### Survival Analysis

# Survival Analysis

# taught by Anthony Babinec

Aim of Course:

This online course, "Survival Analysis" describes the various methods used for modeling and evaluating survival data, also called time-to-event data. Survival models are used in biostatistical, epidemiological, and a variety of health related fields. They are also used for research in the social sciences as well as the physical and biological sciences, including, economic, sociological, psychological, political, and anthropological data. Survival analysis also has been applied to the field of engineering, where it typically is referred to as reliability analysis.

General statistical concepts and methods discussed in this course include survival and hazard functions, Kaplan-Meier graphs, log-rank and related tests, Cox proportional hazards model, and the extended Cox model for time-varying covariates. The course will also require participants to use a convenient statistical package (e.g., SAS, JMP, STATA, R, or S+) to analyze survival analysis data.

This course may be taken individually (one-off) or as part of a certificate program.

Course Program:

## WEEK 1:

- An overview of survival analysis methods
- Censoring
- Key terms: survival and hazard functions
- Goals of a survival analysis
- Data layout for the computer
- Data layout for understanding
- Descriptive statistics for survival analysis- the hazard ratio
- Graphing survival data- Kaplan Meier
- The Log Rank and related tests.

## WEEK 2:

- Introduction to the Cox Proportional Hazards (PH) model- computer example
- Model definition and features
- Maximum likelihood estimation for the Cox PH model
- Computing the hazard ratio in the Cox PH model
- The PH assumption
- Adjusted survival curves
- Checking the proportional hazard assumption
- The likelihood function for the Cox PH model

## WEEK 3:

- Introduction to the Stratified Cox procedure
- The no-interaction Stratified Cox model
- The Stratified Cox model that allows for interaction

## WEEK 4:

- Definition and examples of time-dependent variables
- Definition and features of the extended Cox model
- Stanford Heart Transplant Study Example
- Addicts Dataset Example
- The likelihood function for the extended Cox model.

HOMEWORK:

Homework in this course consists of short answer questions to test concepts, guided data analysis problems using software, and guided data modeling problems using software.

In addition to assigned readings, this course also has supplemental readings available online.

# Survival Analysis

Who Should Take This Course:

Investigators designing, conducting or analyzing medical studies or clinical trials. Researchers in any field (including engineering) working with data on how long things last.

Level:

Intermediate

You should be familiar with introductory statistics. Try these self tests to check your knowledge.

Course participants should also have had some experience with computer procedures for regression modeling.

Organization of the Course:

This course takes place online at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirement:

About 15 hours per week, at times of your choosing.

Credit:

Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:

- You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
- You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
- You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's). For those successfully completing the course, CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:

The required text is *Survival Analysis- A Self Learning Text*, 3rd edition by David G Kleinbaum and Mitchel Klein. It may be purchased here

Software:

Many statistical software packages can perform survival analysis (mainly Cox regression). The readings in this course use SAS illustrations, and the exercises require the use of statistical software. Any package that does survival analysis can be used to do the exercises. Model answers to the exercises will illustrate SAS code. There will also be illustrations and model answers in R, and Stata. Teaching Assistants can be of some help with SAS, JMP, Stata, and R. (Note: If you want to use R with this course, you should have some prior experience and facility with it. If you wish to use R, but no have current expertise in it, you should consider taking one of our introductory R courses before taking this one.) For more information on the above mentioned statistical software, please click here.

# Survival Analysis

March 10, 2017 to April 07, 2017September 15, 2017 to October 13, 2017March 09, 2018 to April 06, 2018September 14, 2018 to October 12, 2018