ECPR Winter School
University of Bamberg, Bamberg
2 - 9 March 2018




WD217 - Event History and Survival Analysis

Instructor Details

Instructor Photo

Janez Stare

Institution:
University of Ljubljana

Instructor Bio

Janez Stare graduated from the Faculty of Mathematics, University of Ljubljana, then held a Master Degree and Ph.D. in Biostatistics from the Faculty of Medicine, University of Ljubljana. He is currently full Professor of Biostatistics at the Faculty of Medicine, Ljubljana, Head of the Institute of Biostatistics and Medical Informatics, Faculty of Medicine, Ljubljana, and Head of the Doctoral Pogramme in Statistics at University of Ljubljana. His research interests are explained variation in survival analysis, predictive ability of regression models in survival analysis, frailties, random effects in survival models, relative survival, goodness of fit of regression models, scientometrics.


Course Dates and Times

Monday 5 to Friday 9 March 2018
09:00-12:30
15 hours over 5 days

Prerequisite Knowledge

Participants should have some working knowledge of linear regression models and be familiar with the basics of inferential statistics. As for mathematics, it is understood that the participants will not have much mathematical skills, but for those that will, the written material contains more rigorous treatment of the subject. Even though I use formulas only to explain the concepts, I would suggest that the participants clear the dust from the mathematics lying buried in their memory, preferably with the notion of the integral included. Not being afraid of the formulas is an advantage and certainly helps in understanding the subject better.

Also, some practical experience with statistical software is assumed, with R being the preferred package.

Short Outline

In event history analysis (and survival analysis, which is the name used mostly in bio sciences, where the methods were first applied) we are interested in time intervals between successive state transitions or events. Typical examples are: duration of unemployment, duration of marriage, recidivism in criminology, duration of political systems, time from diagnosis to death, and so on. The most distinctive feature of time to event data is that the event is often not observed at the time of analysis. Applying standard statistical methods to such data leads to severe bias or loss of information. Special methods are therefore needed to extract information which we are used to get using standard methods (formally this means estimating the distribution function and incorporate predictive variables into such estimation). Further complications arise when covariates change in time, when times between recurring events are correlated, when there are competing risks, or when effects change in time.

In this course we will thoroughly study a situation when there is only one event per subject, but will also review the extensions to a sufficient degree for students to be able to continue their work in the area. Roughly on third of the time will be devoted to practical examples, for which the package R will be used.  Familiarity with R is not assumed, but students will receive a short introductory material to the package before the summer school begins.

While it is impossible to avoid all formulas, I will focus on the concepts in my lectures, but will support the lectures with more rigorous written material.

 

Long Course Outline

Say we are interested in how long people keep their first job. We start our study at some point in time and include a sample of people that obtained their first job after the study started. After some time, say a number of years, the study stops and we want to analyse data. Some people have lost their job in the meantime, some have changed it, but some are still working and we do not have complete data on their time at job. Further, if somebody has stopped working because of his inability to work (accident, death), we also don’t know what his event time would have been had he still been able to work. When the event is not observed at the time of analysis we say that censoring has occurred. With such data we cannot even calculate the mean, or draw a histogram, let alone use linear regression or similar methods. Special methods are therefore needed, and most of them use the hazard (or intensity) function. Since this is defined via the conditional probability of event occurring in some time interval given it has not occurred before, the hazard can be estimated even in the presence of censored data. As we shall see, knowing the hazard function is equivalent to knowing the distribution function, which is the main goal of any analysis. In Survival analysis, and consequently in Event History Analysis, it has become customary to talk about the survival function, which is simply one minus the distribution function.

I will first illustrate usage of logistic regression for event history data, and explain why such an approach is not satisfactory.

Then we will deal with estimating the survival and the hazard function (parametrically and non-parametrically), some measures of central tendency commonly used, and learn how to write down the likelihood function in the presence of censoring.

To continue our example, we might then be interested if there are any differences in keeping the job between men and women, between people with different levels of education, among different working environments and so on, in short, do some covariates influence the time a person stays in her/his first job.

We will therefore learn about tests for comparing survival functions and discuss two most commonly used parametric models for inclusion of covariates.

The main focus of the course will be on the Cox proportional hazards model which is by far most often used in the analysis of time to event data. While the model is very simple, it is also very flexible, and an experienced statistician can make it fit to almost any data. We will learn the basics about the estimating procedure, interpretation, testing, checking the modelling assumptions and relaxing them, and some extensions like the stratified model, time varying effects and frailties.

For now we have not distinguished between a person losing his job, and a person changing his job. We also have not considered studying several spells for one person (one person can change jobs several times in the study period). These problems fall under the headings of competing risks and recurring events. The last two days will be devoted to these, as well as, and, time permitting, some other models.

Here is a list of topics:

Univariate event history analysis

  1. Censoring
  2. Survival function
  3. Hazard and cumulative hazard function
  4. Mean time, mean residual time, median time
  5. Likelihood function for censored time to event data
  6. Parametric models for the survival function (exponential, Weibull)
  7. Non parametric estimation of the survival function (Kaplan Meier and Nelson Aalen estimators)
  8. Variance of the survival function, confidence intervals
  9. Comparison of survival functions

Regression models for time to event data

  1. Parametric models (exponential, Weibull)
  2. Cox model (proportional hazards model):
    1. Estimation (partial likelihood)
    2. Interpretation
    3. Testing the null hypothesis (Wald, score, and likelihood ratio test)
    4. Some model fitting techniques
    5. Categorical variables in the model
    6. Relaxing the linearity assumption for continuous variables using splines
    7. Checking the model assumptions
    8. Goodness-of-fit and explained variation
    9. Stratified model
    10. Time varying covariates
    11. Frailties
    12. Time varying effects
  3. Competing risks
  4. Recurring events
  5. Multistate models
Day-to-Day Schedule

Day 
Topic 
Details 
Monday• Introduction to Event History Analysis • Using logistic regression to analyze survival data • Event History and Social Science • Event history data structures • Basic definitions
  • topics of course
  • course goals
  • overview of course schedule
  • illustration of using logistic regression for survival data
  • examples
  • censoring
  • survival function
  • hazard and cumulative hazard function

2.5 hours lecture, 30´ examples in R

Tuesday• Parametric and nonparametric descriptive methods • Comparison of survival functions • Parametric regression models for single-spell duration data • Methods to check parametric assumptions
  • Mean survival time, mean residual time, median time
  • Exponential and Weibull distribution
  • Kaplan-Meier estimator
  • Life tables
  • Log rank test
  • Exponential and Weibull regression model

2 hours lecture, 1 hour examples in R

WednesdayCox model
  • Estimation (partial likelihood)
  • Interpretation
  • Some model fitting techniques
  • Categorical variables in the model

2 hours lecture, 1 hour examples in R

ThursdayCox model (continued)
  • Relaxing the linearity assumption for continuous variables using splines
  • Checking the model assumptions
  • Stratified model
  • Time varying covariates
  • Frailties
  • Time varying effects

2 hours lecture, 1 hour examples in R

FridayCompeting risks and Multiple events

Cox model for competing risks, repeated events

and multistate models

1.5 hours lecture, 1.5 hours examples in R

Day-to-Day Reading List

Day 
Readings 
 

I have chosen two books to be used as a supplementary reading:

  1. Janet M. Box-Steffensmeier, Bradford S. Jones. Event History Modeling. A Guide for Social Scientists]. Cambridge University Press 2004.
  2. Habs-Peter Blossfeld, Götz Rohwer. Techniques of Event History Analysis. Lawrence Erlbaum Associates, London 2002.
Monday

Box-Steffensmeier 1, 2; Blossfeld 2

Tuesday

Blossfeld 3.1, 3.2, 3.3; Box-Steffensmeier 1,2

Wednesday

Box-Steffensmeier 4, 6

Thursday

Box-Steffensmeier 7, 9: Blossfeld 10.1

Friday

Box-Steffensmeier 10

Software Requirements

R package will be used for illustrations. R is freely available at http://cran.r-project.org/. It is not essential to have any experience with the package, but some familiarity is welcome.

In principle you will not be required to work practically with R, but you will benefit from some hands on experience. Those doing home assignments (to get more 2 ECTS credits) will need to have R (Stata, ...) or similar installed. If there are any problems with the installation of R, we will help you when you are in Bamberg. In particular, the survival package will have to be downloaded. New versions of R are coming often, and we will let you know in advance if you need to install a new version (usually not needed). We will not be helping with other software, but you can of course use something else on your own.

Hardware Requirements

I suggest that participants bring their own laptops (notebooks, …) with R (or something else) installed. In this way we do not depend on the availability of rooms with computers and are much more flexible in carrying out the course.

Literature

In biostatistical field there are a lot of good books on the subject of this course. The following are good examples:

Collett D.  Modelling Survival Data in Medical Research. Chapman and Hall/CRC; 2 edition (March 30, 2003)

Hosmer D.W., Lemeshow S., May S. Applied Survival Analysis: Regression Modeling of Time to Event Data (Wiley Series in Probability and Statistics). Wiley-Interscience; 2 edition (March 7, 2008)

The following other ECPR Methods School courses could be useful in combination with this one in a ‘training track .
Recommended Courses Before

Summer School

Stats Refresher

Winter School

Introduction to R (entry level)

Additional Information

Disclaimer

The information contained in this course description form may be subject to subsequent adaptations (e.g. taking into account new developments in the field, specific participant demands, group size etc.). Registered participants will be informed in due time in case of adaptations.

Note from the Academic Convenors

By registering to this course, you certify that you possess the prerequisite knowledge that is requested to be able to follow this course. The instructor will not teach these prerequisite items. If you are not sure if you possess this knowledge to a sufficient level, we suggest you contact the instructor before you proceed with your registration.


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