1. The Cox Model
In this chapter, we will discuss the Cox model. The Cox model is the most widely used model in survival analysis. Similar to the Weibull model it allows you to compute the effect of covariates on the time-to-event outcome. In the following slides, we will take a look at how to compute and interpret the Cox model and how it differs from the Weibull model.
2. Why use a Cox model?
The Cox model is a semiparametric model and in this sense differs from the fully parametric Weibull model. What this means is that we are less strict about the distribution of the time-to-event outcome. This is often useful and one of the reasons why the Cox model is so popular.
3. The proportional hazards assumption
The cox model is also called the proportional hazards model.
Both the Cox and the Weibull model assume proportional hazards. That means that the instantaneous rate of occurrence of the event is assumed to be proportional. This sounds quite complicated and we won't dig deeper into that assumption but what you have to remember about this assumption is: the survival curves don't cross. So if in reality, if the curves do cross, both the Cox and the Weibull model are not appropriate.
4. Computing the Cox model
Computing a Cox model is very similar to computing a Weibull model. Just replace the survreg with coxph. coxph stands for Cox proportional hazards model. If you look at the coefficients you will not find an Intercept as for the Weibull model. This is because the Cox model is a semi-parametric model which does not estimate this. Contrary to the Weibull model, negative values of the coefficient stand for a positive effect on the duration time. In this case, the negative effect of hormonal therapy means that the survival patients is prolonged. Again, we won't go into the exact meaning of the effect sizes but focus on visualizing the results.
5. Let's practice computing Cox models
Before we go into the visualization of Cox models, let's try computing a Cox model ourselves!