Course manager : Matthieu Clertant
| Formation | M2 Mathematics for data
|
| Semestre | 2 |
| Bloc | Problems and techniques specific to some data types |
| Teaching staff | Lectures : Matthieu Clertant. TA : |
| Credits | 3 ECTS |
| Teaching hours | 15h lectures + 15h of TA sessions |
| Validation scheme | Continuous examination+final exam |
Presentation
In medecine, the statistical processing of data has become a main step in the decision process as well as for scientific validation. Specificities of medical data cover multiple statistical contexts: small samples, missing data, binary and/or longitudinales data. This lectures wants to be an introduction to the most studied methods for treatment of that type of data. Examples considered in lectures and TA sessions will show in context the methodological concepts used in clinical trials.
The lecture will organize along the following points:
The logistic regression is a statistical model of binomial regression. It allows among others to find the factors that characterize group of sick subjects from the group of healthy subjects, or to manage the allocation of subjects to clinical trials with dose adjustments. Logistic regression has specific tests to study the contribution of predictions. It can be extended to categorial data and to correlation of explicative variables.
The survival analysis is a branch of statistic which aims at modelling the remaing time before appearance of a death-type event (for a biological system) or a failure (for artificial system). It primarly takes interest in survival probability up to time t or at the instanteous death rate represening the probability to die in a small time interval. We will focus on non-parametrical methods (Kaplan-Meier estimator) and semi-parametric methods (Cox model) to study these functions.
In medecine, it is typical to work on small samples before exploring to a larger scale. It is then crucial to have some tests that helps the decision to stop or continue the exploration. We will notably take interest in : non-parametrical test of equality in distribution, independence test and measure of dependence.
