MF9555 - Analysis of repeated / correlated measurements
A major assumption behind all traditional regression models is that of independent observations. However, this assumption may not hold in all situations. Often we will have some sort of clustered data where the independence assumption will not be fulfilled. Examples may be repeated measurements made on the same individual over time, multicenter studies where patients are nested within centres, genetic studies where we have information about family structures, or educational studies with pupils nested within classes, which are again nested in schools. Special sampling procedures, like cluster sampling, may also give rise to this type of data. Common to all these situations is that we will need some regression method that can handle the dependencies between observations. Mixed models are one means to this end. In many instances the terms multilevel models, hierarchical models, and random coefficient models also refer to mixed models, adapted to a given setting.
In this course we will give an introduction to the concept of mixed models. We will focus on the so-called linear mixed model with continuous, normally distributed outcomes. Further, we will introduce generalized linear mixed models, which apply to situations where the outcome variable is not necessarily continuous, such as logistic models for binary outcomes and log-linear models for counts. We will also introduce Generalized Estimating Equations (GEE) as an alternative in certain situations.
The focus of the course will be on longitudinal studies, but we will also give examples from other types of studies where such methods are needed.
The course will give you knowledge about methods for analysis of clustered data. More specifically, you will learn about
- Analysis of summary measures (Area under the curve etc.)
- Models for repeated measures in longitudinal design
- Marginal models (including GEE)
- Mixed models / multilevel models.
The course will give you the skills to:
Analyze correlated data by use of the Stata software. The course will mainly focus on longitudinal data, but other types of correlated data will also be discussed; among these the traditional multilevel designs. The course will concentrate on measurements on continuous scale and linear models, and on data of binary type and logistic models. We will focus on an intuitive understanding of the underlying statistical models rather than the mathematical details, with the goal of understanding the assumptions behind the analysis and the interpretation of the results.
The course will make you able to understand the general ideas behind the analysis of correlated data, and to critically evaluate studies based on data of such type.
PhD candidates at UiO will have first priority at admission to the course. Maximum number of particpants is 35.
PhD candidates admitted to a PhD programme at UiO apply in StudentWeb
Applicants who are not admitted to a PhD programme at UiO must apply for a right to study in SøknadsWeb before they can apply for PhD courses in medicine and health Sciences.
Recommended previous knowledge
It is highly recommended that the participants have some practical experience with use of regression models, beyond the contents of the introductory course; alternatively some course in regression analysis (linear or logistic), e.g. MF9510. Participants lacking this experience is required to familiar themselves with central ideas of regression analysis, including modelling and interpretation of interaction. All participants should read Chapters 3 and 4 of Veierød et al. before the course.
Candidates who have completed MF9530 and MF9550 will not get credits for MF9555
The course is organized with six full days of teaching (2×3 days), with a mix of lectures and practical work in the computer lab.
You have to participate in at least 80 % of the teaching to be allowed to take the exam. Attendance will be registered.
Home exam over four weeks in terms of a practical data analysis.
The exam will be given in English, but it is optional to answer in Norwegian if the course is given in Norwegian.
Use of sources and citation
Grades are awarded on a pass/fail scale. Read more about the grading system.
Explanations and appeals
Resit an examination
Withdrawal from an examination
It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.
Special examination arrangements
Application form, deadline and requirements for special examination arrangements.
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.