TMA4275 Lifetime analysis

  • Introduction to the course
    • Time axis, censoring and truncation
    • Survival function and hazard rate
    • Counting processes
    • Modelling of event history data
  • Discrete time martingales
    • Discrete time martingale
    • Variation processes
    • Stopping times and transformations
    • Doob decomposition
  • Continuous time martingales
    • Martingale
    • Stochastic integrals
    • Doob-Meyer decomposition
    • Poisson process
    • Counting processes
    • Stochastic integrals for counting process martingales
  • The Nelson-Aalen estimator
    • Nelson-Aalen estimator
    • Handling of ties for the Nelson-Aalen estimator
    • Gaussian martingales and martingale convergence theorem
    • Large sample properties for the Nelson-Aalen estimator
  • The Kaplan-Meier estimator
    • Kaplan-Meier estimator
    • Large sample properties for the Kaplan-Meier estimator
    • Handling of ties for the Kaplan-Meier estimator
    • Estimation of median and mean survival times
    • Non-parametric tests
  • Kaplan-Meier for a Markov chain
    • Kaplan-Meier for a Markov chain: The general case
    • Competing risks
    • Illness-death model
  • Relative risk regression
    • Regression models and relative risk regression
    • Partial likelihood for relative risk regression
    • Large scale properties of betahat
    • Estimation of cumulative hazard and survival probabilities
    • Stratified relative risk model
    • Model checking in Cox regression
  • Additive regression models
    • Vector-valued counting processes, martingales and stochastic integrals
    • Estimation in the additive hazard model
    • Martingales tests for additive regression models
  • Parametric counting processes
    • Parametric counting process models: In introduction
    • Likelihood for censored survival times
    • Likelihood for counting process models
    • Maximum likelihood estimator and related tests
    • Parametric regression models
  • Frailty models
    • The odd effects of frailty
    • Multivariate frailty models
    • Shared frailty models
    • Empirical Bayes estimate of individual frailty
  • TMA4275 Lifetime analysis
  • Relative risk regression
  • Model checking in Cox regression
  • Problem: Cox-regression, martingale residuals and transformations
  • Hints: Cox-regression, martingale residuals and transformations

Hints: Cox-regression, martingale residuals and transformations

Eksempel

Hints

If you need a refresher on how to find the hazard rate, check out section 1.1.2 in ABG. For tips on what to expect of the martingale residuals you can read section 4.1.3 in ABG or watch the video in Model checking in Cox regression.

Relevante lenker

  • Eksempler:
    • Solution: Cox-regression, martingale residuals and transformations