SESSION 13 - SURVIVAL ANALYSIS

Question 1

What are the contributions of an individual?

Answer 1

Each individual contributes either a time to event or a time to censoring to the analysis.

Question 2

When is an individual censored?

Answer 2

An individual is censored if they do not experience event during the
period in which they are followed up:

-Event has not occurred when study ends or at the cut off date for analysis or
-Individual has been lost to follow up.

Question 3

What are the contents survival object?

Answer 3

Continuous variable (time)
Binary variable (event/ no event)

Question 4

What does survival mean?

Answer 4

“Survival” in this context means “remaining event free”, regardless of the
definition of the event.
Examples:

-If event is diabetes, “survival” means remaining free of diabetes.
-If event is progression of ovarian cancer, “survival” means remaining
progression free.
-If event is recovery from diarrhoea, “survival” means not having recovered.

Question 5

What is a survival function theoretically?

Answer 5

The survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time

Question 6

What is a survival function? Mathematically Explained

Answer 6

Survival Function: S(t) = P(Event happens after time t)

Question 7

What is Kaplan-Meier Method?

Answer 7

The Kaplan-Meier method is a statistical technique that estimates survival rates over time by accounting for factors like patients dropping out or dying.

What it does
The Kaplan-Meier method creates survival curves that show how the proportion of individuals at risk of an event changes over time. The curves are made up of steps, with each step representing the occurrence of one or more events.

How it works
The Kaplan-Meier method accounts for censoring, which happens when a patient is lost to follow-up for any reason. The method also takes into account other outside influences, such as patients who are still alive at the end of the study but are expected to die soon

Question 8

Hazard function

Answer 8

A hazard function in survival analysis is a mathematical equation that describes the likelihood of an item surviving to a certain point in time, given that it has survived to an earlier time. It’s also known as the force of mortality or hazard rate.

The hazard function is calculated by dividing the event rate at time by the probability of survival until time or later. The denominator adjusts for the number of people still alive at time t, and the limit ensures that the calculation is done over a narrow time interval.

The hazard function is closely related to the survival function, and the two can be easily converted to each other. A high hazard rate means that survival declines rapidly, and vice versa.

The hazard function is the basis of proportional hazards (PH) models, which are often used to model survival data