Survival Analysis - 2

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 .

Survival Analysis - 1

I recently was looking for methods to apply to time-to-event data and started exploring Survival Analysis Models. In this post, I'm exploring basic KM estimator. It is a nonparametric estimator of the survival function. There are couple of instances when the KM estimator comes in handy -

• When the survival time is censored
• Comparing survival function for different preassigned groups.

Below I'm computing KM estimator for a real dataset (on time to death for 80 males who were diagnosed with different types of tongue cancer, from package KMsurv) and a simulated dataset (created using package survsim). In addition I am using survival, OIsurv, dplyr, ggplot2 and broom for this analysis. The first example is taken from an openintro tutorial.

The rmarkdown document illustrating below analysis can also be found here. In my future posts, I'm planning to explore more on following survival models -

• Proportional hazards model
• Accelerated failure time Model
• Multiple events model (More than 2 possible events)
• Recurring events (Each subject can experience an event multiple times).