Life Span Analysis

In biostatistics, the lifespan of an individual—or, in reliability analysis, the lifespan of a component—is a quantity whose statistical analysis differs from that of typical data. On the one hand, it involves considering quantities such as the random function and the mean remaining lifetime, among others, which are not as relevant in other areas of statistics. On the other hand, it often involves a censoring mechanism, since the data are incomplete due to the length of the experiments relative to the time allotted for them.

The purpose of this module is to present the basics of survival analysis. The rationale for survival analysis and the main mechanisms of data censoring are discussed. Two main types of statistical approaches are presented: the parametric approach, which, despite its limitations, is often preferred by users because “the parameters speak for themselves”; and the nonparametric approach, which reinforces and complements parametric analyses by providing greater flexibility and depth when dealing with large datasets. The module also presents various models (the Cox model, the accelerated failure rate model, etc.) that link survival to explanatory factors, thereby identifying those that 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 the R software.

By the end of this module, students should be able to conduct a systematic statistical analysis of survival data by selecting the approach best suited to the specific characteristics of the data and the type of censoring encountered. They should be able to estimate unknown parameters and draw relevant inferences. They should be able to establish a link between a set of factors and the survival under study and identify which factors have an impact on survival, as well as the magnitude of that effect. Finally, they should be able to independently perform the computational tasks necessary to produce inferential statements.

HAX710X / HAX814X / HAX815X / HAX912X


Recommended prerequisites: HAX809X, HAX908X

Comprehensive Continuous Monitoring 

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

Parametric approach: The various parametric distributions used. Parameter estimation in the presence of censoring, behavior of estimators, and inference: confidence intervals and hypothesis testing for a survival experiment; comparison of multiple survival curves using the maximum likelihood principle. Models for covariates: 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 the Greenwood formula; other confidence intervals via monotonic transformation. Actuarial estimator. Nonparametric rank tests for comparing multiple groups. Implementation using standard R packages. 

Hours:
Lectures: 6:00 p.m.
Tutorials:
Lab:
Fieldwork: