Lifetime analysis

The lifetime 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 average residual life time, etc., which are not as interesting in other fields 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 compared to the time one wants to allocate to them.

The purpose of this module is to introduce the basics of survival analysis. The rationale and main mechanisms of data censoring 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" and the non-parametric approach which allows to support and complete the parametric analyses by giving them more flexibility and depth when the data are numerous. The module also presents different models (Cox model, accelerated failure rate, etc.) allowing to link survival to explanatory factors, which makes it possible to determine those which can impact this survival. This information is particularly useful in a health context, as it allows the personalization of survival projections for an individual.

The implementation of these methods will be done on the R software.

At the end of this module, the student will be able to conduct a reasoned statistical analysis of survival data by choosing the approach adapted to the particularities of the data and the type of censoring encountered. He/she should be able to estimate unknown quantities and produce relevant inferences. He or she should 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 necessary for the production of inferential statements.

HAX710X / HAX814X / HAX815X / HAX912X


Recommended prerequisites: HAX809X, HAX908X

Continuous control 

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

Parametric approach: The different parametric laws used. Estimation of parameters in the presence of censoring, behavior of estimators and production of inferences: 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 adapted 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 monotonic transformation. Actuarial estimator. Non-parametric rank tests for the comparison of several groups. Implementation of the usual R packages. 

Hourly volumes:
CM: 18h
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TP:
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