• A short course on Survival Analysis
  • Preface
  • Programing language and software
  • Main references and credits
  • About the Author
  • 1 Introduction
    • 1.1 What is survival analysis?
      • 1.1.1 Time, time origen, time scale, event
      • 1.1.2 Goals of the survival analysis
    • 1.2 Censoring
    • 1.3 Some notation
    • 1.4 Survival/hazard functions
    • 1.5 Relation between functions
    • 1.6 Some common distributions
  • 2 Kaplan Meier estimator
    • 2.1 Estimating survival by means of the Kaplan Meier estimator
      • 2.1.1 Other representation
    • 2.2 Pointwise confidence interval for \(S(t)\)
    • 2.3 Comparing survival curves
    • 2.4 Pros and Cons of the Kaplan-Meirs estimator
  • 3 The Cox Proportional Hazards Model
    • 3.1 The semiparametric model
    • 3.2 Estimation
    • 3.3 Computing the Hazard Ratio
    • 3.4 Hypothesis testing
    • 3.5 Adjusting Survival Curves
    • 3.6 How to evaluate the PH assumption?
      • 3.6.1 Graphical approach
      • 3.6.2 Goodness-of-fit test
    • 3.7 Non-Proportional Hazards… and now what?
      • 3.7.1 An example… Stratified Proportional Hazards Models
    • 3.8 Why Cox PH model is so popular? (pros of the model)
    • 3.9 Bonus track 1: Additive Cox model
    • 3.10 Bonus track 2: Machine Learning for estimating the Cox PH model
  • 4 Joint Models for Longitudinal and Time-to-Event Data
    • 4.1 Linear Mixed Models
    • 4.2 Estimation of the Joint Model
    • 4.3 The JM package
  • 5 Conditinal Survival with condSURV
    • 5.1 Introduction
    • 5.2 Notation
    • 5.3 Estimation of the conditional survival
      • 5.3.1 Kaplan-Meier Weighted Estimator (KMW)
      • 5.3.2 The Landmark approach (LDM)
      • 5.3.3 The Presmoothed Landmark approach (PLDM)
    • 5.4 The condSURV package
  • 6 Spoiler!!
    • 6.1 Introduction
    • 6.2 Algortihm
    • 6.3 Aplication to real data
  • Appendix
  • A Installation of R and RStudio
  • B Introduction to RStudio
  • C Introduction to R
  • References
  • Published with bookdown

A short course on Survival Analysis applied to the Financial Industry

3.8 Why Cox PH model is so popular? (pros of the model)

  • It is a “robust” model, so that the results from using the Cox model will closely approximate the results for the correct parametric model (even though the baseline hazard is not specified).

  • Although the baseline hazard part of the model is unspecified, we can estimate the betas in the exponential part of the model (as we have seen). Then, the hazard function \(h(t,\textbf X)\) and its corresponding survival curves \(S(t, \textbf X\)) can also be estimated.

  • Finally, it is preferred over the logistic model when survival time information is available and there is censoring. Because you can obtain more information!