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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.

9.1. EXAMPLES TO MOTIVATE TIME-DEPENDENT COVARIATES 3 9.1 Examples to motivate time-dependent covariates Stanford Heart transplant example: Variables: • survival - days since program enrollment until death or censoring • dead - indicator of death (1) or censoring (0) • transpl - whether patient ever had transplant (1 if yes, 2 if no) • surgery - previous heart surgery …

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