Life cycle analysis

The lifespan of an individual in biostatistics, or of a component in reliability analysis, is a quantity whose statistical analysis differs from the usual data. On the one hand, it leads to the consideration of quantities such as the hazard function, the residual mean life time, etc., which are of less interest in other fields of statistics. On the other hand, it often involves a censoring mechanism, as the data are observed incompletely due to the length of the experiments in relation to the time we want to allocate to them.

The aim of this module is to present the basics of survival analysis. The rationale and main mechanisms of data censoring are discussed. Two main types of statistical approach 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 supports and complements parametric analyses, giving them greater flexibility and depth when data are plentiful. The module also presents various models (Cox model, accelerated failure rate, etc.) linking survival to explanatory factors, enabling us to determine which factors may have an impact on survival. This information is particularly useful in a health context, as it can be used to personalize survival projections for an individual.

These methods will be implemented using R software.

At the end of this module, the student will be able to conduct a reasoned statistical analysis of survival data, choosing the approach best suited to the particularities of the data and the type of censoring encountered. He/she should be able to estimate unknown quantities and produce the relevant inference. He or she must be able to relate 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, he or she must be able to independently carry out the computational aspects required to produce inferential statements.

HAX710X / HAX814X / HAX815X / HAX912X


Recommended prerequisites: HAX809X, HAX908X

Full continuous assessment 

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

Parametric approach: the different parametric laws used. Parameter estimation in the presence of censoring, estimator behavior and inference generation: confidence interval 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.

Non-parametric 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 monotone transformation. Actuarial estimator. Non-parametric rank tests for comparing several groups. Implementation of standard R packages. 

Timetable:
CM: 18h
TD:
TP:
Field :