In my previous post, I went over basics of survival analysis, that included estimating Kaplan-Meier estimate for a given time-to-event data. In this post, I’m exploring on Cox’s proportional hazards model for survival data. KM estimator helps in figuring out whether survival function estimates for different groups are same or different. While survival models like Cox’s proportional hazards model help in finding relationship between different covariates to the survival function.
Some basic notes about Cox model –
- It’s a semi-parametric model, as the hazard function (risk per unit time) does not need to be specified.
- The proportional hazard condition states that the covariates are multiplicatively related to the hazard. (This assumption should always be checked after fitting a Cox model).
- In case of categorical covariates, the hazard ratio (e.g. treatment vs no treatment) is constant and does not change over time. One can do away with this assumption by using extended Cox model which allows covariates to be dependent on time.
- The covariates are constant for each subject and do not vary over time.
(There’s one-to-one mapping between hazard function and the survival function i.e. a specific hazard function uniquely determines the survival function and vice versa. Simple mathematical details on this relationship can be found on this wikipedia page.)
I’m using the same datasets (tongue dataset from package KMsurv and a simulated dataset using survsim) and set of packages as used in the previous post – OIsurv, dplyr, ggplot2 and broom .