Lifetime analysis

The lifetime of an individual in biostatistics, or of a component in reliability analysis, is a quantity whose statistical analysis differs from that of usual data. On the one hand, it leads to considering quantities such as the hazard function, the mean residual lifetime, etc., which are not as interesting in other areas of statistics. On the other hand, it often involves a censoring mechanism, because the data are observed incompletely due to the length of the experiments in relation to the time we want to allocate to them.

The purpose of this module is to present the basics of survival analysis. The reasons for censoring data and the main mechanisms involved are discussed. Two main types of statistical approaches are presented: the parametric approach, which despite its limitations is often favored by users because "the parameters speak for themselves," and the non-parametric approach, which can reinforce and complement parametric analyses by giving them greater flexibility and depth when there is a large amount of data. The module also presents different models (Cox model, accelerated failure rate model, etc.) that link survival to explanatory factors, making it possible to determine which factors may impact survival. This information is particularly useful in a healthcare context, as it allows for the personalization of an individual's survival projections.

These methods will be implemented using R software.

At the end of this module, students will be able to conduct a reasoned statistical analysis of survival data by choosing the approach best suited to the specific characteristics of the data and the type of censoring encountered. They will be able to estimate unknown quantities and produce relevant inferences. They will be able to link a series of factors to the survival studied and identify those that have an impact on it, as well as the magnitude of this effect. Finally, they will be able to independently carry out the computational aspects necessary for producing inferential statements.

HAX710X / HAX814X / HAX815X / HAX912X


Recommended prerequisites: HAX809X, HAX908X

Continuous assessment 

Introduction to survival data: origin, uses, and characteristics; different types of censoring

Parametric approach: Different parametric laws used. Estimation of parameters in the presence of censoring, behavior of estimators, and production of inferences: confidence intervals and hypothesis testing for a survival experiment, comparison of several survival curves using the maximum likelihood principle. Models for co-factors: introduction to accelerated failure rate models, Cox model. Model selection and validation, selection of important explanatory variables. Accelerated survival regression models. Use of appropriate R packages. 

Nonparametric approach: Kaplan-Meier estimator of the survival function and Breslow estimator, Nelson-Aalen estimator of the cumulative hazard function, construction of confidence intervals and Greenwood's formula, other confidence intervals by monotonic transformation. Actuarial estimator. Nonparametric rank tests for comparing several groups. Implementation of standard R packages. 

Hours per week:
CM: 18 hours
TD:
TP:
Fieldwork: