Chapter 9

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Chapter 9Time varying (or time-dependent) covariatesReferences:Allison (*) & LemeshowChapter 7, Section 3Kalbfleisch & PrenticeSection 7KleinbaumChapter 6Cox & OakesChapter 8Andersen & GillPage 168 (Advanced!)12CHAPTER 9. TIME VARYING (OR TIME-DEPENDENT) COVARIATESOur Goal hereSo far, we ve been considering the following Cox PH model: (t,Z)= 0(t) exp( Z)= 0(t)exp p j=1 jZj where the covariatesZjare measured at study entry (t=0).Important feature of this model:The hazard ratio (t,Z=z) (t,Z=0)=exp( z)depends on the covariatesz1, ..., zp, but not on relax this assumption, and allow the hazard ratio to dependon timet.

Waiting transplant? survival post total final time transplant survival status-----49 2 . . 1 52 . . 1 0 1 15 15 1 35 1 3 38 1 17 2 . . 1 11 1 46 57 1 etc (survival is not indicated above for those without transplants, but was available in the dataset) Naive approach: Compare the total survival of transplanted and non-transplanted. Problem ...

  Survival