Multivariate Survival Analysis

Prof. L. DuchateauGhent University

Survival analysis Time-to-event What if no event observed? Need to take into account surviving

subjects For instance, survival likelihood is given by

with N the total number of subjects and the censoring indicatorand the censoring or event time

Multivariate Clusters Correlated event times Criteria to categorise

Cluster size: 1, 2, 3, 4, >4 Event ordering: none or ordered in space/time Hierarchy: 1 or 2 nesting levels

Univariate survival data Clusters of fixed size 1 Example: East Coast fever transmission

dynamics

Bivariate survival data Clusters of fixed size 2 Example: Udder quarter reconstitution

Event times in clusters of varying sizeMany large clusters One level of clustering, but varying cluster

size Example: Time to first insemination of

heifer cows

Clustered event times with ordering Event times in a cluster have a certain

ordering Example: Recurrent asthma attacks in

children

Event times in 2 nested clustering levels Smaller clusters of event times are nested

in a larger cluster Infant mortality in Ethiopia

Reading data in R#Read the reconstitution datasetwd("c://docs//onderwijs//survival//Flames//notas//")reconstitution<-read.table("reconstitution.csv",header=T,sep=";")#Create 5 column vectors, five different variablescowid<- reconstitution $cowid timerec<-reconstitution$timerecstat<- reconstitution$stattrt<- reconstitution$trtheifer<- reconstitution$heifer

Another bivariate survival data Clusters of fixed size 2 Example: diagnosis of fracture healing

Exercise: Reading data in R#Read the diagnosis data in R

Course parts Univariate survival analysis: parametric,

semiparametric (using R) Alternatives to model multivariate survival

data (using R) Frailty models (different software

packages) Want to know more

about frailty models?