# Survival Analysis Part I: Basic concepts and first analyses

**Date read:** `2021-06-01`

**Paper:** https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2394262/pdf/89-6601118a.pdf

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.

- Survival events rarely Normally distributed. Tend to have many early events, few late ones -> requires special methods for analysis

### Censorship

A key concept to survival analysis is censorship, there are two main ones to mention:

- Right censorship - event hasnâ€™t happened before end of study (e.g. person still alive at end of cancer study)
- Left censorship - individual started before observation began (e.g. person had cancer before analysis started)

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.

### Probabilities

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.

### Comparing Survival

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.