Biostatistics

Motivation

This course covers statistical methods that are widely used in medicine and biology. A key topic is the analysis of longitudinal data: that is, methods to evaluate exposures, effects and outcomes that are functions of time. While motivated by real-life problems, some of the material will be abstract. 

Content

• Analysis of time-to-events (survival analysis / failure time analysis)
  • • Counting processes
    • Martingales
    • Censoring
    • Likelihood functions for censored data 
    • Identification of parameters with a clear interpretation
    • Non-parametric and semi-parametric estimators
    • Discrete vs continuous time
• Longitudinal data analysis
  • • Identification algorithms
    • Parametric regression models
    • Semi-parametric models
• Interpretation and evaluation of statistical parameters
  • • Description, Prediction and Causal inference 
    • Biases
    • Sensitivity analyses
• Research synthesis
  • • Transportability and generalizability (Meta analysis)
    • Multiple testing
    • Publication bias

Teaching methods

I will use iPad and the blackboard. Exercises and take-home projects that will require some programming in R. 

The TA (Gellért Géza Perényi) will respond to questions on Ed Discussions (see link below). 

Assessment methods
Final exam (80% of the total grade). 

Midterm exam (20% of the total grade, 15th of April).

Exercises and teaching material

Problem sheets will be made available every Tuesday. Brief solutions will be posted the weekend after the problem sheets are given. 

Teaching resources

• Here is the digital blackboard (continuously updated)
• Aalen, O., Borgan, O. and Gjessing, H., 2008. Survival and event history analysis: a process point of view. Springer
• Andersen, P.K., Borgan, O., Gill, R.D. and Keiding, N., 2012. Statistical models based on counting processes. Springer
• Hernan, M.A. and Robins, J.M., 2020. Causal inference: What if?

 We start with a lecture 10h15.

We will introduce the following:

• Important topics in biostatistics
• Causal inference and counterfactuals

We will cover non parametric structural equation models and causal graphs. 

We will study the backdoor theorem, and we will use this theorem to identify causal effects in a practical example. Then, we will start studying survival analysis (event history analysis). 

On March 18th, we will study properties of martingales and counting processes, which will be very useful when we study applied survival analysis problems later in the course. 

We will continue developing survival analysis with counting process and discuss independent censoring. Then we will start doing some estimation. 

We will continue studying estimators in survival analysis.

This week we continue studying estimators and we will also consider hypothesis testing in survival analysis.

We will continue studying the Cox model. Then we will discuss collapsibility of effect measures. 

I will make some points about hypothesis testing. Then I will talk about competing risks. 

We will continue with infectious disease models. We will specifically consider a stochastic SIR model. This is the last lecture with new material. 

This week, you will take a mock exam during the lecture. The solution will be released shortly afterwards. If you have any questions, please ask them on the forum or in person during the revision session next week.