment. Yes, it is the probability of having an adverse event at the time point where the follow up ends (for both censored and non-censored data). I wonder if we could calculate the probability for every single individual in the survival analysis? – – user32454 Nov 9 '13 at 9:47
• Would such lower bound of the absolute risk be useful? The longer the follow up, the higher the probability. – Michael M Nov 9 '13 at 12:21
• @ michael mayer I don't quite understand the meaning of lower bound of absolute risk. But I need to fit models to predict the absolute risk of developing a clinical event in order to compare the strength of different models. – user32454 Nov 10 '13 at 5:10
• The absolute risk will increase with increasing follow-up. So you end ip with a lower bound. – Michael M Nov 10 '13 at 7:07

So by "absolute risk" I'm going to assume you mean either the cumulative probability of an event at time t, or the hazard at time t.

In short, no, a Cox proportional hazards model doesn't really give you back that information - the model itself doesn't calculate the underlying hazard, just the relative difference in the hazard between covariate values. This rather nicely frees you from having to specify the underlying hazard of your outcome, which in many cases is unknown, not particularly of interest in the first place, or difficult to specify using a parametric model.

If you do want to estimate the underlying hazard function, you need to use parametric survival models, such as those used in survreg. There are a large number of tutorials online, including code, for survreg and parametric models.

This is one of my favorites, as it includes some theoretical treatment and a good bit of code. The 'Survival' package documentation is also a good place to start.

• I wonder if we could get the predicted probability for the censored cases as well, i.e. those who did not develop any event at the end of follow up? – user32454 Nov 8 '13 at 12:03
• @user32454 Parametric survival models can handle censoring - they can actually do it slightly better than Cox models, IIRC. – Fomite Nov 8 '13 at 18:26
• @ EpiGrad Yes, as I am trying to predict the probability of developing an adverse event for each individual in the survival analysis, i.e. the cumulative probability of an event at the time point where the follow up period ends. – user32454 Nov 9 '13 at 9:51
• @Fpmite would it not be possible doing predictions using the Nelson-Aalen estimator of the baseline hazard-function (described here stats.stackexchange.com/questions/36015/… by @ocram) ? – Erosennin Mar 21 '15 at 22:34
• @ErosRam Honestly, I'm not familiar enough at the moment to definitively assert that's true. – Fomite Mar 22 '15 at 9:20