FMS030F

Tillfällig

Survival Analysis

7.5

Ren forskarutbildningskurs

7152 (Matematikcentrum (inst LTH) / Matematisk statistik (LTH))

2024-09-16

Maria Sandsten

Engelska

Vid tillräcklig efterfrågan

The course gives a theoretical mathematical basis for survival analysis based on stochastic processes, especially counting processes, martingale theory and stochastic analysis, as well as for limit distributions in non parametric methods that are specific for survival analysis.

Survival data. Censured and truncated data. Covariance.

Distributions and models for survival data.

Counting processes and martingale theory. Different kinds of filtrations for counting processes.

Estimating the survival function and of the cumulative hazard function (Kaplan-Meier and Nelson-Aalen estimators)

Non parametric one and two sample tests. Kernel estimation of the hazard function.

Semiparametric regression models for data with covariance. Cox model. Allen's model. Likelihood theory for estimating in the Cox model. Projection methods for counting processes for estimation in the Aalen model.

Empirical processes. Statistical functionals and limit distributions in survival analysis.

Bootstrap methods for survival data.

be able to describe survival data and the questions that arise in their models.

be able to describe the estimation methods that are used in survival analysis.

be able to use the methods and theories presented in the course to analyze published applications of survival analysis on empirical data.

be able to use the methods and theories presented in the course to analyze a research report developing mathematical theory in survival analysis.

be able to assess qualitative differences between semiparametric regression models (Cox, Aalen) and nonparametric models.

be able to assess qualitative differences between different regression models.

Föreläsningar

Seminarieföredrag av deltagarna

Underkänd, godkänd

It is recommended to have taken MASM27 non parametric inference, measure and integration theory or MATM30 Mathematical Foundations of Probability; MASC02 inference theory, or equivalent.

Andersen, P., Borgan, Ø., Gill, Richard D. & Keiding, N.: Statistical Models Based on Counting Processes.

FMS030F

2024-09-16

Maria Sandsten