First of 4 part paper series looking at the core concept of Survival Analysis. Main use case is for analysing survival in cancer patients and the impact of treatment on this.
A key concept to survival analysis is censorship, there are two main ones to mention:
In addition there is also inverval censored. This is a bit harder to draw, but essentially it is where individuals go in and out of observation.
Two probabilities underpin survival analysis:
S(t) - probability of survival from time of origin to time t
h(t) / lambda(t) - probability of event at time t
Kaplan-Meier quation can can used to estimate
S(t) based on previous values.
If we want to compare survival curves for different groups we can use a standard chi-squared statistic comparing the observed events with the expected events if there was no difference between groups (null hypothesis). From this p-values can be calculated fof significance tests.
When comparing two groups we can look at the hazard ratio
HR = (O1/E1) / (O2/E2). A HR of 1 is where the is no difference in survival.