1. Multivariate Survival Analysis Prof. L. Duchateau Ghent University

2. 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 indicator and the censoring or event time

3. 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

4. Univariate survival data  Clusters of fixed size 1  Example: East Coast fever transmission dynamics

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

6. Event times in clusters of varying size Many large clusters  One level of clustering, but varying cluster size  Example: Time to first insemination of heifer cows

8. Clustered event times with ordering  Event times in a cluster have a certain ordering  Example: Recurrent asthma attacks in children

9. Event times in 2 nested clustering levels  Smaller clusters of event times are nested in a larger cluster  Infant mortality in Ethiopia

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

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

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

13. 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?