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Event History and Survival Analysis

Course Dates and Times

Monday 5 to Friday 9 March 2018
15 hours over 5 days

Janez Stare

University of Ljubljana

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.

Tasks for ECTS Credits

  • Participants attending the course: 2 credits (pass/fail grade) The workload for the calculation of ECTS credits is based on the assumption that students attend classes and carry out the necessary reading and/or other work prior to, and after, classes.
  • Participants attending the course and completing one task (see below): 3 credits (to be graded)
  • Participants attending the course, and completing two tasks (see below): 4 credits (to be graded)

For 2 ECTS Credits you will have to attend 4 of the 5 lectures.
For 3 ECTS Credits you will additionally have to complete two daily assignments, to be given on Tuesday and Thursday and returned on Wednesday and Friday.
For 4 ECTS Credits you will additionally have to do a take-home exam.


Instructor Bio

Janez Stare graduated from the Faculty of Mathematics, University of Ljubljana, then gained a Master's Degree and PhD in Biostatistics from the University of Ljubljana's Faculty of Medicine.

He is currently full Professor of Biostatistics and Head of the Institute of Biostatistics and Medical Informatics, Faculty of Medicine, Ljubljana, and Head of the Doctoral Programme 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, and scientometrics.

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

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.

Each course includes pre-course assignments, including readings and pre-recorded videos, as well as daily live lectures totalling at least three hours. The instructor will conduct live Q&A sessions and offer designated office hours for one-to-one consultations.

Please check your course format before registering.

Online courses

Live classes will be held daily for three hours on a video meeting platform, allowing you to interact with both the instructor and other participants in real-time. To avoid online fatigue, the course employs a pedagogy that includes small-group work, short and focused tasks, as well as troubleshooting exercises that utilise a variety of online applications to facilitate collaboration and engagement with the course content.

In-person courses

In-person courses will consist of daily three-hour classroom sessions, featuring a range of interactive in-class activities including short lectures, peer feedback, group exercises, and presentations.


This course description may be subject to subsequent adaptations (e.g. taking into account new developments in the field, participant demands, group size, etc.). Registered participants will be informed at the time of change.

By registering for this course, you confirm that you possess the knowledge required to follow it. The instructor will not teach these prerequisite items. If in doubt, please contact us before registering.

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

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

2 hours lecture, 1 hour examples in R

Thursday Cox 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

Friday Competing 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 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.

Box-Steffensmeier 1, 2; Blossfeld 2


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


Box-Steffensmeier 4, 6


Box-Steffensmeier 7, 9: Blossfeld 10.1


Box-Steffensmeier 10

Software Requirements

R package will be used for illustrations. R is freely available at 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.


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)

Recommended Courses to Cover Before this One

Summer School

Stats Refresher

Winter School

Introduction to R (entry level)