#+TITLE: Analysis of multivariate competing risks  data 
#+AUTHOR: Klaus Holst & Thomas Scheike
#+PROPERTY: header-args:R  :session *R* :cache no :width 550 :height 450
#+PROPERTY: header-args  :eval never-export :exports both :results output :tangle yes :comments yes 
#+PROPERTY: header-args:R+ :colnames yes :rownames no :hlines yes
#+INCLUDE: header.org
#+OPTIONS: toc:nil timestamp:nil

#+BEGIN_SRC emacs-lisp :results silent :exports results :eval
(setq org-latex-listings t)
(setq org-latex-compiler-file-string 
"%%\\VignetteIndexEntry{Analysis of multivariate competing riks data}\n%%\\VignetteEngine{R.rsp::tex}\n%%\\VignetteKeyword{R}\n%%\\VignetteKeyword{package}\n%%\\VignetteKeyword{vignette}\n%%\\VignetteKeyword{LaTeX}\n")
#+END_SRC

----- 
# +LaTeX: \clearpage


* Overview 

 - marginal modelling with standard errors cif, 
 - cause specific hazards
 - cumulative incidence modelling 
    - random effects simple cif
    - Luise model



When looking at multivariate survival data with the aim of learning about the 
dependence that is present, possibly after correcting for some covariates 
different approaches are available in the mets package  


   -  Binary models and adjust for censoring with inverse probabilty of  censoring weighting
   -  Bivariate surival models  of Clayton-Oakes type
      - With regression structure on dependence parameter 
      - With additive gamma distributed random effects
      - Special functionality for polygenic random effects modelling 
        such as ACE, ADE ,AE and so forth.
   -  Plackett OR model model 
      - With regression structure on OR dependence parameter 
   - Cluster stratified Cox 


Typically it can be hard or impossible to specify random effects models with special 
structure among the parameters of the random effects. This is possible for 
our specification of the random effects models.

To be concrete about the model structure assume that we have paired binomial 
data \( T_1, \delta_1, T_2, \delta_2,  X_1, X_2 \) where the censored 
survival responses are \( T_1, \delta_1, T_2, \delta_2 \) and we
have covariates \( X_1, X_2 \).


 
