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Multivariate Survival Analysis
Prof. L. DuchateauGhent University
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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
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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
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Univariate survival data Clusters of fixed size 1 Example: East Coast fever transmission
dynamics
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Bivariate survival data Clusters of fixed size 2 Example: Udder quarter reconstitution
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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
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Clustered event times with ordering Event times in a cluster have a certain
ordering Example: Recurrent asthma attacks in
children
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Event times in 2 nested clustering levels Smaller clusters of event times are nested
in a larger cluster Infant mortality in Ethiopia
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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
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Another bivariate survival data Clusters of fixed size 2 Example: diagnosis of fracture healing
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Exercise: Reading data in R#Read the diagnosis data in R
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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?